The University of Sydney Literature Review School of AMME __________________________________________________________ Connection topology optimisation for multi-component systems by combining static

The University of Sydney
Literature Review
School of AMME
__________________________________________________________
Connection topology optimisation for multi-component systems by combining static (stiffness) and dynamic(frequency) criteria
__________________________________________________________________________________
Kian Xun Tan 460491251
The following literature review covers for the necessary articles and methods for the upcoming thesis project on the topology optimisation of interconnection problems
Abbreviation
ESOEvolutionary Structural OptimizationBESOBi-directional Evolutionary Structural OptimizationGAGenetic Algorithm LSMLevel Set MethodSEStrain energyMOCModified optimality criterionOCOptimality criterionSIMPSolid Isotropic Microstructure with penalizationMAPDLANSYS Mechanical AdvancedGUIGraphical User InterfaceAPDLANSYS Parametric Design LanguageTOTopology optimisationV*Target volumeFEAFinite Element AnalysisPPenalty factorRRRejection ratioEREvolution rateFRFilter radiusxeElement fractional relative densityueElemental displacement vectorkeElemental stiffness matrixTNumber of iterations over which convergence is measured
Introduction
It is realised that in many industry, topology optimisation is used to generate a general draft design of a certain application, structures and many more. TO is used to find the best distribution and allocation of materials, by setting up constraints and optimization design goal such as stiffness-based, buckling-based and many more.
In actual mechanical and civil engineering industry, a typical engineering structure is too big to be transported to a certain area to another. Thus, the structure is break down into sub-assemblies, typically assembled through joints, bolts, or other connecting elements upon reaching the destination.

It is therefore crucial to analyse on the number of connecting elements needed, as well as their layout on the mating surfaces. It is very important when comes to choosing the right amount of number of interconnections as well as the layout of the elements. It is realised that a certain quantity and layout of the interconnections might only work well in some loading cases. And in some loading cases, the chosen quantity and layout of the fasteners might not work out well. In the mechanical engineering industry, the fasteners are widely used, whether a permanent or non-permanent joint is needed in the assembly of the structure. A missing fastener between the components can be devastating, as it might lead to catastrophic failure. For example, a truss framework in construction area is made of many sub components and fasteners. If there are any failures due to the poor design of the layout of the fasteners, the personnel in the work site will be exposed to danger.
Thus, this is where the TO comes about. The optimisation method will solve for the most optimal solution, where the most optimal layout and the quantity of the interconnections is proposed, depending on the loading conditions.

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Compare to cross-section or shape optimization, TO is a relatively new method in the industry. Other optimization method are size ADDIN EN.CITE <EndNote><Cite><Author>Prager</Author><Year>1974</Year><RecNum>34</RecNum><DisplayText>3, 4</DisplayText><record><rec-number>34</rec-number><foreign-keys><key app=”EN” db-id=”eef20vv9h99psxes2zox2fsk52pxsf9fss90″ timestamp=”1522992382″>34</key></foreign-keys><ref-type name=”Journal Article”>17</ref-type><contributors><authors><author>Prager, William</author></authors></contributors><titles><title>A note on discretized michell structures</title><secondary-title>Computer Methods in Applied Mechanics and Engineering</secondary-title></titles><periodical><full-title>Computer Methods in Applied Mechanics and Engineering</full-title></periodical><pages>349-355</pages><volume>3</volume><number>3</number><dates><year>1974</year><pub-dates><date>1974/05/01/</date></pub-dates></dates><isbn>0045-7825</isbn><urls><related-urls><url>http://www.sciencedirect.com/science/article/pii/004578257490019X</url></related-urls></urls><electronic-resource-num>https://doi.org/10.1016/0045-7825(74)90019-X</electronic-resource-num></record></Cite><Cite><Author>Svanberg</Author><Year>1981</Year><RecNum>35</RecNum><record><rec-number>35</rec-number><foreign-keys><key app=”EN” db-id=”eef20vv9h99psxes2zox2fsk52pxsf9fss90″ timestamp=”1522992620″>35</key></foreign-keys><ref-type name=”Journal Article”>17</ref-type><contributors><authors><author>Svanberg, Krister</author></authors></contributors><titles><title>Optimization of geometry in truss design</title><secondary-title>Computer Methods in Applied Mechanics and Engineering</secondary-title></titles><periodical><full-title>Computer Methods in Applied Mechanics and Engineering</full-title></periodical><pages>63-80</pages><volume>28</volume><number>1</number><dates><year>1981</year><pub-dates><date>1981/08/01/</date></pub-dates></dates><isbn>0045-7825</isbn><urls><related-urls><url>http://www.sciencedirect.com/science/article/pii/004578258190027X</url></related-urls></urls><electronic-resource-num>https://doi.org/10.1016/0045-7825(81)90027-X</electronic-resource-num></record></Cite></EndNote>3, 4 and shape optimization ADDIN EN.CITE <EndNote><Cite><Author>Haslinger</Author><Year>2003</Year><RecNum>36</RecNum><DisplayText>5, 6</DisplayText><record><rec-number>36</rec-number><foreign-keys><key app=”EN” db-id=”eef20vv9h99psxes2zox2fsk52pxsf9fss90″ timestamp=”1522992802″>36</key></foreign-keys><ref-type name=”Book”>6</ref-type><contributors><authors><author>Haslinger, J.</author><author>Mäkinen, R. A. E.</author></authors></contributors><titles><title>Introduction to shape optimization: theory, approximation, and computation</title></titles><number>Book, Whole</number><keywords><keyword>Structural optimization</keyword><keyword>Mathematics</keyword></keywords><dates><year>2003</year></dates><pub-location>Philadelphia</pub-location><publisher>SIAM, Society for Industrial and Applied Mathematics</publisher><isbn>0898715369;9780898715361;</isbn><urls><related-urls><url>http://usyd.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwdV07D8IgEL5oXXTyGV9NGncNBQrtbGx0cHM3YM-4-Iit_19oq7FGxwuEx_Ad3MfdBwCjCzL_8gkBMxd7IbU4II9kciC-jpiOtC-1faqiVWb7V9xYKUB_MRj2ByUTNNehziX7QGUh7E2lCGSu-Wj6GGSLqFTcedl-RXwvP1HiNjTQlhl0oIaXLrQ-ZAGNtX1rqaY9mG1sMnlSqLx62dVLT-qG3tVg_VwWUfbBjVe75Xpup9mXjMxel-smbACOifJxCB5Brn0VKEVD5GGgND9KFkpMDGiIoHQEg99jjP81TKCZZ57lfMEUnOz-QLfY8BOj7m-J</url></related-urls></urls></record></Cite><Cite><Author>Soko?owski</Author><Year>1992</Year><RecNum>37</RecNum><record><rec-number>37</rec-number><foreign-keys><key app=”EN” db-id=”eef20vv9h99psxes2zox2fsk52pxsf9fss90″ timestamp=”1522993006″>37</key></foreign-keys><ref-type name=”Book”>6</ref-type><contributors><authors><author>Soko?owski, J.</author><author>Zolésio, J.P.</author></authors></contributors><titles><title>Introduction to shape optimization: shape sensitivity analysis</title></titles><dates><year>1992</year></dates><publisher>Springer-Verlag</publisher><isbn>9783540541776</isbn><urls><related-urls><url>https://books.google.com.au/books?id=hg-oAAAAIAAJ</url></related-urls></urls></record></Cite></EndNote>5, 6. Various TO methods and their features are discussed in Rozvany’s article ADDIN EN.CITE ;EndNote;;Cite;;Author;Rozvany;/Author;;Year;2001;/Year;;RecNum;29;/RecNum;;DisplayText;7;/DisplayText;;record;;rec-number;29;/rec-number;;foreign-keys;;key app=”EN” db-id=”eef20vv9h99psxes2zox2fsk52pxsf9fss90″ timestamp=”1522818619″;29;/key;;/foreign-keys;;ref-type name=”Journal Article”;17;/ref-type;;contributors;;authors;;author;Rozvany, G. I. N.;/author;;/authors;;/contributors;;titles;;title;Aims, scope, methods, history and unified terminology of computer-aided topology optimization in structural mechanics;/title;;secondary-title;Structural and Multidisciplinary Optimization;/secondary-title;;/titles;;periodical;;full-title;Structural and Multidisciplinary Optimization;/full-title;;/periodical;;pages;90-108;/pages;;volume;21;/volume;;number;2;/number;;dates;;year;2001;/year;;pub-dates;;date;2001/04/01;/date;;/pub-dates;;/dates;;isbn;1615-1488;/isbn;;urls;;related-urls;;url;https://doi.org/10.1007/s001580050174;/url;;/related-urls;;/urls;;electronic-resource-num;10.1007/s001580050174;/electronic-resource-num;;/record;;/Cite;;/EndNote;7. In short, size optimisation is the optimisation method that focus on change of size of dimensions of the elements, to achieve for optimum design. Shape optimisation process uses the predetermined boundaries as the design variable, to achieve for optimum results.
In earlier days, it is known that TO is done on many design problems, but it is done on the basis of analysing the multi-components as a whole ADDIN EN.CITE ;EndNote;;Cite;;Author;Qing;/Author;;Year;2001;/Year;;RecNum;6;/RecNum;;DisplayText;8;/DisplayText;;record;;rec-number;6;/rec-number;;foreign-keys;;key app=”EN” db-id=”eef20vv9h99psxes2zox2fsk52pxsf9fss90″ timestamp=”1521071566″;6;/key;;/foreign-keys;;ref-type name=”Journal Article”;17;/ref-type;;contributors;;authors;;author;Qing, Li;/author;;author;Grant, P. Steven;/author;;author;Y. M. Xie;/author;;/authors;;/contributors;;titles;;title;Evolutionary structural optimization for connection topology design of multi?component systems;/title;;secondary-title;Engineering Computations;/secondary-title;;/titles;;periodical;;full-title;Engineering Computations;/full-title;;/periodical;;pages;460-479;/pages;;volume;18;/volume;;number;3/4;/number;;dates;;year;2001;/year;;pub-dates;;date;2001/05/01;/date;;/pub-dates;;/dates;;publisher;Emerald;/publisher;;isbn;0264-4401;/isbn;;urls;;related-urls;;url;https://doi.org/10.1108/02644400110387127;/url;;/related-urls;;/urls;;electronic-resource-num;10.1108/02644400110387127;/electronic-resource-num;;access-date;2018/03/13;/access-date;;/record;;/Cite;;/EndNote;8. The interconnections are then treated as a form of sub-boundaries with the load transfer and kinematic constraints, which generates unreliable results from TO ADDIN EN.CITE ;EndNote;;Cite;;Author;Qing;/Author;;Year;2001;/Year;;RecNum;6;/RecNum;;DisplayText;8;/DisplayText;;record;;rec-number;6;/rec-number;;foreign-keys;;key app=”EN” db-id=”eef20vv9h99psxes2zox2fsk52pxsf9fss90″ timestamp=”1521071566″;6;/key;;/foreign-keys;;ref-type name=”Journal Article”;17;/ref-type;;contributors;;authors;;author;Qing, Li;/author;;author;Grant, P. Steven;/author;;author;Y. M. Xie;/author;;/authors;;/contributors;;titles;;title;Evolutionary structural optimization for connection topology design of multi?component systems;/title;;secondary-title;Engineering Computations;/secondary-title;;/titles;;periodical;;full-title;Engineering Computations;/full-title;;/periodical;;pages;460-479;/pages;;volume;18;/volume;;number;3/4;/number;;dates;;year;2001;/year;;pub-dates;;date;2001/05/01;/date;;/pub-dates;;/dates;;publisher;Emerald;/publisher;;isbn;0264-4401;/isbn;;urls;;related-urls;;url;https://doi.org/10.1108/02644400110387127;/url;;/related-urls;;/urls;;electronic-resource-num;10.1108/02644400110387127;/electronic-resource-num;;access-date;2018/03/13;/access-date;;/record;;/Cite;;/EndNote;8. TO essentially gives suggests reliable and efficient layout of fasteners on the mating surfaces ADDIN EN.CITE ;EndNote;;Cite;;Author;Qing;/Author;;Year;2001;/Year;;RecNum;6;/RecNum;;DisplayText;8;/DisplayText;;record;;rec-number;6;/rec-number;;foreign-keys;;key app=”EN” db-id=”eef20vv9h99psxes2zox2fsk52pxsf9fss90″ timestamp=”1521071566″;6;/key;;/foreign-keys;;ref-type name=”Journal Article”;17;/ref-type;;contributors;;authors;;author;Qing, Li;/author;;author;Grant, P. Steven;/author;;author;Y. M. Xie;/author;;/authors;;/contributors;;titles;;title;Evolutionary structural optimization for connection topology design of multi?component systems;/title;;secondary-title;Engineering Computations;/secondary-title;;/titles;;periodical;;full-title;Engineering Computations;/full-title;;/periodical;;pages;460-479;/pages;;volume;18;/volume;;number;3/4;/number;;dates;;year;2001;/year;;pub-dates;;date;2001/05/01;/date;;/pub-dates;;/dates;;publisher;Emerald;/publisher;;isbn;0264-4401;/isbn;;urls;;related-urls;;url;https://doi.org/10.1108/02644400110387127;/url;;/related-urls;;/urls;;electronic-resource-num;10.1108/02644400110387127;/electronic-resource-num;;access-date;2018/03/13;/access-date;;/record;;/Cite;;/EndNote;8. Thus, TO is advised to use in the early stage of a design process, as it generate designs that is accustomed to the constraints and loading conditions ADDIN EN.CITE ;EndNote;;Cite;;Author;Chickermane;/Author;;Year;1997;/Year;;RecNum;5;/RecNum;;DisplayText;9;/DisplayText;;record;;rec-number;5;/rec-number;;foreign-keys;;key app=”EN” db-id=”eef20vv9h99psxes2zox2fsk52pxsf9fss90″ timestamp=”1521071545″;5;/key;;/foreign-keys;;ref-type name=”Journal Article”;17;/ref-type;;contributors;;authors;;author;Chickermane, H.;/author;;author;Gea, H. C.;/author;;/authors;;/contributors;;titles;;title;Design of multi-component structural systems for optimal layout topology and joint locations;/title;;secondary-title;Engineering with Computers;/secondary-title;;/titles;;periodical;;full-title;Engineering with Computers;/full-title;;/periodical;;pages;235-243;/pages;;volume;13;/volume;;number;4;/number;;dates;;year;1997;/year;;pub-dates;;date;1997/12/01;/date;;/pub-dates;;/dates;;isbn;1435-5663;/isbn;;urls;;related-urls;;url;https://doi.org/10.1007/BF01200050;/url;;/related-urls;;/urls;;electronic-resource-num;10.1007/BF01200050;/electronic-resource-num;;/record;;/Cite;;/EndNote;9.
To add on, topology optimisation is a type of structural optimisation, which is different from the typical size and shape optimisation ADDIN EN.CITE ;EndNote;;Cite;;Author;Aremu;/Author;;Year;2010;/Year;;RecNum;1;/RecNum;;DisplayText;10;/DisplayText;;record;;rec-number;1;/rec-number;;foreign-keys;;key app=”EN” db-id=”eef20vv9h99psxes2zox2fsk52pxsf9fss90″ timestamp=”1520762454″;1;/key;;/foreign-keys;;ref-type name=”Book”;6;/ref-type;;contributors;;authors;;author;Aremu, Adedeji;/author;;author;Ashcroft, Ian;/author;;author;Hague, Richard;/author;;author;Wildman, Ricky;/author;;author;Tuck, Christopher;/author;;/authors;;/contributors;;titles;;title;Suitability of SIMP and BESO topology optimization algorithms for additive manufacture;/title;;/titles;;pages;679-692;/pages;;dates;;year;2010;/year;;/dates;;urls;;/urls;;/record;;/Cite;;/EndNote;10. Unlike the size and shape optimisation, TO is not constrained by the nature of the nature of the initial design ADDIN EN.CITE ;EndNote;;Cite;;Author;Aremu;/Author;;Year;2010;/Year;;RecNum;1;/RecNum;;DisplayText;10;/DisplayText;;record;;rec-number;1;/rec-number;;foreign-keys;;key app=”EN” db-id=”eef20vv9h99psxes2zox2fsk52pxsf9fss90″ timestamp=”1520762454″;1;/key;;/foreign-keys;;ref-type name=”Book”;6;/ref-type;;contributors;;authors;;author;Aremu, Adedeji;/author;;author;Ashcroft, Ian;/author;;author;Hague, Richard;/author;;author;Wildman, Ricky;/author;;author;Tuck, Christopher;/author;;/authors;;/contributors;;titles;;title;Suitability of SIMP and BESO topology optimization algorithms for additive manufacture;/title;;/titles;;pages;679-692;/pages;;dates;;year;2010;/year;;/dates;;urls;;/urls;;/record;;/Cite;;/EndNote;10. That said, all the optimization methods are used in decrease stress, increase stiffness and ensure uniform stress distribution in the final design domain ADDIN EN.CITE ;EndNote;;Cite;;Author;Razvan;/Author;;Year;2014;/Year;;RecNum;4;/RecNum;;DisplayText;11;/DisplayText;;record;;rec-number;4;/rec-number;;foreign-keys;;key app=”EN” db-id=”eef20vv9h99psxes2zox2fsk52pxsf9fss90″ timestamp=”1520762826″;4;/key;;/foreign-keys;;ref-type name=”Book”;6;/ref-type;;contributors;;authors;;author;Razvan, Cazacu;/author;;/authors;;/contributors;;titles;;title;OVERVIEW OF STRUCTURAL TOPOLOGY OPTIMIZATION METHODS FOR PLANE AND SOLID STRUCTURES;/title;;/titles;;volume;XXIII (XIII), 2014/3;/volume;;dates;;year;2014;/year;;/dates;;urls;;/urls;;electronic-resource-num;10.15660/AUOFMTE.2014-3.3043;/electronic-resource-num;;/record;;/Cite;;/EndNote;11. TO is also known as the most common and general approach when comes to structural optimisation ADDIN EN.CITE ;EndNote;;Cite;;Author;Razvan;/Author;;Year;2014;/Year;;RecNum;4;/RecNum;;DisplayText;11;/DisplayText;;record;;rec-number;4;/rec-number;;foreign-keys;;key app=”EN” db-id=”eef20vv9h99psxes2zox2fsk52pxsf9fss90″ timestamp=”1520762826″;4;/key;;/foreign-keys;;ref-type name=”Book”;6;/ref-type;;contributors;;authors;;author;Razvan, Cazacu;/author;;/authors;;/contributors;;titles;;title;OVERVIEW OF STRUCTURAL TOPOLOGY OPTIMIZATION METHODS FOR PLANE AND SOLID STRUCTURES;/title;;/titles;;volume;XXIII (XIII), 2014/3;/volume;;dates;;year;2014;/year;;/dates;;urls;;/urls;;electronic-resource-num;10.15660/AUOFMTE.2014-3.3043;/electronic-resource-num;;/record;;/Cite;;/EndNote;11. It essentially creates a structure that has the most advantageous material distribution ADDIN EN.CITE ;EndNote;;Cite;;Author;Razvan;/Author;;Year;2014;/Year;;RecNum;4;/RecNum;;DisplayText;11;/DisplayText;;record;;rec-number;4;/rec-number;;foreign-keys;;key app=”EN” db-id=”eef20vv9h99psxes2zox2fsk52pxsf9fss90″ timestamp=”1520762826″;4;/key;;/foreign-keys;;ref-type name=”Book”;6;/ref-type;;contributors;;authors;;author;Razvan, Cazacu;/author;;/authors;;/contributors;;titles;;title;OVERVIEW OF STRUCTURAL TOPOLOGY OPTIMIZATION METHODS FOR PLANE AND SOLID STRUCTURES;/title;;/titles;;volume;XXIII (XIII), 2014/3;/volume;;dates;;year;2014;/year;;/dates;;urls;;/urls;;electronic-resource-num;10.15660/AUOFMTE.2014-3.3043;/electronic-resource-num;;/record;;/Cite;;/EndNote;11. Size and shape optimisation are then used in the post-processing, which is used to further modify the model ADDIN EN.CITE ;EndNote;;Cite;;Author;Razvan;/Author;;Year;2014;/Year;;RecNum;4;/RecNum;;DisplayText;11;/DisplayText;;record;;rec-number;4;/rec-number;;foreign-keys;;key app=”EN” db-id=”eef20vv9h99psxes2zox2fsk52pxsf9fss90″ timestamp=”1520762826″;4;/key;;/foreign-keys;;ref-type name=”Book”;6;/ref-type;;contributors;;authors;;author;Razvan, Cazacu;/author;;/authors;;/contributors;;titles;;title;OVERVIEW OF STRUCTURAL TOPOLOGY OPTIMIZATION METHODS FOR PLANE AND SOLID STRUCTURES;/title;;/titles;;volume;XXIII (XIII), 2014/3;/volume;;dates;;year;2014;/year;;/dates;;urls;;/urls;;electronic-resource-num;10.15660/AUOFMTE.2014-3.3043;/electronic-resource-num;;/record;;/Cite;;/EndNote;11. TO is generally used in the industry to give an optimal design that fulfils both functionality and manufacturing ADDIN EN.CITE ;EndNote;;Cite;;Author;Wang;/Author;;Year;2005;/Year;;RecNum;24;/RecNum;;DisplayText;12;/DisplayText;;record;;rec-number;24;/rec-number;;foreign-keys;;key app=”EN” db-id=”eef20vv9h99psxes2zox2fsk52pxsf9fss90″ timestamp=”1522727290″;24;/key;;/foreign-keys;;ref-type name=”Journal Article”;17;/ref-type;;contributors;;authors;;author;Wang, S. Y.;/author;;author;Tai, K.;/author;;/authors;;/contributors;;titles;;title;Structural topology design optimization using Genetic Algorithms with a bit-array representation;/title;;secondary-title;Computer Methods in Applied Mechanics and Engineering;/secondary-title;;/titles;;periodical;;full-title;Computer Methods in Applied Mechanics and Engineering;/full-title;;/periodical;;pages;3749-3770;/pages;;volume;194;/volume;;number;36;/number;;keywords;;keyword;Structural topology optimization;/keyword;;keyword;Bit-array representation;/keyword;;keyword;Design connectivity;/keyword;;keyword;Representation degeneracy;/keyword;;keyword;Genetic Algorithms;/keyword;;/keywords;;dates;;year;2005;/year;;pub-dates;;date;2005/09/23/;/date;;/pub-dates;;/dates;;isbn;0045-7825;/isbn;;urls;;related-urls;;url;http://www.sciencedirect.com/science/article/pii/S0045782504004530;/url;;/related-urls;;/urls;;electronic-resource-num;https://doi.org/10.1016/j.cma.2004.09.003;/electronic-resource-num;;/record;;/Cite;;/EndNote;12. As such, TO is a useful tool for generating optimal initial shape of a mechanical structure ADDIN EN.CITE ;EndNote;;Cite;;Author;Kütük;/Author;;Year;2013;/Year;;RecNum;46;/RecNum;;DisplayText;13;/DisplayText;;record;;rec-number;46;/rec-number;;foreign-keys;;key app=”EN” db-id=”eef20vv9h99psxes2zox2fsk52pxsf9fss90″ timestamp=”1523503955″;46;/key;;/foreign-keys;;ref-type name=”Journal Article”;17;/ref-type;;contributors;;authors;;author;M. Akif Kütük;/author;;author;?brahim Göv;/author;;/authors;;/contributors;;titles;;title;A Finite Element Removal Method for 3D Topology Optimization;/title;;secondary-title;Advances in Mechanical Engineering;/secondary-title;;/titles;;periodical;;full-title;Advances in Mechanical Engineering;/full-title;;/periodical;;pages;413463;/pages;;volume;5;/volume;;dates;;year;2013;/year;;/dates;;urls;;related-urls;;url;http://journals.sagepub.com/doi/abs/10.1155/2013/413463;/url;;/related-urls;;/urls;;electronic-resource-num;10.1155/2013/413463;/electronic-resource-num;;/record;;/Cite;;/EndNote;13.
Generally, in the current industry, the mainstream TO methods are ESO, BESO, SIMP, LSM and GA methods. This literature review will give a brief discussion on different topology optimisation methods that are used in industry, while these methods are the possible ways to use in the topology optimisation for interconnecting elements. The SIMP method that is used for this thesis project will be elaborated in a more detailed manner in the later section.

FEA will be first introduced, then followed by the TO methods as mentioned. The details of interfacing MATLAB and FEA will be covered in the later section.

FEA (Finite Element Analysis)
Introduction
FEA is a method of making various analysis and simulations of the possible physical phenomenon by using the Finite Element Method (FEM). FEA is generally used to carry out analysis on new designs by engineers in the industry. It is widely used in many industries such as structural analysis, computational fluid dynamics and many more.

In mechanical industry, FEA proved to be very useful in a way that it shows possible deformations and outcomes when applying different boundary and loading conditions. In most of the application, FEA is used on analysing a certain structure design, and the engineers use the software to find out the weak spots and high stress concentration region.
FEA uses FEM to discretise the design domain into small elements and they are all connected by network of nodes. Of which the mesh size can change the quantity and density of elements in the design domain. One can have denser mesh of elements around any regions to give a more accurate results and analysis. The elements shape can be ranged from cubes to tetrahedrons. This is all achievable in FEA package. The main advantage of using FEM enables FEA to select a range of different element discretisation method in the design domain, depending on the structural design of the design problem. In the industry, it is noted that smaller and denser elements are used in the important areas such as an interior surface of the hole, which is subjected to bearing load.
In the FEA software, it is noted that the accuracy of the solution is closely related to the number of the iterations and quantity ADDIN EN.CITE ;EndNote;;Cite;;Author;Kütük;/Author;;Year;2013;/Year;;RecNum;46;/RecNum;;DisplayText;13;/DisplayText;;record;;rec-number;46;/rec-number;;foreign-keys;;key app=”EN” db-id=”eef20vv9h99psxes2zox2fsk52pxsf9fss90″ timestamp=”1523503955″;46;/key;;/foreign-keys;;ref-type name=”Journal Article”;17;/ref-type;;contributors;;authors;;author;M. Akif Kütük;/author;;author;?brahim Göv;/author;;/authors;;/contributors;;titles;;title;A Finite Element Removal Method for 3D Topology Optimization;/title;;secondary-title;Advances in Mechanical Engineering;/secondary-title;;/titles;;periodical;;full-title;Advances in Mechanical Engineering;/full-title;;/periodical;;pages;413463;/pages;;volume;5;/volume;;dates;;year;2013;/year;;/dates;;urls;;related-urls;;url;http://journals.sagepub.com/doi/abs/10.1155/2013/413463;/url;;/related-urls;;/urls;;electronic-resource-num;10.1155/2013/413463;/electronic-resource-num;;/record;;/Cite;;/EndNote;13. It is seen that the FEA is essential for all kinds of optimisation methods as mentioned in this literature review. It is one of the important process of discretising the design domain into small elements before initialising the algorithm for different optimisation method.

As mentioned, to achieve a high accuracy solution, the design domain is required to discretised into high number of elements. However, this will require high CPU usage and the processing time will be lengthened.
ESO and BESO
Introduction
ESO method is firstly introduced by Xie and Steven ADDIN EN.CITE ;EndNote;;Cite;;Author;Xie;/Author;;Year;1993;/Year;;RecNum;9;/RecNum;;DisplayText;14;/DisplayText;;record;;rec-number;9;/rec-number;;foreign-keys;;key app=”EN” db-id=”eef20vv9h99psxes2zox2fsk52pxsf9fss90″ timestamp=”1521343796″;9;/key;;/foreign-keys;;ref-type name=”Journal Article”;17;/ref-type;;contributors;;authors;;author;Xie, Y. M.;/author;;author;Steven, G. P.;/author;;/authors;;/contributors;;titles;;title;A simple evolutionary procedure for structural optimization;/title;;secondary-title;Computers ;amp; Structures;/secondary-title;;/titles;;periodical;;full-title;Computers ;amp; Structures;/full-title;;/periodical;;pages;885-896;/pages;;volume;49;/volume;;number;5;/number;;dates;;year;1993;/year;;pub-dates;;date;1993/12/03/;/date;;/pub-dates;;/dates;;isbn;0045-7949;/isbn;;urls;;related-urls;;url;http://www.sciencedirect.com/science/article/pii/004579499390035C;/url;;/related-urls;;/urls;;electronic-resource-num;https://doi.org/10.1016/0045-7949(93)90035-C;/electronic-resource-num;;/record;;/Cite;;/EndNote;14. The key concept of ESO is to remove the low stressed elements from the initial design problem, and create an optimum solution in an evolutionary fashion ADDIN EN.CITE ;EndNote;;Cite;;Author;Xie;/Author;;Year;1993;/Year;;RecNum;9;/RecNum;;DisplayText;14, 15;/DisplayText;;record;;rec-number;9;/rec-number;;foreign-keys;;key app=”EN” db-id=”eef20vv9h99psxes2zox2fsk52pxsf9fss90″ timestamp=”1521343796″;9;/key;;/foreign-keys;;ref-type name=”Journal Article”;17;/ref-type;;contributors;;authors;;author;Xie, Y. M.;/author;;author;Steven, G. P.;/author;;/authors;;/contributors;;titles;;title;A simple evolutionary procedure for structural optimization;/title;;secondary-title;Computers ;amp; Structures;/secondary-title;;/titles;;periodical;;full-title;Computers ;amp; Structures;/full-title;;/periodical;;pages;885-896;/pages;;volume;49;/volume;;number;5;/number;;dates;;year;1993;/year;;pub-dates;;date;1993/12/03/;/date;;/pub-dates;;/dates;;isbn;0045-7949;/isbn;;urls;;related-urls;;url;http://www.sciencedirect.com/science/article/pii/004579499390035C;/url;;/related-urls;;/urls;;electronic-resource-num;https://doi.org/10.1016/0045-7949(93)90035-C;/electronic-resource-num;;/record;;/Cite;;Cite;;Author;Huang;/Author;;Year;2010;/Year;;RecNum;8;/RecNum;;record;;rec-number;8;/rec-number;;foreign-keys;;key app=”EN” db-id=”eef20vv9h99psxes2zox2fsk52pxsf9fss90″ timestamp=”1521342927″;8;/key;;/foreign-keys;;ref-type name=”Book”;6;/ref-type;;contributors;;authors;;author;Huang, X.;/author;;author;Xie, Yi;/author;;/authors;;/contributors;;titles;;title;A further review of ESO type methods for topology optimization;/title;;/titles;;pages;671-683;/pages;;volume;41;/volume;;dates;;year;2010;/year;;/dates;;urls;;/urls;;electronic-resource-num;10.1007/s00158-010-0487-9;/electronic-resource-num;;/record;;/Cite;;/EndNote;14, 15. The resulting design will then be a structure that is fully-stressed ADDIN EN.CITE ;EndNote;;Cite;;Author;Querin;/Author;;Year;2018;/Year;;RecNum;16;/RecNum;;DisplayText;16;/DisplayText;;record;;rec-number;16;/rec-number;;foreign-keys;;key app=”EN” db-id=”eef20vv9h99psxes2zox2fsk52pxsf9fss90″ timestamp=”1522218770″;16;/key;;/foreign-keys;;ref-type name=”Book”;6;/ref-type;;contributors;;authors;;author;Querin, Osvaldo;/author;;/authors;;/contributors;;titles;;title;Evolutionary Structural Optimisation: Stress Based Formulation and Implementation;/title;;/titles;;dates;;year;2018;/year;;/dates;;urls;;/urls;;/record;;/Cite;;/EndNote;16.

ESO method generally utilise the RR as a parameter to remove the low stressed elements ADDIN EN.CITE ;EndNote;;Cite;;Author;Xie;/Author;;Year;1993;/Year;;RecNum;9;/RecNum;;DisplayText;14;/DisplayText;;record;;rec-number;9;/rec-number;;foreign-keys;;key app=”EN” db-id=”eef20vv9h99psxes2zox2fsk52pxsf9fss90″ timestamp=”1521343796″;9;/key;;/foreign-keys;;ref-type name=”Journal Article”;17;/ref-type;;contributors;;authors;;author;Xie, Y. M.;/author;;author;Steven, G. P.;/author;;/authors;;/contributors;;titles;;title;A simple evolutionary procedure for structural optimization;/title;;secondary-title;Computers ;amp; Structures;/secondary-title;;/titles;;periodical;;full-title;Computers ;amp; Structures;/full-title;;/periodical;;pages;885-896;/pages;;volume;49;/volume;;number;5;/number;;dates;;year;1993;/year;;pub-dates;;date;1993/12/03/;/date;;/pub-dates;;/dates;;isbn;0045-7949;/isbn;;urls;;related-urls;;url;http://www.sciencedirect.com/science/article/pii/004579499390035C;/url;;/related-urls;;/urls;;electronic-resource-num;https://doi.org/10.1016/0045-7949(93)90035-C;/electronic-resource-num;;/record;;/Cite;;/EndNote;14. During the initial design stage, the elements in the design domain are subjected to the von Mises stress due to the initial parameters settings with the boundary conditions and the loading conditions. To explain the usage of the RR, element’s stress values is compared with the value of the multiplication of RR and the maximum von Mises stress over the design domain. If the element’s stress value is lower than the multiplication value, it will be removed from the design domain ADDIN EN.CITE ;EndNote;;Cite;;Author;Xie;/Author;;Year;1993;/Year;;RecNum;9;/RecNum;;DisplayText;14;/DisplayText;;record;;rec-number;9;/rec-number;;foreign-keys;;key app=”EN” db-id=”eef20vv9h99psxes2zox2fsk52pxsf9fss90″ timestamp=”1521343796″;9;/key;;/foreign-keys;;ref-type name=”Journal Article”;17;/ref-type;;contributors;;authors;;author;Xie, Y. M.;/author;;author;Steven, G. P.;/author;;/authors;;/contributors;;titles;;title;A simple evolutionary procedure for structural optimization;/title;;secondary-title;Computers ;amp; Structures;/secondary-title;;/titles;;periodical;;full-title;Computers ;amp; Structures;/full-title;;/periodical;;pages;885-896;/pages;;volume;49;/volume;;number;5;/number;;dates;;year;1993;/year;;pub-dates;;date;1993/12/03/;/date;;/pub-dates;;/dates;;isbn;0045-7949;/isbn;;urls;;related-urls;;url;http://www.sciencedirect.com/science/article/pii/004579499390035C;/url;;/related-urls;;/urls;;electronic-resource-num;https://doi.org/10.1016/0045-7949(93)90035-C;/electronic-resource-num;;/record;;/Cite;;/EndNote;14. Due to the fact that the ESO method only eliminate the elements from the original design, the initial design domain is over-sized to ensure the final optimum design can be represented ADDIN EN.CITE ;EndNote;;Cite;;Author;Yang;/Author;;Year;1999;/Year;;RecNum;14;/RecNum;;DisplayText;17;/DisplayText;;record;;rec-number;14;/rec-number;;foreign-keys;;key app=”EN” db-id=”eef20vv9h99psxes2zox2fsk52pxsf9fss90″ timestamp=”1521680714″;14;/key;;/foreign-keys;;ref-type name=”Journal Article”;17;/ref-type;;contributors;;authors;;author;Yang, X. Y.;/author;;author;Xei, Y. M.;/author;;author;Steven, G. P.;/author;;author;Querin, O. M.;/author;;/authors;;/contributors;;titles;;title;Bidirectional Evolutionary Method for Stiffness Optimization;/title;;secondary-title;AIAA Journal;/secondary-title;;/titles;;periodical;;full-title;AIAA Journal;/full-title;;/periodical;;pages;1483-1488;/pages;;volume;37;/volume;;number;11;/number;;dates;;year;1999;/year;;pub-dates;;date;1999/11/01;/date;;/pub-dates;;/dates;;publisher;American Institute of Aeronautics and Astronautics;/publisher;;isbn;0001-1452;/isbn;;urls;;related-urls;;url;https://doi.org/10.2514/2.626;/url;;/related-urls;;/urls;;electronic-resource-num;10.2514/2.626;/electronic-resource-num;;access-date;2018/03/21;/access-date;;/record;;/Cite;;/EndNote;17.

Whereas BESO is introduced by Querin et al ADDIN EN.CITE ;EndNote;;Cite;;Author;Querin;/Author;;Year;1998;/Year;;RecNum;13;/RecNum;;DisplayText;18;/DisplayText;;record;;rec-number;13;/rec-number;;foreign-keys;;key app=”EN” db-id=”eef20vv9h99psxes2zox2fsk52pxsf9fss90″ timestamp=”1521346059″;13;/key;;/foreign-keys;;ref-type name=”Journal Article”;17;/ref-type;;contributors;;authors;;author;O. M. Querin;/author;;author;G. P. Steven;/author;;author;Y. M. Xie;/author;;/authors;;/contributors;;titles;;title;Evolutionary structural optimisation (ESO) using a bidirectional algorithm;/title;;secondary-title;Engineering Computations;/secondary-title;;/titles;;periodical;;full-title;Engineering Computations;/full-title;;/periodical;;pages;1031-1048;/pages;;volume;15;/volume;;number;8;/number;;dates;;year;1998;/year;;pub-dates;;date;1998/12/01;/date;;/pub-dates;;/dates;;publisher;Emerald;/publisher;;isbn;0264-4401;/isbn;;urls;;related-urls;;url;https://doi.org/10.1108/02644409810244129;/url;;/related-urls;;/urls;;electronic-resource-num;10.1108/02644409810244129;/electronic-resource-num;;access-date;2018/03/17;/access-date;;/record;;/Cite;;/EndNote;18. BESO method is built up upon the concept of ESO method. ESO only focus on removing elements from the design domain and the elements are not able to be recovered ADDIN EN.CITE ;EndNote;;Cite;;Author;Yang;/Author;;Year;1999;/Year;;RecNum;14;/RecNum;;DisplayText;17;/DisplayText;;record;;rec-number;14;/rec-number;;foreign-keys;;key app=”EN” db-id=”eef20vv9h99psxes2zox2fsk52pxsf9fss90″ timestamp=”1521680714″;14;/key;;/foreign-keys;;ref-type name=”Journal Article”;17;/ref-type;;contributors;;authors;;author;Yang, X. Y.;/author;;author;Xei, Y. M.;/author;;author;Steven, G. P.;/author;;author;Querin, O. M.;/author;;/authors;;/contributors;;titles;;title;Bidirectional Evolutionary Method for Stiffness Optimization;/title;;secondary-title;AIAA Journal;/secondary-title;;/titles;;periodical;;full-title;AIAA Journal;/full-title;;/periodical;;pages;1483-1488;/pages;;volume;37;/volume;;number;11;/number;;dates;;year;1999;/year;;pub-dates;;date;1999/11/01;/date;;/pub-dates;;/dates;;publisher;American Institute of Aeronautics and Astronautics;/publisher;;isbn;0001-1452;/isbn;;urls;;related-urls;;url;https://doi.org/10.2514/2.626;/url;;/related-urls;;/urls;;electronic-resource-num;10.2514/2.626;/electronic-resource-num;;access-date;2018/03/21;/access-date;;/record;;/Cite;;/EndNote;17. Thus, BESO is introduced, which works similarly as ESO, removing the low stress elements, but also adding elements in the low stress regions ADDIN EN.CITE ;EndNote;;Cite;;Author;Huang;/Author;;Year;2010;/Year;;RecNum;8;/RecNum;;DisplayText;15;/DisplayText;;record;;rec-number;8;/rec-number;;foreign-keys;;key app=”EN” db-id=”eef20vv9h99psxes2zox2fsk52pxsf9fss90″ timestamp=”1521342927″;8;/key;;/foreign-keys;;ref-type name=”Book”;6;/ref-type;;contributors;;authors;;author;Huang, X.;/author;;author;Xie, Yi;/author;;/authors;;/contributors;;titles;;title;A further review of ESO type methods for topology optimization;/title;;/titles;;pages;671-683;/pages;;volume;41;/volume;;dates;;year;2010;/year;;/dates;;urls;;/urls;;electronic-resource-num;10.1007/s00158-010-0487-9;/electronic-resource-num;;/record;;/Cite;;/EndNote;15. BESO’s concepts allow the structure to be self-designed, and create the shape of the structure with different loading and boundary conditions ADDIN EN.CITE <EndNote><Cite><Author>Querin</Author><Year>1998</Year><RecNum>13</RecNum><DisplayText>18</DisplayText><record><rec-number>13</rec-number><foreign-keys><key app=”EN” db-id=”eef20vv9h99psxes2zox2fsk52pxsf9fss90″ timestamp=”1521346059″>13</key></foreign-keys><ref-type name=”Journal Article”>17</ref-type><contributors><authors><author>O. M. Querin</author><author>G. P. Steven</author><author>Y. M. Xie</author></authors></contributors><titles><title>Evolutionary structural optimisation (ESO) using a bidirectional algorithm</title><secondary-title>Engineering Computations</secondary-title></titles><periodical><full-title>Engineering Computations</full-title></periodical><pages>1031-1048</pages><volume>15</volume><number>8</number><dates><year>1998</year><pub-dates><date>1998/12/01</date></pub-dates></dates><publisher>Emerald</publisher><isbn>0264-4401</isbn><urls><related-urls><url>https://doi.org/10.1108/02644409810244129</url></related-urls></urls><electronic-resource-num>10.1108/02644409810244129</electronic-resource-num><access-date>2018/03/17</access-date></record></Cite></EndNote>18. Generally, BESO is widely used to improve the reliability and the efficiency of ESO method ADDIN EN.CITE <EndNote><Cite><Author>Yang</Author><Year>1999</Year><RecNum>14</RecNum><DisplayText>17</DisplayText><record><rec-number>14</rec-number><foreign-keys><key app=”EN” db-id=”eef20vv9h99psxes2zox2fsk52pxsf9fss90″ timestamp=”1521680714″>14</key></foreign-keys><ref-type name=”Journal Article”>17</ref-type><contributors><authors><author>Yang, X. Y.</author><author>Xei, Y. M.</author><author>Steven, G. P.</author><author>Querin, O. M.</author></authors></contributors><titles><title>Bidirectional Evolutionary Method for Stiffness Optimization</title><secondary-title>AIAA Journal</secondary-title></titles><periodical><full-title>AIAA Journal</full-title></periodical><pages>1483-1488</pages><volume>37</volume><number>11</number><dates><year>1999</year><pub-dates><date>1999/11/01</date></pub-dates></dates><publisher>American Institute of Aeronautics and Astronautics</publisher><isbn>0001-1452</isbn><urls><related-urls><url>https://doi.org/10.2514/2.626</url></related-urls></urls><electronic-resource-num>10.2514/2.626</electronic-resource-num><access-date>2018/03/21</access-date></record></Cite></EndNote>17. And it is computationally more effective in many design problems ADDIN EN.CITE <EndNote><Cite><Author>Yang</Author><Year>1999</Year><RecNum>14</RecNum><DisplayText>17</DisplayText><record><rec-number>14</rec-number><foreign-keys><key app=”EN” db-id=”eef20vv9h99psxes2zox2fsk52pxsf9fss90″ timestamp=”1521680714″>14</key></foreign-keys><ref-type name=”Journal Article”>17</ref-type><contributors><authors><author>Yang, X. Y.</author><author>Xei, Y. M.</author><author>Steven, G. P.</author><author>Querin, O. M.</author></authors></contributors><titles><title>Bidirectional Evolutionary Method for Stiffness Optimization</title><secondary-title>AIAA Journal</secondary-title></titles><periodical><full-title>AIAA Journal</full-title></periodical><pages>1483-1488</pages><volume>37</volume><number>11</number><dates><year>1999</year><pub-dates><date>1999/11/01</date></pub-dates></dates><publisher>American Institute of Aeronautics and Astronautics</publisher><isbn>0001-1452</isbn><urls><related-urls><url>https://doi.org/10.2514/2.626</url></related-urls></urls><electronic-resource-num>10.2514/2.626</electronic-resource-num><access-date>2018/03/21</access-date></record></Cite></EndNote>17.

All in all, both ESO and BESO methods are based on the principles of achieving a uniform stress by removing or adding necessary elements step-by-step at the correct regions until a termination criteria is met ADDIN EN.CITE <EndNote><Cite><Author>Hinton</Author><Year>1995</Year><RecNum>17</RecNum><DisplayText>19</DisplayText><record><rec-number>17</rec-number><foreign-keys><key app=”EN” db-id=”eef20vv9h99psxes2zox2fsk52pxsf9fss90″ timestamp=”1522403217″>17</key></foreign-keys><ref-type name=”Journal Article”>17</ref-type><contributors><authors><author>E. Hinton</author><author>J. Sienz</author></authors></contributors><titles><title>Fully stressed topological design of structures using an evolutionary procedure</title><secondary-title>Engineering Computations</secondary-title></titles><periodical><full-title>Engineering Computations</full-title></periodical><pages>229-244</pages><volume>12</volume><number>3</number><dates><year>1995</year><pub-dates><date>1995/03/01</date></pub-dates></dates><publisher>Emerald</publisher><isbn>0264-4401</isbn><urls><related-urls><url>https://doi.org/10.1108/02644409510799578</url></related-urls></urls><electronic-resource-num>10.1108/02644409510799578</electronic-resource-num><access-date>2018/03/30</access-date></record></Cite></EndNote>19. This allow the structure to have an uniform stress throughout eventually, and the end results looks like a continuum with holes ADDIN EN.CITE <EndNote><Cite><Author>Hinton</Author><Year>1995</Year><RecNum>17</RecNum><DisplayText>19</DisplayText><record><rec-number>17</rec-number><foreign-keys><key app=”EN” db-id=”eef20vv9h99psxes2zox2fsk52pxsf9fss90″ timestamp=”1522403217″>17</key></foreign-keys><ref-type name=”Journal Article”>17</ref-type><contributors><authors><author>E. Hinton</author><author>J. Sienz</author></authors></contributors><titles><title>Fully stressed topological design of structures using an evolutionary procedure</title><secondary-title>Engineering Computations</secondary-title></titles><periodical><full-title>Engineering Computations</full-title></periodical><pages>229-244</pages><volume>12</volume><number>3</number><dates><year>1995</year><pub-dates><date>1995/03/01</date></pub-dates></dates><publisher>Emerald</publisher><isbn>0264-4401</isbn><urls><related-urls><url>https://doi.org/10.1108/02644409510799578</url></related-urls></urls><electronic-resource-num>10.1108/02644409510799578</electronic-resource-num><access-date>2018/03/30</access-date></record></Cite></EndNote>19. The ESO and BESO algorithm can only work well if the only small amount of material is removed at each iterations, so that this will create a smoot transition from one stage to another ADDIN EN.CITE <EndNote><Cite><Author>Hinton</Author><Year>1995</Year><RecNum>17</RecNum><DisplayText>19</DisplayText><record><rec-number>17</rec-number><foreign-keys><key app=”EN” db-id=”eef20vv9h99psxes2zox2fsk52pxsf9fss90″ timestamp=”1522403217″>17</key></foreign-keys><ref-type name=”Journal Article”>17</ref-type><contributors><authors><author>E. Hinton</author><author>J. Sienz</author></authors></contributors><titles><title>Fully stressed topological design of structures using an evolutionary procedure</title><secondary-title>Engineering Computations</secondary-title></titles><periodical><full-title>Engineering Computations</full-title></periodical><pages>229-244</pages><volume>12</volume><number>3</number><dates><year>1995</year><pub-dates><date>1995/03/01</date></pub-dates></dates><publisher>Emerald</publisher><isbn>0264-4401</isbn><urls><related-urls><url>https://doi.org/10.1108/02644409510799578</url></related-urls></urls><electronic-resource-num>10.1108/02644409510799578</electronic-resource-num><access-date>2018/03/30</access-date></record></Cite></EndNote>19. In this topology optimisation for the interconnections, the design domain will be first discretised into small elements, where these elements in fact, are the interconnections. The simulation then will run to optimise for the best solution of layout of interconnections, where the number of the interconnection elements are reduced in each iteration.

Both ESO and BESO works by assigning a non-zero property number initially ADDIN EN.CITE <EndNote><Cite><Author>Yang</Author><Year>1999</Year><RecNum>14</RecNum><DisplayText>17</DisplayText><record><rec-number>14</rec-number><foreign-keys><key app=”EN” db-id=”eef20vv9h99psxes2zox2fsk52pxsf9fss90″ timestamp=”1521680714″>14</key></foreign-keys><ref-type name=”Journal Article”>17</ref-type><contributors><authors><author>Yang, X. Y.</author><author>Xei, Y. M.</author><author>Steven, G. P.</author><author>Querin, O. M.</author></authors></contributors><titles><title>Bidirectional Evolutionary Method for Stiffness Optimization</title><secondary-title>AIAA Journal</secondary-title></titles><periodical><full-title>AIAA Journal</full-title></periodical><pages>1483-1488</pages><volume>37</volume><number>11</number><dates><year>1999</year><pub-dates><date>1999/11/01</date></pub-dates></dates><publisher>American Institute of Aeronautics and Astronautics</publisher><isbn>0001-1452</isbn><urls><related-urls><url>https://doi.org/10.2514/2.626</url></related-urls></urls><electronic-resource-num>10.2514/2.626</electronic-resource-num><access-date>2018/03/21</access-date></record></Cite></EndNote>17. If an element is to be removed from the design domain, its property number will be changed to zero ADDIN EN.CITE <EndNote><Cite><Author>Yang</Author><Year>1999</Year><RecNum>14</RecNum><DisplayText>17</DisplayText><record><rec-number>14</rec-number><foreign-keys><key app=”EN” db-id=”eef20vv9h99psxes2zox2fsk52pxsf9fss90″ timestamp=”1521680714″>14</key></foreign-keys><ref-type name=”Journal Article”>17</ref-type><contributors><authors><author>Yang, X. Y.</author><author>Xei, Y. M.</author><author>Steven, G. P.</author><author>Querin, O. M.</author></authors></contributors><titles><title>Bidirectional Evolutionary Method for Stiffness Optimization</title><secondary-title>AIAA Journal</secondary-title></titles><periodical><full-title>AIAA Journal</full-title></periodical><pages>1483-1488</pages><volume>37</volume><number>11</number><dates><year>1999</year><pub-dates><date>1999/11/01</date></pub-dates></dates><publisher>American Institute of Aeronautics and Astronautics</publisher><isbn>0001-1452</isbn><urls><related-urls><url>https://doi.org/10.2514/2.626</url></related-urls></urls><electronic-resource-num>10.2514/2.626</electronic-resource-num><access-date>2018/03/21</access-date></record></Cite></EndNote>17. On the other hand, if an element is to be added, its property number will change from zero to non-zero ADDIN EN.CITE <EndNote><Cite><Author>Yang</Author><Year>1999</Year><RecNum>14</RecNum><DisplayText>17</DisplayText><record><rec-number>14</rec-number><foreign-keys><key app=”EN” db-id=”eef20vv9h99psxes2zox2fsk52pxsf9fss90″ timestamp=”1521680714″>14</key></foreign-keys><ref-type name=”Journal Article”>17</ref-type><contributors><authors><author>Yang, X. Y.</author><author>Xei, Y. M.</author><author>Steven, G. P.</author><author>Querin, O. M.</author></authors></contributors><titles><title>Bidirectional Evolutionary Method for Stiffness Optimization</title><secondary-title>AIAA Journal</secondary-title></titles><periodical><full-title>AIAA Journal</full-title></periodical><pages>1483-1488</pages><volume>37</volume><number>11</number><dates><year>1999</year><pub-dates><date>1999/11/01</date></pub-dates></dates><publisher>American Institute of Aeronautics and Astronautics</publisher><isbn>0001-1452</isbn><urls><related-urls><url>https://doi.org/10.2514/2.626</url></related-urls></urls><electronic-resource-num>10.2514/2.626</electronic-resource-num><access-date>2018/03/21</access-date></record></Cite></EndNote>17. Elements with non-zero property number will be added to the global stiffness matrix ADDIN EN.CITE <EndNote><Cite><Author>Yang</Author><Year>1999</Year><RecNum>14</RecNum><DisplayText>17</DisplayText><record><rec-number>14</rec-number><foreign-keys><key app=”EN” db-id=”eef20vv9h99psxes2zox2fsk52pxsf9fss90″ timestamp=”1521680714″>14</key></foreign-keys><ref-type name=”Journal Article”>17</ref-type><contributors><authors><author>Yang, X. Y.</author><author>Xei, Y. M.</author><author>Steven, G. P.</author><author>Querin, O. M.</author></authors></contributors><titles><title>Bidirectional Evolutionary Method for Stiffness Optimization</title><secondary-title>AIAA Journal</secondary-title></titles><periodical><full-title>AIAA Journal</full-title></periodical><pages>1483-1488</pages><volume>37</volume><number>11</number><dates><year>1999</year><pub-dates><date>1999/11/01</date></pub-dates></dates><publisher>American Institute of Aeronautics and Astronautics</publisher><isbn>0001-1452</isbn><urls><related-urls><url>https://doi.org/10.2514/2.626</url></related-urls></urls><electronic-resource-num>10.2514/2.626</electronic-resource-num><access-date>2018/03/21</access-date></record></Cite></EndNote>17. Whereas elements with zero property will be neglected during the global stiffness assembly ADDIN EN.CITE <EndNote><Cite><Author>Yang</Author><Year>1999</Year><RecNum>14</RecNum><DisplayText>17</DisplayText><record><rec-number>14</rec-number><foreign-keys><key app=”EN” db-id=”eef20vv9h99psxes2zox2fsk52pxsf9fss90″ timestamp=”1521680714″>14</key></foreign-keys><ref-type name=”Journal Article”>17</ref-type><contributors><authors><author>Yang, X. Y.</author><author>Xei, Y. M.</author><author>Steven, G. P.</author><author>Querin, O. M.</author></authors></contributors><titles><title>Bidirectional Evolutionary Method for Stiffness Optimization</title><secondary-title>AIAA Journal</secondary-title></titles><periodical><full-title>AIAA Journal</full-title></periodical><pages>1483-1488</pages><volume>37</volume><number>11</number><dates><year>1999</year><pub-dates><date>1999/11/01</date></pub-dates></dates><publisher>American Institute of Aeronautics and Astronautics</publisher><isbn>0001-1452</isbn><urls><related-urls><url>https://doi.org/10.2514/2.626</url></related-urls></urls><electronic-resource-num>10.2514/2.626</electronic-resource-num><access-date>2018/03/21</access-date></record></Cite></EndNote>17. Of which the stiffness matrix is essential for the TO algorithm to work.

Generally, ESO and BESO can be done in the following steps, this is as reviewed in Querin’s thesis paper ADDIN EN.CITE ;EndNote;;Cite;;Author;Querin;/Author;;Year;2018;/Year;;RecNum;16;/RecNum;;DisplayText;16;/DisplayText;;record;;rec-number;16;/rec-number;;foreign-keys;;key app=”EN” db-id=”eef20vv9h99psxes2zox2fsk52pxsf9fss90″ timestamp=”1522218770″;16;/key;;/foreign-keys;;ref-type name=”Book”;6;/ref-type;;contributors;;authors;;author;Querin, Osvaldo;/author;;/authors;;/contributors;;titles;;title;Evolutionary Structural Optimisation: Stress Based Formulation and Implementation;/title;;/titles;;dates;;year;2018;/year;;/dates;;urls;;/urls;;/record;;/Cite;;/EndNote;16.

Mesh the elements in the domain in a dense fashion, which covers throughout the entire design domains
Apply loading and boundary conditions, as well as the material properties. Set the final target volume, performance index value as well.

Apply the type of criteria used in the optimisation, e.g. von Mises stress, frequency, buckling, stiffness, etc.

Specify the ESO driving parameter. This can be the maximum, minimum, mean von Mises stress of the design domain
Run the linear static Finite Element Analysis of the structure problem
Compare the stress value in every element against the multiplication of maximum von Mises stress or any other selected criterion in step IV with rejection ratio.If the element stress values is lesser than the multiplication value, it is removed from the design domain. This is used in both ESO and BESO method.In BESO method, if the value is larger than the multiplication value, element is added in place.

A steady state is achieved when all the elements in the design domain no longer satisfy the conditions in step VI. In order to initiate the next iteration, the steady state number (SS) is increased by 1, and the step VI is repeated.

Step V to VII is repeated until the performance index reaches the minimum value. Or the target volume is reached. In interconnection topology optimisation, this will be the target quantity of interconnection.

Important parameters
Performance Index (PI) is the parameter that is used to determine how optimum the final design is ADDIN EN.CITE ;EndNote;;Cite;;Author;Querin;/Author;;Year;2018;/Year;;RecNum;16;/RecNum;;DisplayText;16;/DisplayText;;record;;rec-number;16;/rec-number;;foreign-keys;;key app=”EN” db-id=”eef20vv9h99psxes2zox2fsk52pxsf9fss90″ timestamp=”1522218770″;16;/key;;/foreign-keys;;ref-type name=”Book”;6;/ref-type;;contributors;;authors;;author;Querin, Osvaldo;/author;;/authors;;/contributors;;titles;;title;Evolutionary Structural Optimisation: Stress Based Formulation and Implementation;/title;;/titles;;dates;;year;2018;/year;;/dates;;urls;;/urls;;/record;;/Cite;;/EndNote;16. It is a non-dimensional parameter that relates the average stress, total volume, applied load and nominal distances of the structure ADDIN EN.CITE ;EndNote;;Cite;;Author;Querin;/Author;;Year;2018;/Year;;RecNum;16;/RecNum;;DisplayText;16;/DisplayText;;record;;rec-number;16;/rec-number;;foreign-keys;;key app=”EN” db-id=”eef20vv9h99psxes2zox2fsk52pxsf9fss90″ timestamp=”1522218770″;16;/key;;/foreign-keys;;ref-type name=”Book”;6;/ref-type;;contributors;;authors;;author;Querin, Osvaldo;/author;;/authors;;/contributors;;titles;;title;Evolutionary Structural Optimisation: Stress Based Formulation and Implementation;/title;;/titles;;dates;;year;2018;/year;;/dates;;urls;;/urls;;/record;;/Cite;;/EndNote;16.

On the other hand, Rejection Ratio (RR) is an important parameter when comes to ESO method. It is the parameter that is used to control the reject quantity of the elements. In other words, it is used to dampen or slowing down the design domain’s element removal process in every iterations ADDIN EN.CITE <EndNote><Cite><Author>Querin</Author><Year>2018</Year><RecNum>16</RecNum><DisplayText>16</DisplayText><record><rec-number>16</rec-number><foreign-keys><key app=”EN” db-id=”eef20vv9h99psxes2zox2fsk52pxsf9fss90″ timestamp=”1522218770″>16</key></foreign-keys><ref-type name=”Book”>6</ref-type><contributors><authors><author>Querin, Osvaldo</author></authors></contributors><titles><title>Evolutionary Structural Optimisation: Stress Based Formulation and Implementation</title></titles><dates><year>2018</year></dates><urls></urls></record></Cite></EndNote>16.

0?RR?1The higher the RR value, the more elements will be removed. It is noted that the RR and ER should be start off with small values. This is to prevent over rejection phenomenon from happening ADDIN EN.CITE <EndNote><Cite><Author>Xie</Author><Year>1993</Year><RecNum>9</RecNum><DisplayText>14</DisplayText><record><rec-number>9</rec-number><foreign-keys><key app=”EN” db-id=”eef20vv9h99psxes2zox2fsk52pxsf9fss90″ timestamp=”1521343796″>9</key></foreign-keys><ref-type name=”Journal Article”>17</ref-type><contributors><authors><author>Xie, Y. M.</author><author>Steven, G. P.</author></authors></contributors><titles><title>A simple evolutionary procedure for structural optimization</title><secondary-title>Computers &amp; Structures</secondary-title></titles><periodical><full-title>Computers &amp; Structures</full-title></periodical><pages>885-896</pages><volume>49</volume><number>5</number><dates><year>1993</year><pub-dates><date>1993/12/03/</date></pub-dates></dates><isbn>0045-7949</isbn><urls><related-urls><url>http://www.sciencedirect.com/science/article/pii/004579499390035C</url></related-urls></urls><electronic-resource-num>https://doi.org/10.1016/0045-7949(93)90035-C</electronic-resource-num></record></Cite></EndNote>14. If such phenomenon occurs, the structure might become singular ADDIN EN.CITE <EndNote><Cite><Author>Xie</Author><Year>1993</Year><RecNum>9</RecNum><DisplayText>14</DisplayText><record><rec-number>9</rec-number><foreign-keys><key app=”EN” db-id=”eef20vv9h99psxes2zox2fsk52pxsf9fss90″ timestamp=”1521343796″>9</key></foreign-keys><ref-type name=”Journal Article”>17</ref-type><contributors><authors><author>Xie, Y. M.</author><author>Steven, G. P.</author></authors></contributors><titles><title>A simple evolutionary procedure for structural optimization</title><secondary-title>Computers &amp; Structures</secondary-title></titles><periodical><full-title>Computers &amp; Structures</full-title></periodical><pages>885-896</pages><volume>49</volume><number>5</number><dates><year>1993</year><pub-dates><date>1993/12/03/</date></pub-dates></dates><isbn>0045-7949</isbn><urls><related-urls><url>http://www.sciencedirect.com/science/article/pii/004579499390035C</url></related-urls></urls><electronic-resource-num>https://doi.org/10.1016/0045-7949(93)90035-C</electronic-resource-num></record></Cite></EndNote>14.

********why SIMP is better
GA (Genetic Algorithm)
Introduction
Genetic algorithm is another method that is used in topology optimisation. It is first introduced by Holland in 1975 ADDIN EN.CITE <EndNote><Cite><Author>Holland</Author><Year>1992</Year><RecNum>23</RecNum><DisplayText>20</DisplayText><record><rec-number>23</rec-number><foreign-keys><key app=”EN” db-id=”eef20vv9h99psxes2zox2fsk52pxsf9fss90″ timestamp=”1522726853″>23</key></foreign-keys><ref-type name=”Book”>6</ref-type><contributors><authors><author>Holland, John H.</author></authors></contributors><titles><title>Adaptation in natural and artificial systems: an introductory analysis with applications to biology, control, and artificial intelligence</title></titles><number>Book, Whole</number><edition>1st MIT Press</edition><keywords><keyword>Mathematical models</keyword><keyword>Adaptation (Biology)</keyword><keyword>Adaptive control systems</keyword></keywords><dates><year>1992</year></dates><pub-location>Cambridge, Mass</pub-location><publisher>MIT Press</publisher><isbn>0262581116;9780262581110;9780262082136;0262082136;</isbn><urls><related-urls><url>http://usyd.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwdV3JCgIxDA0uCIIHV1yhH6BS25l2ehQZ8QO8S51mQJBB0It_b5cRHNFjCA0EkmZp8grA2Zquvu4EjSgMKh4pnpxtBpvbMoEZZTTNuU1AsNrZ_lU3VhbQ3x0MBybOpb2B65HkH14Zcl9lo6f7x4E60PWEbbgoiTixHi5K-J0P5pv2fFpB5vPhZt-FhltB6EENiz60Ug8s_RzAcmv0LTydk0tBPCanvhJdGOIMIGBBkIDNfB_CYp8ed4eVk34quzSnc6kLZSPoaDfdXjz8FpwZA8lExky-QR7FGMVUJwwZ09KekHEmhZrA6Lew6T_GDNph8NQ1E-bQzK2x4yJo_AJ9dXUr</url></related-urls></urls></record></Cite></EndNote>20. It is a method that is evolved from the Darwinian survival-of-fittest principle ADDIN EN.CITE <EndNote><Cite><Author>Kane</Author><Year>1997</Year><RecNum>31</RecNum><DisplayText>21</DisplayText><record><rec-number>31</rec-number><foreign-keys><key app=”EN” db-id=”eef20vv9h99psxes2zox2fsk52pxsf9fss90″ timestamp=”1522824408″>31</key></foreign-keys><ref-type name=”Book”>6</ref-type><contributors><authors><author>Kane, Couro</author><author>Schoenauer, Marc</author></authors></contributors><titles><title>Topological Optimum Design using Genetic Algorithms</title></titles><volume>25</volume><dates><year>1997</year></dates><urls></urls></record></Cite></EndNote>21
In general, it is a search strategy based on the rules of genetic evolution ADDIN EN.CITE <EndNote><Cite><Author>Goldberg</Author><Year>1988</Year><RecNum>19</RecNum><DisplayText>22, 23</DisplayText><record><rec-number>19</rec-number><foreign-keys><key app=”EN” db-id=”eef20vv9h99psxes2zox2fsk52pxsf9fss90″ timestamp=”1522725669″>19</key></foreign-keys><ref-type name=”Journal Article”>17</ref-type><contributors><authors><author>Goldberg, David E.</author><author>Holland, John H.</author></authors></contributors><titles><title>Genetic Algorithms and Machine Learning</title><secondary-title>Machine Learning</secondary-title></titles><periodical><full-title>Machine Learning</full-title></periodical><pages>95-99</pages><volume>3</volume><number>2</number><dates><year>1988</year><pub-dates><date>1988/10/01</date></pub-dates></dates><isbn>1573-0565</isbn><urls><related-urls><url>https://doi.org/10.1023/A:1022602019183</url></related-urls></urls><electronic-resource-num>10.1023/A:1022602019183</electronic-resource-num></record></Cite><Cite><Author>Hajela</Author><Year>1993</Year><RecNum>22</RecNum><record><rec-number>22</rec-number><foreign-keys><key app=”EN” db-id=”eef20vv9h99psxes2zox2fsk52pxsf9fss90″ timestamp=”1522726617″>22</key></foreign-keys><ref-type name=”Book Section”>5</ref-type><contributors><authors><author>Hajela, P.</author><author>Lee, E.</author><author>Lin, C. Y.</author></authors><secondary-authors><author>Bendsøe, Martin Philip</author><author>Soares, Carlos A. Mota</author></secondary-authors></contributors><titles><title>Genetic Algorithms in Structural Topology Optimization</title><secondary-title>Topology Design of Structures</secondary-title></titles><pages>117-133</pages><dates><year>1993</year><pub-dates><date>1993//</date></pub-dates></dates><pub-location>Dordrecht</pub-location><publisher>Springer Netherlands</publisher><isbn>978-94-011-1804-0</isbn><urls><related-urls><url>https://doi.org/10.1007/978-94-011-1804-0_10</url></related-urls></urls><electronic-resource-num>10.1007/978-94-011-1804-0_10</electronic-resource-num></record></Cite></EndNote>22, 23. The method itself simulate the natural evolutionary process in the world, which produces better or fitter species to survive in the environment ADDIN EN.CITE <EndNote><Cite><Author>Hajela</Author><Year>1993</Year><RecNum>22</RecNum><DisplayText>23</DisplayText><record><rec-number>22</rec-number><foreign-keys><key app=”EN” db-id=”eef20vv9h99psxes2zox2fsk52pxsf9fss90″ timestamp=”1522726617″>22</key></foreign-keys><ref-type name=”Book Section”>5</ref-type><contributors><authors><author>Hajela, P.</author><author>Lee, E.</author><author>Lin, C. Y.</author></authors><secondary-authors><author>Bendsøe, Martin Philip</author><author>Soares, Carlos A. Mota</author></secondary-authors></contributors><titles><title>Genetic Algorithms in Structural Topology Optimization</title><secondary-title>Topology Design of Structures</secondary-title></titles><pages>117-133</pages><dates><year>1993</year><pub-dates><date>1993//</date></pub-dates></dates><pub-location>Dordrecht</pub-location><publisher>Springer Netherlands</publisher><isbn>978-94-011-1804-0</isbn><urls><related-urls><url>https://doi.org/10.1007/978-94-011-1804-0_10</url></related-urls></urls><electronic-resource-num>10.1007/978-94-011-1804-0_10</electronic-resource-num></record></Cite></EndNote>23.
Not only is used in many fields, GA recently is adopted in the engineering field as well ADDIN EN.CITE <EndNote><Cite><Author>Ohsaki</Author><Year>1995</Year><RecNum>18</RecNum><DisplayText>24</DisplayText><record><rec-number>18</rec-number><foreign-keys><key app=”EN” db-id=”eef20vv9h99psxes2zox2fsk52pxsf9fss90″ timestamp=”1522725470″>18</key></foreign-keys><ref-type name=”Journal Article”>17</ref-type><contributors><authors><author>Ohsaki, M.</author></authors></contributors><titles><title>Genetic algorithm for topology optimization of trusses</title><secondary-title>Computers &amp; Structures</secondary-title></titles><periodical><full-title>Computers &amp; Structures</full-title></periodical><pages>219-225</pages><volume>57</volume><number>2</number><dates><year>1995</year><pub-dates><date>1995/10/17/</date></pub-dates></dates><isbn>0045-7949</isbn><urls><related-urls><url>http://www.sciencedirect.com/science/article/pii/004579499400617C</url></related-urls></urls><electronic-resource-num>https://doi.org/10.1016/0045-7949(94)00617-C</electronic-resource-num></record></Cite></EndNote>24. The reason is so favourable in many industries is because its gradients of cost function and constraint function is not needed to find the most optimal solution of the problem ADDIN EN.CITE <EndNote><Cite><Author>Ohsaki</Author><Year>1995</Year><RecNum>18</RecNum><DisplayText>24</DisplayText><record><rec-number>18</rec-number><foreign-keys><key app=”EN” db-id=”eef20vv9h99psxes2zox2fsk52pxsf9fss90″ timestamp=”1522725470″>18</key></foreign-keys><ref-type name=”Journal Article”>17</ref-type><contributors><authors><author>Ohsaki, M.</author></authors></contributors><titles><title>Genetic algorithm for topology optimization of trusses</title><secondary-title>Computers &amp; Structures</secondary-title></titles><periodical><full-title>Computers &amp; Structures</full-title></periodical><pages>219-225</pages><volume>57</volume><number>2</number><dates><year>1995</year><pub-dates><date>1995/10/17/</date></pub-dates></dates><isbn>0045-7949</isbn><urls><related-urls><url>http://www.sciencedirect.com/science/article/pii/004579499400617C</url></related-urls></urls><electronic-resource-num>https://doi.org/10.1016/0045-7949(94)00617-C</electronic-resource-num></record></Cite></EndNote>24. Goldberg discuss more about the application and usage of GA in his various publication as well PEVuZE5vdGU+PENpdGU+PEF1dGhvcj5Hb2xkYmVyZzwvQXV0aG9yPjxZZWFyPjE5ODk8L1llYXI+
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ADDIN EN.CITE.DATA 22, 25. Ohsaki’s paper discussed about using the GA algorithm to solve for topology optimization of trusses, that is subjected to stress and displacement constraints under multiple static loading conditions ADDIN EN.CITE ;EndNote;;Cite;;Author;Hajela;/Author;;Year;1993;/Year;;RecNum;20;/RecNum;;DisplayText;23;/DisplayText;;record;;rec-number;20;/rec-number;;foreign-keys;;key app=”EN” db-id=”eef20vv9h99psxes2zox2fsk52pxsf9fss90″ timestamp=”1522726274″;20;/key;;/foreign-keys;;ref-type name=”Book Section”;5;/ref-type;;contributors;;authors;;author;Hajela, P.;/author;;author;Lee, E.;/author;;author;Lin, C. Y.;/author;;/authors;;secondary-authors;;author;Bendsøe, Martin Philip;/author;;author;Soares, Carlos A. Mota;/author;;/secondary-authors;;/contributors;;titles;;title;Genetic Algorithms in Structural Topology Optimization;/title;;secondary-title;Topology Design of Structures;/secondary-title;;/titles;;pages;117-133;/pages;;dates;;year;1993;/year;;pub-dates;;date;1993//;/date;;/pub-dates;;/dates;;pub-location;Dordrecht;/pub-location;;publisher;Springer Netherlands;/publisher;;isbn;978-94-011-1804-0;/isbn;;urls;;related-urls;;url;https://doi.org/10.1007/978-94-011-1804-0_10;/url;;/related-urls;;/urls;;electronic-resource-num;10.1007/978-94-011-1804-0_10;/electronic-resource-num;;/record;;/Cite;;/EndNote;23.

Wang et al. uses the GA method in structural topology design optimization with bit-array representation, the method suggests that the GA performance can be improved if the design connectivity is handled properly ADDIN EN.CITE ;EndNote;;Cite;;Author;Wang;/Author;;Year;2005;/Year;;RecNum;24;/RecNum;;DisplayText;12;/DisplayText;;record;;rec-number;24;/rec-number;;foreign-keys;;key app=”EN” db-id=”eef20vv9h99psxes2zox2fsk52pxsf9fss90″ timestamp=”1522727290″;24;/key;;/foreign-keys;;ref-type name=”Journal Article”;17;/ref-type;;contributors;;authors;;author;Wang, S. Y.;/author;;author;Tai, K.;/author;;/authors;;/contributors;;titles;;title;Structural topology design optimization using Genetic Algorithms with a bit-array representation;/title;;secondary-title;Computer Methods in Applied Mechanics and Engineering;/secondary-title;;/titles;;periodical;;full-title;Computer Methods in Applied Mechanics and Engineering;/full-title;;/periodical;;pages;3749-3770;/pages;;volume;194;/volume;;number;36;/number;;keywords;;keyword;Structural topology optimization;/keyword;;keyword;Bit-array representation;/keyword;;keyword;Design connectivity;/keyword;;keyword;Representation degeneracy;/keyword;;keyword;Genetic Algorithms;/keyword;;/keywords;;dates;;year;2005;/year;;pub-dates;;date;2005/09/23/;/date;;/pub-dates;;/dates;;isbn;0045-7825;/isbn;;urls;;related-urls;;url;http://www.sciencedirect.com/science/article/pii/S0045782504004530;/url;;/related-urls;;/urls;;electronic-resource-num;https://doi.org/10.1016/j.cma.2004.09.003;/electronic-resource-num;;/record;;/Cite;;/EndNote;12. Other than bit-array representation, the GA method can also be done in binary- string representation ADDIN EN.CITE ;EndNote;;Cite;;Author;Chapman;/Author;;Year;1994;/Year;;RecNum;25;/RecNum;;DisplayText;26, 27;/DisplayText;;record;;rec-number;25;/rec-number;;foreign-keys;;key app=”EN” db-id=”eef20vv9h99psxes2zox2fsk52pxsf9fss90″ timestamp=”1522732066″;25;/key;;/foreign-keys;;ref-type name=”Journal Article”;17;/ref-type;;contributors;;authors;;author;Chapman, C. D.;/author;;author;Saitou, K.;/author;;author;Jakiela, M. J.;/author;;/authors;;/contributors;;titles;;title;Genetic Algorithms as an Approach to Configuration and Topology Design;/title;;secondary-title;Journal of Mechanical Design;/secondary-title;;/titles;;periodical;;full-title;Journal of Mechanical Design;/full-title;;/periodical;;pages;1005-1012;/pages;;volume;116;/volume;;number;4;/number;;dates;;year;1994;/year;;/dates;;publisher;ASME;/publisher;;isbn;1050-0472;/isbn;;urls;;related-urls;;url;http://dx.doi.org/10.1115/1.2919480;/url;;/related-urls;;/urls;;electronic-resource-num;10.1115/1.2919480;/electronic-resource-num;;/record;;/Cite;;Cite;;Author;Chapman;/Author;;Year;1996;/Year;;RecNum;26;/RecNum;;record;;rec-number;26;/rec-number;;foreign-keys;;key app=”EN” db-id=”eef20vv9h99psxes2zox2fsk52pxsf9fss90″ timestamp=”1522732207″;26;/key;;/foreign-keys;;ref-type name=”Journal Article”;17;/ref-type;;contributors;;authors;;author;Chapman, C. D.;/author;;author;Jakiela, M. J.;/author;;/authors;;/contributors;;titles;;title;Genetic Algorithm-Based Structural Topology Design With Compliance and Topology Simplification Considerations;/title;;secondary-title;Journal of Mechanical Design;/secondary-title;;/titles;;periodical;;full-title;Journal of Mechanical Design;/full-title;;/periodical;;pages;89-98;/pages;;volume;118;/volume;;number;1;/number;;dates;;year;1996;/year;;/dates;;publisher;ASME;/publisher;;isbn;1050-0472;/isbn;;urls;;related-urls;;url;http://dx.doi.org/10.1115/1.2826862;/url;;/related-urls;;/urls;;electronic-resource-num;10.1115/1.2826862;/electronic-resource-num;;/record;;/Cite;;/EndNote;26, 27. Nevertheless, both binary and bit-array representation discretises the two-dimensional design domain, and meshes the domain into square elements, which is contained either material or void (1 or 0), and treated as the binary design variable ADDIN EN.CITE ;EndNote;;Cite;;Author;Wang;/Author;;Year;2005;/Year;;RecNum;24;/RecNum;;DisplayText;12;/DisplayText;;record;;rec-number;24;/rec-number;;foreign-keys;;key app=”EN” db-id=”eef20vv9h99psxes2zox2fsk52pxsf9fss90″ timestamp=”1522727290″;24;/key;;/foreign-keys;;ref-type name=”Journal Article”;17;/ref-type;;contributors;;authors;;author;Wang, S. Y.;/author;;author;Tai, K.;/author;;/authors;;/contributors;;titles;;title;Structural topology design optimization using Genetic Algorithms with a bit-array representation;/title;;secondary-title;Computer Methods in Applied Mechanics and Engineering;/secondary-title;;/titles;;periodical;;full-title;Computer Methods in Applied Mechanics and Engineering;/full-title;;/periodical;;pages;3749-3770;/pages;;volume;194;/volume;;number;36;/number;;keywords;;keyword;Structural topology optimization;/keyword;;keyword;Bit-array representation;/keyword;;keyword;Design connectivity;/keyword;;keyword;Representation degeneracy;/keyword;;keyword;Genetic Algorithms;/keyword;;/keywords;;dates;;year;2005;/year;;pub-dates;;date;2005/09/23/;/date;;/pub-dates;;/dates;;isbn;0045-7825;/isbn;;urls;;related-urls;;url;http://www.sciencedirect.com/science/article/pii/S0045782504004530;/url;;/related-urls;;/urls;;electronic-resource-num;https://doi.org/10.1016/j.cma.2004.09.003;/electronic-resource-num;;/record;;/Cite;;/EndNote;12.

Method
GA method initialises by creating a random population with N elements, each has its own genetic properties. The algorithm will then evaluate the fitness score in each element in the population and build up a mating pool . The elements will then be assigned with a probability value that is relative to their fitness score.
Reproduction or selection is the third step. It picks two parents from the mating pool, with the probability assigned earlier on and the reproduction process is repeated for N times. There are two ways for the process. The first one is crossover method. Crossover method essentially create a ‘child’ by combining the genetic properties from the parents. The second way is mutation method. This method mutates the child’s genetic properties by an assigned probability value. For both crossover and mutation operators, there can be many methods. They are as discussed in Couro et al.’s article ADDIN EN.CITE ;EndNote;;Cite;;Author;Kane;/Author;;Year;1997;/Year;;RecNum;31;/RecNum;;DisplayText;21;/DisplayText;;record;;rec-number;31;/rec-number;;foreign-keys;;key app=”EN” db-id=”eef20vv9h99psxes2zox2fsk52pxsf9fss90″ timestamp=”1522824408″;31;/key;;/foreign-keys;;ref-type name=”Book”;6;/ref-type;;contributors;;authors;;author;Kane, Couro;/author;;author;Schoenauer, Marc;/author;;/authors;;/contributors;;titles;;title;Topological Optimum Design using Genetic Algorithms;/title;;/titles;;volume;25;/volume;;dates;;year;1997;/year;;/dates;;urls;;/urls;;/record;;/Cite;;/EndNote;21.

The final step replaces the old population with the new population created in the reproduction stage. This means that the old elements are updated with the new elements with better fitness values. The iterations carry on until the elements’ fitness value converges to a specific value.

While the fitness value can be essentially determined by different criteria. One example of fitness calculation can be stiffness to weight ratio, as discussed by Chapman et al. ADDIN EN.CITE <EndNote><Cite><Author>Chapman</Author><Year>1994</Year><RecNum>25</RecNum><DisplayText>26</DisplayText><record><rec-number>25</rec-number><foreign-keys><key app=”EN” db-id=”eef20vv9h99psxes2zox2fsk52pxsf9fss90″ timestamp=”1522732066″>25</key></foreign-keys><ref-type name=”Journal Article”>17</ref-type><contributors><authors><author>Chapman, C. D.</author><author>Saitou, K.</author><author>Jakiela, M. J.</author></authors></contributors><titles><title>Genetic Algorithms as an Approach to Configuration and Topology Design</title><secondary-title>Journal of Mechanical Design</secondary-title></titles><periodical><full-title>Journal of Mechanical Design</full-title></periodical><pages>1005-1012</pages><volume>116</volume><number>4</number><dates><year>1994</year></dates><publisher>ASME</publisher><isbn>1050-0472</isbn><urls><related-urls><url>http://dx.doi.org/10.1115/1.2919480</url></related-urls></urls><electronic-resource-num>10.1115/1.2919480</electronic-resource-num></record></Cite></EndNote>26. The function essentially assign high fitness value to the structure which are best in combining light weight and load-carrying ability ADDIN EN.CITE <EndNote><Cite><Author>Chapman</Author><Year>1996</Year><RecNum>26</RecNum><DisplayText>27</DisplayText><record><rec-number>26</rec-number><foreign-keys><key app=”EN” db-id=”eef20vv9h99psxes2zox2fsk52pxsf9fss90″ timestamp=”1522732207″>26</key></foreign-keys><ref-type name=”Journal Article”>17</ref-type><contributors><authors><author>Chapman, C. D.</author><author>Jakiela, M. J.</author></authors></contributors><titles><title>Genetic Algorithm-Based Structural Topology Design With Compliance and Topology Simplification Considerations</title><secondary-title>Journal of Mechanical Design</secondary-title></titles><periodical><full-title>Journal of Mechanical Design</full-title></periodical><pages>89-98</pages><volume>118</volume><number>1</number><dates><year>1996</year></dates><publisher>ASME</publisher><isbn>1050-0472</isbn><urls><related-urls><url>http://dx.doi.org/10.1115/1.2826862</url></related-urls></urls><electronic-resource-num>10.1115/1.2826862</electronic-resource-num></record></Cite></EndNote>27.
Similar to fitness value, the selection criteria in reproduction stage can be varied. Different criteria will then have different search performance and efficiency in the GA method ADDIN EN.CITE <EndNote><Cite><Author>Chapman</Author><Year>1994</Year><RecNum>25</RecNum><DisplayText>26</DisplayText><record><rec-number>25</rec-number><foreign-keys><key app=”EN” db-id=”eef20vv9h99psxes2zox2fsk52pxsf9fss90″ timestamp=”1522732066″>25</key></foreign-keys><ref-type name=”Journal Article”>17</ref-type><contributors><authors><author>Chapman, C. D.</author><author>Saitou, K.</author><author>Jakiela, M. J.</author></authors></contributors><titles><title>Genetic Algorithms as an Approach to Configuration and Topology Design</title><secondary-title>Journal of Mechanical Design</secondary-title></titles><periodical><full-title>Journal of Mechanical Design</full-title></periodical><pages>1005-1012</pages><volume>116</volume><number>4</number><dates><year>1994</year></dates><publisher>ASME</publisher><isbn>1050-0472</isbn><urls><related-urls><url>http://dx.doi.org/10.1115/1.2919480</url></related-urls></urls><electronic-resource-num>10.1115/1.2919480</electronic-resource-num></record></Cite></EndNote>26. Different selection criteria is as discussed in Baker’s paper ADDIN EN.CITE ;EndNote;;Cite;;Author;Baker;/Author;;Year;1987;/Year;;RecNum;28;/RecNum;;DisplayText;28;/DisplayText;;record;;rec-number;28;/rec-number;;foreign-keys;;key app=”EN” db-id=”eef20vv9h99psxes2zox2fsk52pxsf9fss90″ timestamp=”1522812367″;28;/key;;/foreign-keys;;ref-type name=”Conference Paper”;47;/ref-type;;contributors;;authors;;author;James E. Baker;/author;;/authors;;/contributors;;titles;;title;Reducing bias and inefficiency in the selection algorithm;/title;;secondary-title;Proceedings of the Second International Conference on Genetic Algorithms on Genetic algorithms and their application;/secondary-title;;/titles;;pages;14-21;/pages;;dates;;year;1987;/year;;/dates;;pub-location;Cambridge, Massachusetts, USA;/pub-location;;publisher;L. Erlbaum Associates Inc.;/publisher;;urls;;/urls;;custom1;42515;/custom1;;/record;;/Cite;;/EndNote;28.

Thus, the end result of GA computes for an optimal solution that is evolved from the previous generations of parents, to adapt the environment better.

Bit-array representation method is widely used in the present study of topology optimization problem, to use the GA method more efficiently ADDIN EN.CITE ;EndNote;;Cite;;Author;Wang;/Author;;Year;2005;/Year;;RecNum;24;/RecNum;;DisplayText;12;/DisplayText;;record;;rec-number;24;/rec-number;;foreign-keys;;key app=”EN” db-id=”eef20vv9h99psxes2zox2fsk52pxsf9fss90″ timestamp=”1522727290″;24;/key;;/foreign-keys;;ref-type name=”Journal Article”;17;/ref-type;;contributors;;authors;;author;Wang, S. Y.;/author;;author;Tai, K.;/author;;/authors;;/contributors;;titles;;title;Structural topology design optimization using Genetic Algorithms with a bit-array representation;/title;;secondary-title;Computer Methods in Applied Mechanics and Engineering;/secondary-title;;/titles;;periodical;;full-title;Computer Methods in Applied Mechanics and Engineering;/full-title;;/periodical;;pages;3749-3770;/pages;;volume;194;/volume;;number;36;/number;;keywords;;keyword;Structural topology optimization;/keyword;;keyword;Bit-array representation;/keyword;;keyword;Design connectivity;/keyword;;keyword;Representation degeneracy;/keyword;;keyword;Genetic Algorithms;/keyword;;/keywords;;dates;;year;2005;/year;;pub-dates;;date;2005/09/23/;/date;;/pub-dates;;/dates;;isbn;0045-7825;/isbn;;urls;;related-urls;;url;http://www.sciencedirect.com/science/article/pii/S0045782504004530;/url;;/related-urls;;/urls;;electronic-resource-num;https://doi.org/10.1016/j.cma.2004.09.003;/electronic-resource-num;;/record;;/Cite;;/EndNote;12. The design domain is mapped with chromosome, that is formed by ‘0’ and ‘1’, which represents void and material respectively ADDIN EN.CITE ;EndNote;;Cite;;Author;Chapman;/Author;;Year;1996;/Year;;RecNum;26;/RecNum;;DisplayText;27;/DisplayText;;record;;rec-number;26;/rec-number;;foreign-keys;;key app=”EN” db-id=”eef20vv9h99psxes2zox2fsk52pxsf9fss90″ timestamp=”1522732207″;26;/key;;/foreign-keys;;ref-type name=”Journal Article”;17;/ref-type;;contributors;;authors;;author;Chapman, C. D.;/author;;author;Jakiela, M. J.;/author;;/authors;;/contributors;;titles;;title;Genetic Algorithm-Based Structural Topology Design With Compliance and Topology Simplification Considerations;/title;;secondary-title;Journal of Mechanical Design;/secondary-title;;/titles;;periodical;;full-title;Journal of Mechanical Design;/full-title;;/periodical;;pages;89-98;/pages;;volume;118;/volume;;number;1;/number;;dates;;year;1996;/year;;/dates;;publisher;ASME;/publisher;;isbn;1050-0472;/isbn;;urls;;related-urls;;url;http://dx.doi.org/10.1115/1.2826862;/url;;/related-urls;;/urls;;electronic-resource-num;10.1115/1.2826862;/electronic-resource-num;;/record;;/Cite;;/EndNote;27.
In the Chapman’s paper, connectivity analysis is used ADDIN EN.CITE <EndNote><Cite><Author>Chapman</Author><Year>1996</Year><RecNum>26</RecNum><DisplayText>27</DisplayText><record><rec-number>26</rec-number><foreign-keys><key app=”EN” db-id=”eef20vv9h99psxes2zox2fsk52pxsf9fss90″ timestamp=”1522732207″>26</key></foreign-keys><ref-type name=”Journal Article”>17</ref-type><contributors><authors><author>Chapman, C. D.</author><author>Jakiela, M. J.</author></authors></contributors><titles><title>Genetic Algorithm-Based Structural Topology Design With Compliance and Topology Simplification Considerations</title><secondary-title>Journal of Mechanical Design</secondary-title></titles><periodical><full-title>Journal of Mechanical Design</full-title></periodical><pages>89-98</pages><volume>118</volume><number>1</number><dates><year>1996</year></dates><publisher>ASME</publisher><isbn>1050-0472</isbn><urls><related-urls><url>http://dx.doi.org/10.1115/1.2826862</url></related-urls></urls><electronic-resource-num>10.1115/1.2826862</electronic-resource-num></record></Cite></EndNote>27. However, this is not necessary in TO of interconnections, as according to article published by Qing et al., the interconnections between the components does not necessary linked to one elements to another ADDIN EN.CITE <EndNote><Cite><Author>Qing</Author><Year>2001</Year><RecNum>6</RecNum><DisplayText>8</DisplayText><record><rec-number>6</rec-number><foreign-keys><key app=”EN” db-id=”eef20vv9h99psxes2zox2fsk52pxsf9fss90″ timestamp=”1521071566″>6</key></foreign-keys><ref-type name=”Journal Article”>17</ref-type><contributors><authors><author>Qing, Li</author><author>Grant, P. Steven</author><author>Y. M. Xie</author></authors></contributors><titles><title>Evolutionary structural optimization for connection topology design of multi?component systems</title><secondary-title>Engineering Computations</secondary-title></titles><periodical><full-title>Engineering Computations</full-title></periodical><pages>460-479</pages><volume>18</volume><number>3/4</number><dates><year>2001</year><pub-dates><date>2001/05/01</date></pub-dates></dates><publisher>Emerald</publisher><isbn>0264-4401</isbn><urls><related-urls><url>https://doi.org/10.1108/02644400110387127</url></related-urls></urls><electronic-resource-num>10.1108/02644400110387127</electronic-resource-num><access-date>2018/03/13</access-date></record></Cite></EndNote>8. The connectivity analysis is needed in structural TO to check if any two elements in the design domain share the same edge. Thus, the analysis is not necessary in interconnection TO.

All in all, the GA method is one of the ways to carry out the TO analysis. But as mentioned above, the method requires a few more steps and processes as compared to SIMP method. SIMP method is only considering the relevancy of the elements by solving the iterations by density criteria. Which will be simpler and more straight forward. SIMP method will be covered more in the later section of this literature review.
LSM (Level Set Method)
In general, LSM is a type of numerical method which tracks the interfaces and shapes in a geometry. It is widely used in many industries such as image processing, computer graphics, computational fluid dynamics and many more. The method is first proposed by Osher and Sethian in the year of 1988 ADDIN EN.CITE <EndNote><Cite><Author>Osher</Author><Year>1988</Year><RecNum>39</RecNum><DisplayText>29</DisplayText><record><rec-number>39</rec-number><foreign-keys><key app=”EN” db-id=”eef20vv9h99psxes2zox2fsk52pxsf9fss90″ timestamp=”1522993833″>39</key></foreign-keys><ref-type name=”Journal Article”>17</ref-type><contributors><authors><author>Osher, Stanley</author><author>Sethian, James A.</author></authors></contributors><titles><title>Fronts propagating with curvature-dependent speed: Algorithms based on Hamilton-Jacobi formulations</title><secondary-title>Journal of Computational Physics</secondary-title></titles><periodical><full-title>Journal of Computational Physics</full-title></periodical><pages>12-49</pages><volume>79</volume><number>1</number><dates><year>1988</year><pub-dates><date>1988/11/01/</date></pub-dates></dates><isbn>0021-9991</isbn><urls><related-urls><url>http://www.sciencedirect.com/science/article/pii/0021999188900022</url></related-urls></urls><electronic-resource-num>https://doi.org/10.1016/0021-9991(88)90002-2</electronic-resource-num></record></Cite></EndNote>29. LSM is used in TO, to implicitly set the target structural design domain in an Eulerian coordinate system using the iso-surface of the scalar level set function ADDIN EN.CITE <EndNote><Cite><Author>Yamada</Author><Year>2010</Year><RecNum>33</RecNum><DisplayText>30</DisplayText><record><rec-number>33</rec-number><foreign-keys><key app=”EN” db-id=”eef20vv9h99psxes2zox2fsk52pxsf9fss90″ timestamp=”1522992042″>33</key></foreign-keys><ref-type name=”Journal Article”>17</ref-type><contributors><authors><author>Yamada, Takayuki</author><author>Izui, Kazuhiro</author><author>Nishiwaki, Shinji</author><author>Takezawa, Akihiro</author></authors></contributors><titles><title>A topology optimization method based on the level set method incorporating a fictitious interface energy</title><secondary-title>Computer Methods in Applied Mechanics and Engineering</secondary-title></titles><periodical><full-title>Computer Methods in Applied Mechanics and Engineering</full-title></periodical><pages>2876-2891</pages><volume>199</volume><number>45</number><keywords><keyword>Topology optimization</keyword><keyword>Finite element method</keyword><keyword>Level set method</keyword><keyword>Phase field method</keyword><keyword>Tikhonov regularization method</keyword></keywords><dates><year>2010</year><pub-dates><date>2010/11/15/</date></pub-dates></dates><isbn>0045-7825</isbn><urls><related-urls><url>http://www.sciencedirect.com/science/article/pii/S0045782510001623</url></related-urls></urls><electronic-resource-num>https://doi.org/10.1016/j.cma.2010.05.013</electronic-resource-num></record></Cite></EndNote>30. An Eularian coordinate system is feasible as the initial design domain changes as a function of time and space. Then, the outlines of the target structure are updated as the optimization process changes the level set function in each iteration process ADDIN EN.CITE <EndNote><Cite><Author>Yamada</Author><Year>2010</Year><RecNum>33</RecNum><DisplayText>30</DisplayText><record><rec-number>33</rec-number><foreign-keys><key app=”EN” db-id=”eef20vv9h99psxes2zox2fsk52pxsf9fss90″ timestamp=”1522992042″>33</key></foreign-keys><ref-type name=”Journal Article”>17</ref-type><contributors><authors><author>Yamada, Takayuki</author><author>Izui, Kazuhiro</author><author>Nishiwaki, Shinji</author><author>Takezawa, Akihiro</author></authors></contributors><titles><title>A topology optimization method based on the level set method incorporating a fictitious interface energy</title><secondary-title>Computer Methods in Applied Mechanics and Engineering</secondary-title></titles><periodical><full-title>Computer Methods in Applied Mechanics and Engineering</full-title></periodical><pages>2876-2891</pages><volume>199</volume><number>45</number><keywords><keyword>Topology optimization</keyword><keyword>Finite element method</keyword><keyword>Level set method</keyword><keyword>Phase field method</keyword><keyword>Tikhonov regularization method</keyword></keywords><dates><year>2010</year><pub-dates><date>2010/11/15/</date></pub-dates></dates><isbn>0045-7825</isbn><urls><related-urls><url>http://www.sciencedirect.com/science/article/pii/S0045782510001623</url></related-urls></urls><electronic-resource-num>https://doi.org/10.1016/j.cma.2010.05.013</electronic-resource-num></record></Cite></EndNote>30. Level set method has an advantage over the other TO conventional methods. Unlike the other methods, which produces checkerboard patterns, grayscales or other numerical instability problem, LSM does not have such issues as the structural boundaries are represented as the iso-surface of the level set functions ADDIN EN.CITE <EndNote><Cite><Author>Yamada</Author><Year>2010</Year><RecNum>33</RecNum><DisplayText>30</DisplayText><record><rec-number>33</rec-number><foreign-keys><key app=”EN” db-id=”eef20vv9h99psxes2zox2fsk52pxsf9fss90″ timestamp=”1522992042″>33</key></foreign-keys><ref-type name=”Journal Article”>17</ref-type><contributors><authors><author>Yamada, Takayuki</author><author>Izui, Kazuhiro</author><author>Nishiwaki, Shinji</author><author>Takezawa, Akihiro</author></authors></contributors><titles><title>A topology optimization method based on the level set method incorporating a fictitious interface energy</title><secondary-title>Computer Methods in Applied Mechanics and Engineering</secondary-title></titles><periodical><full-title>Computer Methods in Applied Mechanics and Engineering</full-title></periodical><pages>2876-2891</pages><volume>199</volume><number>45</number><keywords><keyword>Topology optimization</keyword><keyword>Finite element method</keyword><keyword>Level set method</keyword><keyword>Phase field method</keyword><keyword>Tikhonov regularization method</keyword></keywords><dates><year>2010</year><pub-dates><date>2010/11/15/</date></pub-dates></dates><isbn>0045-7825</isbn><urls><related-urls><url>http://www.sciencedirect.com/science/article/pii/S0045782510001623</url></related-urls></urls><electronic-resource-num>https://doi.org/10.1016/j.cma.2010.05.013</electronic-resource-num></record></Cite></EndNote>30. 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ADDIN EN.CITE.DATA 31-33.

LSM is not only used in TO. LSM method is flexible in many ways and different method of LSM optimization method are proposed over the years. Sethian et al. proposed to use LSM in structural optimization which uses the von Mises stress as the key design parameter in the level set function ADDIN EN.CITE <EndNote><Cite><Author>Sethian</Author><Year>2000</Year><RecNum>32</RecNum><DisplayText>34</DisplayText><record><rec-number>32</rec-number><foreign-keys><key app=”EN” db-id=”eef20vv9h99psxes2zox2fsk52pxsf9fss90″ timestamp=”1522974943″>32</key></foreign-keys><ref-type name=”Book”>6</ref-type><contributors><authors><author>Sethian, J. A.</author><author>Wiegmann, Andreas</author></authors></contributors><titles><title>Structural Boundary Design via Level Set and Immersed Interface Methods</title></titles><pages>489-528</pages><volume>163</volume><dates><year>2000</year></dates><urls></urls><electronic-resource-num>10.1006/jcph.2000.6581</electronic-resource-num></record></Cite></EndNote>34. Chen et al. proposes to use LSM with the quadratic energy functional, of which LSM can express boundary with high precision, that is used in calculation of the quadratic energy functional ADDIN EN.CITE <EndNote><Cite><Author>Chen</Author><Year>2008</Year><RecNum>42</RecNum><DisplayText>35</DisplayText><record><rec-number>42</rec-number><foreign-keys><key app=”EN” db-id=”eef20vv9h99psxes2zox2fsk52pxsf9fss90″ timestamp=”1523063969″>42</key></foreign-keys><ref-type name=”Journal Article”>17</ref-type><contributors><authors><author>Chen, Shikui</author><author>Wang, Michael Yu</author><author>Liu, Ai Qun</author></authors></contributors><titles><title>Shape feature control in structural topology optimization</title><secondary-title>Computer-Aided Design</secondary-title></titles><periodical><full-title>Computer-Aided Design</full-title></periodical><pages>951-962</pages><volume>40</volume><number>9</number><keywords><keyword>Shape feature control</keyword><keyword>The level set method</keyword><keyword>Structural topology optimization</keyword><keyword>Quadratic energy functional</keyword><keyword>Shape gradient</keyword></keywords><dates><year>2008</year><pub-dates><date>2008/09/01/</date></pub-dates></dates><isbn>0010-4485</isbn><urls><related-urls><url>http://www.sciencedirect.com/science/article/pii/S0010448508001279</url></related-urls></urls><electronic-resource-num>https://doi.org/10.1016/j.cad.2008.07.004</electronic-resource-num></record></Cite></EndNote>35. LSM can also be applied in shape optimization ADDIN EN.CITE <EndNote><Cite><Author>Allaire</Author><Year>2002</Year><RecNum>43</RecNum><DisplayText>31</DisplayText><record><rec-number>43</rec-number><foreign-keys><key app=”EN” db-id=”eef20vv9h99psxes2zox2fsk52pxsf9fss90″ timestamp=”1523257834″>43</key></foreign-keys><ref-type name=”Journal Article”>17</ref-type><contributors><authors><author>Allaire, Grégoire</author><author>Jouve, François</author><author>Toader, Anca-Maria</author></authors></contributors><titles><title>A level-set method for shape optimization</title><secondary-title>Comptes Rendus Mathematique</secondary-title></titles><periodical><full-title>Comptes Rendus Mathematique</full-title></periodical><pages>1125-1130</pages><volume>334</volume><number>12</number><dates><year>2002</year><pub-dates><date>2002/01/01/</date></pub-dates></dates><isbn>1631-073X</isbn><urls><related-urls><url>http://www.sciencedirect.com/science/article/pii/S1631073X02024123</url></related-urls></urls><electronic-resource-num>https://doi.org/10.1016/S1631-073X(02)02412-3</electronic-resource-num></record></Cite></EndNote>31.
Due to the nature of the LSM, the generated boundary of the solution can be represented exactly ADDIN EN.CITE <EndNote><Cite><Author>Li</Author><Year>2012</Year><RecNum>63</RecNum><DisplayText>2</DisplayText><record><rec-number>63</rec-number><foreign-keys><key app=”EN” db-id=”eef20vv9h99psxes2zox2fsk52pxsf9fss90″ timestamp=”1525314633″>63</key></foreign-keys><ref-type name=”Journal Article”>17</ref-type><contributors><authors><author>Li, Li</author><author>Wang, Michael Yu</author><author>Wei, Peng</author></authors></contributors><titles><title>XFEM schemes for level set based structural optimization</title><secondary-title>Frontiers of Mechanical Engineering</secondary-title></titles><periodical><full-title>Frontiers of Mechanical Engineering</full-title></periodical><pages>335-356</pages><volume>7</volume><number>4</number><dates><year>2012</year><pub-dates><date>December 01</date></pub-dates></dates><isbn>2095-0241</isbn><label>Li2012</label><work-type>journal article</work-type><urls><related-urls><url>https://doi.org/10.1007/s11465-012-0351-2</url></related-urls></urls><electronic-resource-num>10.1007/s11465-012-0351-2</electronic-resource-num></record></Cite></EndNote>2. This is unlike the other methods such as ESO and BESO, whose optimised results is depending on the type of mesh shape used. The results will have uneven edge as shown in the figure ** below.
left3868002922212207800
2942590281997Figure SEQ Figure * ARABIC 1 Optimised solution for LSM method ADDIN EN.CITE <EndNote><Cite><Author>Li</Author><Year>2012</Year><RecNum>63</RecNum><DisplayText>2</DisplayText><record><rec-number>63</rec-number><foreign-keys><key app=”EN” db-id=”eef20vv9h99psxes2zox2fsk52pxsf9fss90″ timestamp=”1525314633″>63</key></foreign-keys><ref-type name=”Journal Article”>17</ref-type><contributors><authors><author>Li, Li</author><author>Wang, Michael Yu</author><author>Wei, Peng</author></authors></contributors><titles><title>XFEM schemes for level set based structural optimization</title><secondary-title>Frontiers of Mechanical Engineering</secondary-title></titles><periodical><full-title>Frontiers of Mechanical Engineering</full-title></periodical><pages>335-356</pages><volume>7</volume><number>4</number><dates><year>2012</year><pub-dates><date>December 01</date></pub-dates></dates><isbn>2095-0241</isbn><label>Li2012</label><work-type>journal article</work-type><urls><related-urls><url>https://doi.org/10.1007/s11465-012-0351-2</url></related-urls></urls><electronic-resource-num>10.1007/s11465-012-0351-2</electronic-resource-num></record></Cite></EndNote>2
Figure SEQ Figure * ARABIC 1 Optimised solution for LSM method ADDIN EN.CITE <EndNote><Cite><Author>Li</Author><Year>2012</Year><RecNum>63</RecNum><DisplayText>2</DisplayText><record><rec-number>63</rec-number><foreign-keys><key app=”EN” db-id=”eef20vv9h99psxes2zox2fsk52pxsf9fss90″ timestamp=”1525314633″>63</key></foreign-keys><ref-type name=”Journal Article”>17</ref-type><contributors><authors><author>Li, Li</author><author>Wang, Michael Yu</author><author>Wei, Peng</author></authors></contributors><titles><title>XFEM schemes for level set based structural optimization</title><secondary-title>Frontiers of Mechanical Engineering</secondary-title></titles><periodical><full-title>Frontiers of Mechanical Engineering</full-title></periodical><pages>335-356</pages><volume>7</volume><number>4</number><dates><year>2012</year><pub-dates><date>December 01</date></pub-dates></dates><isbn>2095-0241</isbn><label>Li2012</label><work-type>journal article</work-type><urls><related-urls><url>https://doi.org/10.1007/s11465-012-0351-2</url></related-urls></urls><electronic-resource-num>10.1007/s11465-012-0351-2</electronic-resource-num></record></Cite></EndNote>2
62057261447Figure SEQ Figure * ARABIC 2 Optimised solution for mesh shape-dependant TO methods ADDIN EN.CITE <EndNote><Cite><Author>LeBaron</Author><Year>2013</Year><RecNum>62</RecNum><DisplayText>1</DisplayText><record><rec-number>62</rec-number><foreign-keys><key app=”EN” db-id=”eef20vv9h99psxes2zox2fsk52pxsf9fss90″ timestamp=”1525314372″>62</key></foreign-keys><ref-type name=”Journal Article”>17</ref-type><contributors><authors><author>LeBaron, Devin D.</author><author>Mattson, Christopher A.</author></authors></contributors><titles><title>Using Topology Optimization to Numerically Improve Barriers to Reverse Engineering</title><secondary-title>Journal of Mechanical Design</secondary-title></titles><periodical><full-title>Journal of Mechanical Design</full-title></periodical><pages>021007-021007-8</pages><volume>136</volume><number>2</number><dates><year>2013</year></dates><publisher>ASME</publisher><isbn>1050-0472</isbn><urls><related-urls><url>http://dx.doi.org/10.1115/1.4025962</url></related-urls></urls><electronic-resource-num>10.1115/1.4025962</electronic-resource-num></record></Cite></EndNote>1
Figure SEQ Figure * ARABIC 2 Optimised solution for mesh shape-dependant TO methods ADDIN EN.CITE <EndNote><Cite><Author>LeBaron</Author><Year>2013</Year><RecNum>62</RecNum><DisplayText>1</DisplayText><record><rec-number>62</rec-number><foreign-keys><key app=”EN” db-id=”eef20vv9h99psxes2zox2fsk52pxsf9fss90″ timestamp=”1525314372″>62</key></foreign-keys><ref-type name=”Journal Article”>17</ref-type><contributors><authors><author>LeBaron, Devin D.</author><author>Mattson, Christopher A.</author></authors></contributors><titles><title>Using Topology Optimization to Numerically Improve Barriers to Reverse Engineering</title><secondary-title>Journal of Mechanical Design</secondary-title></titles><periodical><full-title>Journal of Mechanical Design</full-title></periodical><pages>021007-021007-8</pages><volume>136</volume><number>2</number><dates><year>2013</year></dates><publisher>ASME</publisher><isbn>1050-0472</isbn><urls><related-urls><url>http://dx.doi.org/10.1115/1.4025962</url></related-urls></urls><electronic-resource-num>10.1115/1.4025962</electronic-resource-num></record></Cite></EndNote>1

As seen in the figures above, optimised solution using LSM can have its boundary of the structure clearly defined. Whereas other TO methods which are relied upon the mesh shapes used in the optimisation, will have uneven boundary edges. Thus, this might pose a problem in optimising the interconnection TO problems.

This is because the optimised solution will most likely have its shape of interconnection determined. Of which, this might be not accurate when using the optimised interconnection layout and quantity in the real life application. This is due to the fact that the type and shape of the optimised interconnection in the LSM method can fulfil the design problem requirements, but when comes to applying the layout of interconnection in the real life application, it might not be possible as due to the fact that the optimised interconnection shape in LSM can be irregular. Again, this needs to be proven by carrying out the LSM in interconnection TO, to determine if the method is relevant.

Homogenisation method
Homogenisation method has an advantage of performing TO with no explicit and implicit resistance on the optimisation process ADDIN EN.CITE <EndNote><Cite><Author>Allaire</Author><Year>2005</Year><RecNum>49</RecNum><DisplayText>36</DisplayText><record><rec-number>49</rec-number><foreign-keys><key app=”EN” db-id=”eef20vv9h99psxes2zox2fsk52pxsf9fss90″ timestamp=”1523932368″>49</key></foreign-keys><ref-type name=”Conference Proceedings”>10</ref-type><contributors><authors><author>Allaire, G.</author></authors><secondary-authors><author>Castañeda, P. Ponte</author><author>Telega, J. J.</author><author>Gambin, B.</author></secondary-authors></contributors><titles><title>Topology Optimization with the Homogenization and the Level-Set Methods</title><secondary-title>Nonlinear Homogenization and its Applications to Composites, Polycrystals and Smart Materials</secondary-title></titles><pages>1-13</pages><dates><year>2005</year><pub-dates><date>2005//</date></pub-dates></dates><pub-location>Dordrecht</pub-location><publisher>Springer Netherlands</publisher><isbn>978-1-4020-2623-2</isbn><urls></urls></record></Cite></EndNote>36. Homogenisation method in TO process is first introduced by the Kikuchi et al. ADDIN EN.CITE <EndNote><Cite><Author>Bendsøe</Author><Year>1988</Year><RecNum>66</RecNum><DisplayText>37</DisplayText><record><rec-number>66</rec-number><foreign-keys><key app=”EN” db-id=”eef20vv9h99psxes2zox2fsk52pxsf9fss90″ timestamp=”1525318228″>66</key></foreign-keys><ref-type name=”Book”>6</ref-type><contributors><authors><author>Bendsøe, Martin</author><author>Kikuchi, Noboru</author></authors></contributors><titles><title>Generating optimal topologies in structural design using a homogenization method</title></titles><pages>197-224</pages><volume>71</volume><dates><year>1988</year></dates><urls></urls><electronic-resource-num>10.1016/0045-7825(88)90086-2</electronic-resource-num></record></Cite></EndNote>37. The key concept of homogenisation method is to replace the material distribution in the design domain into easier problem by treating it as a homogeneous material, in such a way that effective density and properties can be achieved by reducing the material in the design domain in each iteration processes ADDIN EN.CITE <EndNote><Cite><Author>Allaire</Author><Year>1996</Year><RecNum>68</RecNum><DisplayText>38</DisplayText><record><rec-number>68</rec-number><foreign-keys><key app=”EN” db-id=”eef20vv9h99psxes2zox2fsk52pxsf9fss90″ timestamp=”1525318399″>68</key></foreign-keys><ref-type name=”Journal Article”>17</ref-type><contributors><authors><author>Allaire, Grégoire</author><author>Belhachmi, Zakaria</author><author>Jouve, François</author></authors></contributors><titles><title>The homogenization method for topology and shape optimization. Single and multiple loads case</title><secondary-title>Revue Européenne des Éléments Finis</secondary-title></titles><periodical><full-title>Revue Européenne des Éléments Finis</full-title></periodical><pages>649-672</pages><volume>5</volume><number>5-6</number><dates><year>1996</year><pub-dates><date>1996/01/01</date></pub-dates></dates><publisher>Taylor &amp; Francis</publisher><isbn>1250-6559</isbn><urls><related-urls><url>https://doi.org/10.1080/12506559.1996.10511241</url></related-urls></urls><electronic-resource-num>10.1080/12506559.1996.10511241</electronic-resource-num></record></Cite></EndNote>38. In simpler terms, it means that the design domain is initially a design problem that is filled with element cells that are non-homogeneous. Which in this case, filled and void elements. Homogenization method then gather the filled elements in the design domain into a structure that satisfy the loading conditions in each iteration process. Void elements are then left out, which is treated as the unnecessary elements for the design problem. The optimal structure produced will then homogeneous elements, which gives the same material properties throughout the entire structure produced. This is as described in the article ADDIN EN.CITE <EndNote><Cite><Author>Bendsøe</Author><Year>1988</Year><RecNum>66</RecNum><DisplayText>37, 39</DisplayText><record><rec-number>66</rec-number><foreign-keys><key app=”EN” db-id=”eef20vv9h99psxes2zox2fsk52pxsf9fss90″ timestamp=”1525318228″>66</key></foreign-keys><ref-type name=”Book”>6</ref-type><contributors><authors><author>Bendsøe, Martin</author><author>Kikuchi, Noboru</author></authors></contributors><titles><title>Generating optimal topologies in structural design using a homogenization method</title></titles><pages>197-224</pages><volume>71</volume><dates><year>1988</year></dates><urls></urls><electronic-resource-num>10.1016/0045-7825(88)90086-2</electronic-resource-num></record></Cite><Cite><Author>Tenek</Author><Year>1993</Year><RecNum>82</RecNum><record><rec-number>82</rec-number><foreign-keys><key app=”EN” db-id=”eef20vv9h99psxes2zox2fsk52pxsf9fss90″ timestamp=”1526214501″>82</key></foreign-keys><ref-type name=”Journal Article”>17</ref-type><contributors><authors><author>Tenek, Lazarus H.</author><author>Hagiwara, Ichiro</author></authors></contributors><titles><title>Static and vibrational shape and topology optimization using homogenization and mathematical programming</title><secondary-title>Computer Methods in Applied Mechanics and Engineering</secondary-title></titles><periodical><full-title>Computer Methods in Applied Mechanics and Engineering</full-title></periodical><pages>143-154</pages><volume>109</volume><number>1</number><dates><year>1993</year><pub-dates><date>1993/01/01/</date></pub-dates></dates><isbn>0045-7825</isbn><urls><related-urls><url>http://www.sciencedirect.com/science/article/pii/004578259390229Q</url></related-urls></urls><electronic-resource-num>https://doi.org/10.1016/0045-7825(93)90229-Q</electronic-resource-num></record></Cite></EndNote>37, 39.
SIMP
Introduction
SIMP method, also known as the Solid Isotropic Microstructure with penalization, is the method that is going to be used for the interconnection TO process in this project. In this section, it will be detailing the past work of the SIMP method, featuring the pros and cons of the method, as well as any existing methods to eliminate the problems.

SIMP method is also known as the density method ADDIN EN.CITE <EndNote><Cite><Author>Aremu</Author><Year>2010</Year><RecNum>1</RecNum><DisplayText>10</DisplayText><record><rec-number>1</rec-number><foreign-keys><key app=”EN” db-id=”eef20vv9h99psxes2zox2fsk52pxsf9fss90″ timestamp=”1520762454″>1</key></foreign-keys><ref-type name=”Book”>6</ref-type><contributors><authors><author>Aremu, Adedeji</author><author>Ashcroft, Ian</author><author>Hague, Richard</author><author>Wildman, Ricky</author><author>Tuck, Christopher</author></authors></contributors><titles><title>Suitability of SIMP and BESO topology optimization algorithms for additive manufacture</title></titles><pages>679-692</pages><dates><year>2010</year></dates><urls></urls></record></Cite></EndNote>10. It uses the element relative density as the design variable, and assume the element’s material property are uniform ADDIN EN.CITE ;EndNote;;Cite;;Author;Wang;/Author;;Year;2005;/Year;;RecNum;24;/RecNum;;DisplayText;12;/DisplayText;;record;;rec-number;24;/rec-number;;foreign-keys;;key app=”EN” db-id=”eef20vv9h99psxes2zox2fsk52pxsf9fss90″ timestamp=”1522727290″;24;/key;;/foreign-keys;;ref-type name=”Journal Article”;17;/ref-type;;contributors;;authors;;author;Wang, S. Y.;/author;;author;Tai, K.;/author;;/authors;;/contributors;;titles;;title;Structural topology design optimization using Genetic Algorithms with a bit-array representation;/title;;secondary-title;Computer Methods in Applied Mechanics and Engineering;/secondary-title;;/titles;;periodical;;full-title;Computer Methods in Applied Mechanics and Engineering;/full-title;;/periodical;;pages;3749-3770;/pages;;volume;194;/volume;;number;36;/number;;keywords;;keyword;Structural topology optimization;/keyword;;keyword;Bit-array representation;/keyword;;keyword;Design connectivity;/keyword;;keyword;Representation degeneracy;/keyword;;keyword;Genetic Algorithms;/keyword;;/keywords;;dates;;year;2005;/year;;pub-dates;;date;2005/09/23/;/date;;/pub-dates;;/dates;;isbn;0045-7825;/isbn;;urls;;related-urls;;url;http://www.sciencedirect.com/science/article/pii/S0045782504004530;/url;;/related-urls;;/urls;;electronic-resource-num;https://doi.org/10.1016/j.cma.2004.09.003;/electronic-resource-num;;/record;;/Cite;;/EndNote;12. Initial parameters such as the target volume, penalty factor, filter radius/distance limit and etc are first set ADDIN EN.CITE ;EndNote;;Cite;;Author;Aremu;/Author;;Year;2010;/Year;;RecNum;1;/RecNum;;DisplayText;10;/DisplayText;;record;;rec-number;1;/rec-number;;foreign-keys;;key app=”EN” db-id=”eef20vv9h99psxes2zox2fsk52pxsf9fss90″ timestamp=”1520762454″;1;/key;;/foreign-keys;;ref-type name=”Book”;6;/ref-type;;contributors;;authors;;author;Aremu, Adedeji;/author;;author;Ashcroft, Ian;/author;;author;Hague, Richard;/author;;author;Wildman, Ricky;/author;;author;Tuck, Christopher;/author;;/authors;;/contributors;;titles;;title;Suitability of SIMP and BESO topology optimization algorithms for additive manufacture;/title;;/titles;;pages;679-692;/pages;;dates;;year;2010;/year;;/dates;;urls;;/urls;;/record;;/Cite;;/EndNote;10. The fractional density of the elements are then initialised with the even density distribution, and FEA is performed ADDIN EN.CITE ;EndNote;;Cite;;Author;Aremu;/Author;;Year;2010;/Year;;RecNum;1;/RecNum;;DisplayText;10;/DisplayText;;record;;rec-number;1;/rec-number;;foreign-keys;;key app=”EN” db-id=”eef20vv9h99psxes2zox2fsk52pxsf9fss90″ timestamp=”1520762454″;1;/key;;/foreign-keys;;ref-type name=”Book”;6;/ref-type;;contributors;;authors;;author;Aremu, Adedeji;/author;;author;Ashcroft, Ian;/author;;author;Hague, Richard;/author;;author;Wildman, Ricky;/author;;author;Tuck, Christopher;/author;;/authors;;/contributors;;titles;;title;Suitability of SIMP and BESO topology optimization algorithms for additive manufacture;/title;;/titles;;pages;679-692;/pages;;dates;;year;2010;/year;;/dates;;urls;;/urls;;/record;;/Cite;;/EndNote;10.

Sensitivities are then calculated, of which sensitivity filtering is then used to eliminate checkerboard patterns ADDIN EN.CITE ;EndNote;;Cite;;Author;Aremu;/Author;;Year;2010;/Year;;RecNum;1;/RecNum;;DisplayText;10, 11;/DisplayText;;record;;rec-number;1;/rec-number;;foreign-keys;;key app=”EN” db-id=”eef20vv9h99psxes2zox2fsk52pxsf9fss90″ timestamp=”1520762454″;1;/key;;/foreign-keys;;ref-type name=”Book”;6;/ref-type;;contributors;;authors;;author;Aremu, Adedeji;/author;;author;Ashcroft, Ian;/author;;author;Hague, Richard;/author;;author;Wildman, Ricky;/author;;author;Tuck, Christopher;/author;;/authors;;/contributors;;titles;;title;Suitability of SIMP and BESO topology optimization algorithms for additive manufacture;/title;;/titles;;pages;679-692;/pages;;dates;;year;2010;/year;;/dates;;urls;;/urls;;/record;;/Cite;;Cite;;Author;Razvan;/Author;;Year;2014;/Year;;RecNum;4;/RecNum;;record;;rec-number;4;/rec-number;;foreign-keys;;key app=”EN” db-id=”eef20vv9h99psxes2zox2fsk52pxsf9fss90″ timestamp=”1520762826″;4;/key;;/foreign-keys;;ref-type name=”Book”;6;/ref-type;;contributors;;authors;;author;Razvan, Cazacu;/author;;/authors;;/contributors;;titles;;title;OVERVIEW OF STRUCTURAL TOPOLOGY OPTIMIZATION METHODS FOR PLANE AND SOLID STRUCTURES;/title;;/titles;;volume;XXIII (XIII), 2014/3;/volume;;dates;;year;2014;/year;;/dates;;urls;;/urls;;electronic-resource-num;10.15660/AUOFMTE.2014-3.3043;/electronic-resource-num;;/record;;/Cite;;/EndNote;10, 11. MOC method is then used to update the density of the fractional elements ADDIN EN.CITE ;EndNote;;Cite;;Author;Du;/Author;;Year;2012;/Year;;RecNum;2;/RecNum;;DisplayText;40;/DisplayText;;record;;rec-number;2;/rec-number;;foreign-keys;;key app=”EN” db-id=”eef20vv9h99psxes2zox2fsk52pxsf9fss90″ timestamp=”1520762747″;2;/key;;/foreign-keys;;ref-type name=”Book”;6;/ref-type;;contributors;;authors;;author;Du, Yixian;/author;;author;Chen, De;/author;;/authors;;/contributors;;titles;;title;Suppressing Gray-Scale Elements in Topology Optimization of Continua Using Modified Optimality Criterion Methods;/title;;/titles;;pages;53-70;/pages;;volume;86;/volume;;dates;;year;2012;/year;;/dates;;urls;;/urls;;/record;;/Cite;;/EndNote;40. Compare to traditional OC method, MOC method is preferred as it could reduce the number of gray-scale elements in the design domain ADDIN EN.CITE ;EndNote;;Cite;;Author;Du;/Author;;Year;2012;/Year;;RecNum;2;/RecNum;;DisplayText;40;/DisplayText;;record;;rec-number;2;/rec-number;;foreign-keys;;key app=”EN” db-id=”eef20vv9h99psxes2zox2fsk52pxsf9fss90″ timestamp=”1520762747″;2;/key;;/foreign-keys;;ref-type name=”Book”;6;/ref-type;;contributors;;authors;;author;Du, Yixian;/author;;author;Chen, De;/author;;/authors;;/contributors;;titles;;title;Suppressing Gray-Scale Elements in Topology Optimization of Continua Using Modified Optimality Criterion Methods;/title;;/titles;;pages;53-70;/pages;;volume;86;/volume;;dates;;year;2012;/year;;/dates;;urls;;/urls;;/record;;/Cite;;/EndNote;40. However, it is an additional process step that is built up upon OC method. Therefore, if the optimisation problem does not significant gray-scale element problem, MOC method would not be used, considering that will be additional computational time, which is not feasible when comes to solving a more complicated design problem.

Convergence criterion is then used, and the change in the strain energy in the design domain must be smaller than a certain epsilon value, to ensure the produced results are accurate ADDIN EN.CITE ;EndNote;;Cite;;Author;Du;/Author;;Year;2012;/Year;;RecNum;2;/RecNum;;DisplayText;40;/DisplayText;;record;;rec-number;2;/rec-number;;foreign-keys;;key app=”EN” db-id=”eef20vv9h99psxes2zox2fsk52pxsf9fss90″ timestamp=”1520762747″;2;/key;;/foreign-keys;;ref-type name=”Book”;6;/ref-type;;contributors;;authors;;author;Du, Yixian;/author;;author;Chen, De;/author;;/authors;;/contributors;;titles;;title;Suppressing Gray-Scale Elements in Topology Optimization of Continua Using Modified Optimality Criterion Methods;/title;;/titles;;pages;53-70;/pages;;volume;86;/volume;;dates;;year;2012;/year;;/dates;;urls;;/urls;;/record;;/Cite;;/EndNote;40. Thus, a number of iterations are needed to reach the final result.

Details for each process steps are then covered in the later segment.

Setting up initial parameters
Design Domain
The design domain will be first discretised into small elements, with an initial assigned density values. The design domain will then be further analysed, with the necessary boundary and loading conditions applied. The relative density of the elements can be initially set as even relative density values as according to Sigmund ADDIN EN.CITE ;EndNote;;Cite;;Author;Sigmund;/Author;;Year;2001;/Year;;RecNum;53;/RecNum;;DisplayText;41;/DisplayText;;record;;rec-number;53;/rec-number;;foreign-keys;;key app=”EN” db-id=”eef20vv9h99psxes2zox2fsk52pxsf9fss90″ timestamp=”1524993428″;53;/key;;/foreign-keys;;ref-type name=”Book”;6;/ref-type;;contributors;;authors;;author;Sigmund, Ole;/author;;/authors;;/contributors;;titles;;title;Sigmund, O.: A 99 Line Topology Optimization Code Written in MATLAB. Structural and Multidisciplinary Optimization 21, 120-127;/title;;/titles;;pages;120-127;/pages;;volume;21;/volume;;dates;;year;2001;/year;;/dates;;urls;;/urls;;electronic-resource-num;10.1007/s001580050176;/electronic-resource-num;;/record;;/Cite;;/EndNote;41 or some other random values ADDIN EN.CITE ;EndNote;;Cite;;Author;Bendsøe;/Author;;Year;2004;/Year;;RecNum;77;/RecNum;;DisplayText;42;/DisplayText;;record;;rec-number;77;/rec-number;;foreign-keys;;key app=”EN” db-id=”eef20vv9h99psxes2zox2fsk52pxsf9fss90″ timestamp=”1525862304″;77;/key;;/foreign-keys;;ref-type name=”Book”;6;/ref-type;;contributors;;authors;;author;Bendsøe, Martin;/author;;author;Sigmund, Ole;/author;;/authors;;/contributors;;titles;;title;Topology optimization. Theory, methods, and applications. 2nd ed., corrected printing;/title;;/titles;;dates;;year;2004;/year;;/dates;;urls;;/urls;;electronic-resource-num;10.1007/978-3-662-05086-6;/electronic-resource-num;;/record;;/Cite;;/EndNote;42. However, the result can be very different as according to Aremu et al. article ADDIN EN.CITE ;EndNote;;Cite;;Author;Aremu;/Author;;Year;2010;/Year;;RecNum;1;/RecNum;;DisplayText;10;/DisplayText;;record;;rec-number;1;/rec-number;;foreign-keys;;key app=”EN” db-id=”eef20vv9h99psxes2zox2fsk52pxsf9fss90″ timestamp=”1520762454″;1;/key;;/foreign-keys;;ref-type name=”Book”;6;/ref-type;;contributors;;authors;;author;Aremu, Adedeji;/author;;author;Ashcroft, Ian;/author;;author;Hague, Richard;/author;;author;Wildman, Ricky;/author;;author;Tuck, Christopher;/author;;/authors;;/contributors;;titles;;title;Suitability of SIMP and BESO topology optimization algorithms for additive manufacture;/title;;/titles;;pages;679-692;/pages;;dates;;year;2010;/year;;/dates;;urls;;/urls;;/record;;/Cite;;/EndNote;10.

The relative density values of the elements will be categorised by ‘0’ and ‘1’. With ‘0’, the elements is considered as void elements, where the void elements will not be considered and included in the following iteration calculation process. On the other hand, elements with relative density value of ‘1’, the placing that the element in the design domain will be filled, representing the solid material in the design domain. These concepts are as describe in the articles of PEVuZE5vdGU+PENpdGU+PEF1dGhvcj5DaGlja2VybWFuZTwvQXV0aG9yPjxZZWFyPjE5OTc8L1ll
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ADDIN EN.CITE.DATA 9-11, 40, 43
Penalty factor, PPenalty factor is one of the most parameters in SIMP method. Depending on its values, it can generate different results. A low penalty factor such as 1.0, there will be difficulties in the convergence process step ADDIN EN.CITE ;EndNote;;Cite;;Author;Du;/Author;;Year;2012;/Year;;RecNum;2;/RecNum;;DisplayText;40;/DisplayText;;record;;rec-number;2;/rec-number;;foreign-keys;;key app=”EN” db-id=”eef20vv9h99psxes2zox2fsk52pxsf9fss90″ timestamp=”1520762747″;2;/key;;/foreign-keys;;ref-type name=”Book”;6;/ref-type;;contributors;;authors;;author;Du, Yixian;/author;;author;Chen, De;/author;;/authors;;/contributors;;titles;;title;Suppressing Gray-Scale Elements in Topology Optimization of Continua Using Modified Optimality Criterion Methods;/title;;/titles;;pages;53-70;/pages;;volume;86;/volume;;dates;;year;2012;/year;;/dates;;urls;;/urls;;/record;;/Cite;;/EndNote;40, it will also contribute to grey-scale elements, as there will be unpenalized densities in the design domain ADDIN EN.CITE ;EndNote;;Cite;;Author;Aremu;/Author;;Year;2010;/Year;;RecNum;1;/RecNum;;DisplayText;10;/DisplayText;;record;;rec-number;1;/rec-number;;foreign-keys;;key app=”EN” db-id=”eef20vv9h99psxes2zox2fsk52pxsf9fss90″ timestamp=”1520762454″;1;/key;;/foreign-keys;;ref-type name=”Book”;6;/ref-type;;contributors;;authors;;author;Aremu, Adedeji;/author;;author;Ashcroft, Ian;/author;;author;Hague, Richard;/author;;author;Wildman, Ricky;/author;;author;Tuck, Christopher;/author;;/authors;;/contributors;;titles;;title;Suitability of SIMP and BESO topology optimization algorithms for additive manufacture;/title;;/titles;;pages;679-692;/pages;;dates;;year;2010;/year;;/dates;;urls;;/urls;;/record;;/Cite;;/EndNote;10. On the other hand, a high penalty factor such as 9.0, during the filtering process step, it will delete too many high-relative density elements, leading to inaccurate results ADDIN EN.CITE ;EndNote;;Cite;;Author;Du;/Author;;Year;2012;/Year;;RecNum;2;/RecNum;;DisplayText;40;/DisplayText;;record;;rec-number;2;/rec-number;;foreign-keys;;key app=”EN” db-id=”eef20vv9h99psxes2zox2fsk52pxsf9fss90″ timestamp=”1520762747″;2;/key;;/foreign-keys;;ref-type name=”Book”;6;/ref-type;;contributors;;authors;;author;Du, Yixian;/author;;author;Chen, De;/author;;/authors;;/contributors;;titles;;title;Suppressing Gray-Scale Elements in Topology Optimization of Continua Using Modified Optimality Criterion Methods;/title;;/titles;;pages;53-70;/pages;;volume;86;/volume;;dates;;year;2012;/year;;/dates;;urls;;/urls;;/record;;/Cite;;/EndNote;40. It is advised to use penalty factor of 3.0 as a guideline ADDIN EN.CITE ;EndNote;;Cite;;Author;Du;/Author;;Year;2012;/Year;;RecNum;2;/RecNum;;DisplayText;40;/DisplayText;;record;;rec-number;2;/rec-number;;foreign-keys;;key app=”EN” db-id=”eef20vv9h99psxes2zox2fsk52pxsf9fss90″ timestamp=”1520762747″;2;/key;;/foreign-keys;;ref-type name=”Book”;6;/ref-type;;contributors;;authors;;author;Du, Yixian;/author;;author;Chen, De;/author;;/authors;;/contributors;;titles;;title;Suppressing Gray-Scale Elements in Topology Optimization of Continua Using Modified Optimality Criterion Methods;/title;;/titles;;pages;53-70;/pages;;volume;86;/volume;;dates;;year;2012;/year;;/dates;;urls;;/urls;;/record;;/Cite;;/EndNote;40. That said, experimentations are needed to achieve optimum results.

During the initialisation of the elements, their relative density ranges from 0 to 1. As stated in the article ADDIN EN.CITE ;EndNote;;Cite;;Author;Du;/Author;;Year;2012;/Year;;RecNum;2;/RecNum;;DisplayText;40;/DisplayText;;record;;rec-number;2;/rec-number;;foreign-keys;;key app=”EN” db-id=”eef20vv9h99psxes2zox2fsk52pxsf9fss90″ timestamp=”1520762747″;2;/key;;/foreign-keys;;ref-type name=”Book”;6;/ref-type;;contributors;;authors;;author;Du, Yixian;/author;;author;Chen, De;/author;;/authors;;/contributors;;titles;;title;Suppressing Gray-Scale Elements in Topology Optimization of Continua Using Modified Optimality Criterion Methods;/title;;/titles;;pages;53-70;/pages;;volume;86;/volume;;dates;;year;2012;/year;;/dates;;urls;;/urls;;/record;;/Cite;;/EndNote;40, the power scheme is used to push the intermediate elements to the value of 0 or 1, in terms relative Young’s Modulus. Using the scheme, elements which has the relative Young Modulus of 0 will be represented as white/empty elements whereas elements have relative Young Modulus of 1 will be represented as black/solid elements. Elements which have intermediate relative Young Modulus will be represented as gray-scale elements. The power scheme is as stated below ADDIN EN.CITE <EndNote><Cite><Author>Du</Author><Year>2012</Year><RecNum>2</RecNum><DisplayText>40</DisplayText><record><rec-number>2</rec-number><foreign-keys><key app=”EN” db-id=”eef20vv9h99psxes2zox2fsk52pxsf9fss90″ timestamp=”1520762747″>2</key></foreign-keys><ref-type name=”Book”>6</ref-type><contributors><authors><author>Du, Yixian</author><author>Chen, De</author></authors></contributors><titles><title>Suppressing Gray-Scale Elements in Topology Optimization of Continua Using Modified Optimality Criterion Methods</title></titles><pages>53-70</pages><volume>86</volume><dates><year>2012</year></dates><urls></urls></record></Cite></EndNote>40.

Eexe=xepE0While
Ee=Actual relative Young’s Modulus of element ‘e’xe=Fractional relative density of element ‘e’ and (0?xe?1)p=Penalty factorE0=Initial Young’s Modulus of the whole design (relative value of 1.0)And the density of the element’s material density can be represented in the equation below.

?exe=xe?0While
?0=material’s density of solid state?e=element material’s densityNote that the variables Ee and ?e are iteratively updated in the iteration loop ADDIN EN.CITE ;EndNote;;Cite;;Author;Du;/Author;;Year;2012;/Year;;RecNum;2;/RecNum;;DisplayText;40;/DisplayText;;record;;rec-number;2;/rec-number;;foreign-keys;;key app=”EN” db-id=”eef20vv9h99psxes2zox2fsk52pxsf9fss90″ timestamp=”1520762747″;2;/key;;/foreign-keys;;ref-type name=”Book”;6;/ref-type;;contributors;;authors;;author;Du, Yixian;/author;;author;Chen, De;/author;;/authors;;/contributors;;titles;;title;Suppressing Gray-Scale Elements in Topology Optimization of Continua Using Modified Optimality Criterion Methods;/title;;/titles;;pages;53-70;/pages;;volume;86;/volume;;dates;;year;2012;/year;;/dates;;urls;;/urls;;/record;;/Cite;;/EndNote;40. With the incrementation of penalty factor, the produced result of Eexe will be better, as the equation is an exponential equation. However, with a very high penalty factor, it will lead to numerical instabilities, porous material, checkerboard phenomenon, and many more consequences ADDIN EN.CITE ;EndNote;;Cite;;Author;Du;/Author;;Year;2012;/Year;;RecNum;2;/RecNum;;DisplayText;40;/DisplayText;;record;;rec-number;2;/rec-number;;foreign-keys;;key app=”EN” db-id=”eef20vv9h99psxes2zox2fsk52pxsf9fss90″ timestamp=”1520762747″;2;/key;;/foreign-keys;;ref-type name=”Book”;6;/ref-type;;contributors;;authors;;author;Du, Yixian;/author;;author;Chen, De;/author;;/authors;;/contributors;;titles;;title;Suppressing Gray-Scale Elements in Topology Optimization of Continua Using Modified Optimality Criterion Methods;/title;;/titles;;pages;53-70;/pages;;volume;86;/volume;;dates;;year;2012;/year;;/dates;;urls;;/urls;;/record;;/Cite;;/EndNote;40. This is therefore very important when comes to establishing the algorithm needed for the SIMP method. Whether the TO is used on the generating the optimised design of structural members, or the optimisation on the layout and the quantity needed for the interconnections between the two mating surfaces.

Sensitivity Filter and Filter Radius, FR
Sensitivity filter process essentially removed the checkerboard pattern problem that is commonly exist in SIMP method. It is notes that the process does not hinder the computational time or set any excess constraints while searching for the mesh independent solution, which overall, is very beneficial to the whole SIMP TO process ADDIN EN.CITE ;EndNote;;Cite;;Author;Larsson;/Author;;Year;2016;/Year;;RecNum;76;/RecNum;;DisplayText;43;/DisplayText;;record;;rec-number;76;/rec-number;;foreign-keys;;key app=”EN” db-id=”eef20vv9h99psxes2zox2fsk52pxsf9fss90″ timestamp=”1525848533″;76;/key;;/foreign-keys;;ref-type name=”Thesis”;32;/ref-type;;contributors;;authors;;author;Robin Larsson;/author;;/authors;;/contributors;;titles;;title;Methodology for Topology and Shape Optimization: Application to a Rear Lower Control Arm;/title;;secondary-title;Department of Applied Mechanics;/secondary-title;;/titles;;pages;53;/pages;;volume;Master;/volume;;dates;;year;2016;/year;;/dates;;publisher;Chalmers University of Technology;/publisher;;urls;;/urls;;/record;;/Cite;;/EndNote;43. Of course, there are many other methods available, but filtering method proved to be a simple and effective of solving the problem ADDIN EN.CITE ;EndNote;;Cite;;Author;Du;/Author;;Year;2012;/Year;;RecNum;2;/RecNum;;DisplayText;40;/DisplayText;;record;;rec-number;2;/rec-number;;foreign-keys;;key app=”EN” db-id=”eef20vv9h99psxes2zox2fsk52pxsf9fss90″ timestamp=”1520762747″;2;/key;;/foreign-keys;;ref-type name=”Book”;6;/ref-type;;contributors;;authors;;author;Du, Yixian;/author;;author;Chen, De;/author;;/authors;;/contributors;;titles;;title;Suppressing Gray-Scale Elements in Topology Optimization of Continua Using Modified Optimality Criterion Methods;/title;;/titles;;pages;53-70;/pages;;volume;86;/volume;;dates;;year;2012;/year;;/dates;;urls;;/urls;;/record;;/Cite;;/EndNote;40.

Filter radius is a parameter that is used with conjunction with the penalty factor. It is also known as the distance limit parameter ADDIN EN.CITE ;EndNote;;Cite;;Author;Aremu;/Author;;Year;2010;/Year;;RecNum;1;/RecNum;;DisplayText;10;/DisplayText;;record;;rec-number;1;/rec-number;;foreign-keys;;key app=”EN” db-id=”eef20vv9h99psxes2zox2fsk52pxsf9fss90″ timestamp=”1520762454″;1;/key;;/foreign-keys;;ref-type name=”Book”;6;/ref-type;;contributors;;authors;;author;Aremu, Adedeji;/author;;author;Ashcroft, Ian;/author;;author;Hague, Richard;/author;;author;Wildman, Ricky;/author;;author;Tuck, Christopher;/author;;/authors;;/contributors;;titles;;title;Suitability of SIMP and BESO topology optimization algorithms for additive manufacture;/title;;/titles;;pages;679-692;/pages;;dates;;year;2010;/year;;/dates;;urls;;/urls;;/record;;/Cite;;/EndNote;10. It is generally used to eliminate the checkerboard patterns in the design domain. It is realised that a low FR value would not fully eliminate the checkerboard error ADDIN EN.CITE ;EndNote;;Cite;;Author;Aremu;/Author;;Year;2010;/Year;;RecNum;1;/RecNum;;DisplayText;10;/DisplayText;;record;;rec-number;1;/rec-number;;foreign-keys;;key app=”EN” db-id=”eef20vv9h99psxes2zox2fsk52pxsf9fss90″ timestamp=”1520762454″;1;/key;;/foreign-keys;;ref-type name=”Book”;6;/ref-type;;contributors;;authors;;author;Aremu, Adedeji;/author;;author;Ashcroft, Ian;/author;;author;Hague, Richard;/author;;author;Wildman, Ricky;/author;;author;Tuck, Christopher;/author;;/authors;;/contributors;;titles;;title;Suitability of SIMP and BESO topology optimization algorithms for additive manufacture;/title;;/titles;;pages;679-692;/pages;;dates;;year;2010;/year;;/dates;;urls;;/urls;;/record;;/Cite;;/EndNote;10.

Figure SEQ Figure * ARABIC 3 Difference between solutions with and without filtering scheme ADDIN EN.CITE ;EndNote;;Cite;;Author;Larsson;/Author;;Year;2016;/Year;;RecNum;76;/RecNum;;DisplayText;43;/DisplayText;;record;;rec-number;76;/rec-number;;foreign-keys;;key app=”EN” db-id=”eef20vv9h99psxes2zox2fsk52pxsf9fss90″ timestamp=”1525848533″;76;/key;;/foreign-keys;;ref-type name=”Thesis”;32;/ref-type;;contributors;;authors;;author;Robin Larsson;/author;;/authors;;/contributors;;titles;;title;Methodology for Topology and Shape Optimization: Application to a Rear Lower Control Arm;/title;;secondary-title;Department of Applied Mechanics;/secondary-title;;/titles;;pages;53;/pages;;volume;Master;/volume;;dates;;year;2016;/year;;/dates;;publisher;Chalmers University of Technology;/publisher;;urls;;/urls;;/record;;/Cite;;/EndNote;43
First and foremost, the sensitivity analysis will be done on every element in the design domain. The following formula will be used, the sensitivity objective function of the element is essentially,
dSEd?e=-p?ep-1ueTkeueWhere,
?e=relative density of the element ‘e’p=penalty factorue=nodal displacement vector of element ‘e’T=number of iterationske=stiffness matrix of element ‘e’ Using sensitivities that are calculated for all the elements in the design domain, using the formula above, sensitivity filter process step is then carried out next to eliminate the checkerboard pattern. Note that the FR parameter is used in the convolution operator as follow. Where,
dSEd?e=1?ef=1NHf f=1NHf?fdSEd?f While,
dSEd?e=estimator of the senstivity of the element ‘e’Hf=convolution operator, FR-dist(e,f)And,
diste,f=distance between centre of element ‘e’and ‘f’Using the above formula, it will be used on every single element in the design domain. Where in this example, assuming the element ‘e’ is the current element being applied. Element ‘e’ is surrounded by other element ‘f’. Of which the sensitivity of the element ‘e’ will be computed, by using the sensitivity of other elements that are within the range of the convolution operator.
This thus creates a balancing effect, as element ‘e’ relative density will then be affected by the surrounding elements’ density, and the specific element will be evaluated many times due to the weighted average operation ADDIN EN.CITE <EndNote><Cite><Author>Du</Author><Year>2012</Year><RecNum>2</RecNum><DisplayText>40</DisplayText><record><rec-number>2</rec-number><foreign-keys><key app=”EN” db-id=”eef20vv9h99psxes2zox2fsk52pxsf9fss90″ timestamp=”1520762747″>2</key></foreign-keys><ref-type name=”Book”>6</ref-type><contributors><authors><author>Du, Yixian</author><author>Chen, De</author></authors></contributors><titles><title>Suppressing Gray-Scale Elements in Topology Optimization of Continua Using Modified Optimality Criterion Methods</title></titles><pages>53-70</pages><volume>86</volume><dates><year>2012</year></dates><urls></urls></record></Cite></EndNote>40.

Note that the filtering scheme here is useful when it comes to reducing the problem of having checkerboard pattern in the optimised design domain. However, by introducing the convolution factor, where diste,f is increased, the problem of having gray-scale elements also increases, this is as according to Chen et al. ADDIN EN.CITE <EndNote><Cite><Author>Du</Author><Year>2012</Year><RecNum>2</RecNum><DisplayText>40</DisplayText><record><rec-number>2</rec-number><foreign-keys><key app=”EN” db-id=”eef20vv9h99psxes2zox2fsk52pxsf9fss90″ timestamp=”1520762747″>2</key></foreign-keys><ref-type name=”Book”>6</ref-type><contributors><authors><author>Du, Yixian</author><author>Chen, De</author></authors></contributors><titles><title>Suppressing Gray-Scale Elements in Topology Optimization of Continua Using Modified Optimality Criterion Methods</title></titles><pages>53-70</pages><volume>86</volume><dates><year>2012</year></dates><urls></urls></record></Cite></EndNote>40. That said, this process step will be used in this interconnection TO thesis project despite its underlying cons.
Optimality Criterion
OC method is used in the SIMP process step to speed up the convergence process in the later stage. It is also the process step where the relative density of the elements is updated into either solid or void elements.

Unlike the traditional OC method, MOC method is a better choice when comes to suppressing the gray-scale elements. Gray-scale elements are elements which are represented as blurred elements in the final design domain. Typically, the optimum design should not have any gray-scale elements, as it is unclear whether the elements are omitted or not. Forming of the gray-scale elements is related to their fractional relative density. This is as covered in the previous section, ‘Penalty factor, P’.

Traditional OC method has advantages of fast convergence, and having the level of complexity that is not associated with the number of variables and structural re-analysis ADDIN EN.CITE <EndNote><Cite><Author>Du</Author><Year>2012</Year><RecNum>2</RecNum><DisplayText>40</DisplayText><record><rec-number>2</rec-number><foreign-keys><key app=”EN” db-id=”eef20vv9h99psxes2zox2fsk52pxsf9fss90″ timestamp=”1520762747″>2</key></foreign-keys><ref-type name=”Book”>6</ref-type><contributors><authors><author>Du, Yixian</author><author>Chen, De</author></authors></contributors><titles><title>Suppressing Gray-Scale Elements in Topology Optimization of Continua Using Modified Optimality Criterion Methods</title></titles><pages>53-70</pages><volume>86</volume><dates><year>2012</year></dates><urls></urls></record></Cite></EndNote>40. The scheme to update the element densities are as below. The fractional relative density of the elements are updated in three conditions ADDIN EN.CITE <EndNote><Cite><Author>Du</Author><Year>2012</Year><RecNum>2</RecNum><DisplayText>40</DisplayText><record><rec-number>2</rec-number><foreign-keys><key app=”EN” db-id=”eef20vv9h99psxes2zox2fsk52pxsf9fss90″ timestamp=”1520762747″>2</key></foreign-keys><ref-type name=”Book”>6</ref-type><contributors><authors><author>Du, Yixian</author><author>Chen, De</author></authors></contributors><titles><title>Suppressing Gray-Scale Elements in Topology Optimization of Continua Using Modified Optimality Criterion Methods</title></titles><pages>53-70</pages><volume>86</volume><dates><year>2012</year></dates><urls></urls></record></Cite></EndNote>40.

if xe?e??maxxmin, xe-mxnew=max?(xmin,xe-m)if max?(xmin,xe-m)?xeBe??min?(1, xe+m)xnew=xeBe?if min?(1,xe+m)?xeBe?xnew=min?(1,xe+m)While ADDIN EN.CITE <EndNote><Cite><Author>Du</Author><Year>2012</Year><RecNum>2</RecNum><DisplayText>40</DisplayText><record><rec-number>2</rec-number><foreign-keys><key app=”EN” db-id=”eef20vv9h99psxes2zox2fsk52pxsf9fss90″ timestamp=”1520762747″>2</key></foreign-keys><ref-type name=”Book”>6</ref-type><contributors><authors><author>Du, Yixian</author><author>Chen, De</author></authors></contributors><titles><title>Suppressing Gray-Scale Elements in Topology Optimization of Continua Using Modified Optimality Criterion Methods</title></titles><pages>53-70</pages><volume>86</volume><dates><year>2012</year></dates><urls></urls></record></Cite></EndNote>40,
Be=-dSEdxe?dVdxe? is a Lagrangian multiplier which is found by a bi-sectioning algorithm.
MOC method is built on top of the OC method, and it focuses on making the low-relative-density elements, such as the ones lower than 0.5, to become 0 ADDIN EN.CITE <EndNote><Cite><Author>Du</Author><Year>2012</Year><RecNum>2</RecNum><DisplayText>40</DisplayText><record><rec-number>2</rec-number><foreign-keys><key app=”EN” db-id=”eef20vv9h99psxes2zox2fsk52pxsf9fss90″ timestamp=”1520762747″>2</key></foreign-keys><ref-type name=”Book”>6</ref-type><contributors><authors><author>Du, Yixian</author><author>Chen, De</author></authors></contributors><titles><title>Suppressing Gray-Scale Elements in Topology Optimization of Continua Using Modified Optimality Criterion Methods</title></titles><pages>53-70</pages><volume>86</volume><dates><year>2012</year></dates><urls></urls></record></Cite></EndNote>40. On the other hand, making the high-relative-density elements that exceeds 0.5 to become 1.0 ADDIN EN.CITE <EndNote><Cite><Author>Du</Author><Year>2012</Year><RecNum>2</RecNum><DisplayText>40</DisplayText><record><rec-number>2</rec-number><foreign-keys><key app=”EN” db-id=”eef20vv9h99psxes2zox2fsk52pxsf9fss90″ timestamp=”1520762747″>2</key></foreign-keys><ref-type name=”Book”>6</ref-type><contributors><authors><author>Du, Yixian</author><author>Chen, De</author></authors></contributors><titles><title>Suppressing Gray-Scale Elements in Topology Optimization of Continua Using Modified Optimality Criterion Methods</title></titles><pages>53-70</pages><volume>86</volume><dates><year>2012</year></dates><urls></urls></record></Cite></EndNote>40. This essentially speed up the iteration process as well as the convergence process step later on.
This allows low-relative-density elements to have lesser impact on the design problem, and allowing the high-relative density elements to have greater effect to the system ADDIN EN.CITE <EndNote><Cite><Author>Du</Author><Year>2012</Year><RecNum>2</RecNum><DisplayText>40</DisplayText><record><rec-number>2</rec-number><foreign-keys><key app=”EN” db-id=”eef20vv9h99psxes2zox2fsk52pxsf9fss90″ timestamp=”1520762747″>2</key></foreign-keys><ref-type name=”Book”>6</ref-type><contributors><authors><author>Du, Yixian</author><author>Chen, De</author></authors></contributors><titles><title>Suppressing Gray-Scale Elements in Topology Optimization of Continua Using Modified Optimality Criterion Methods</title></titles><pages>53-70</pages><volume>86</volume><dates><year>2012</year></dates><urls></urls></record></Cite></EndNote>40. Thus, this suppresses the formation of gray-scale elements, as MOC method updates the intermediate relative density to the value of 0 or 1.
There are total of two methods or formulas to implement the MOC method.
xnew’=e(- a2+axnew)1+e(- a2+axnew)xnew’=2.55arctanb2xnew-141+e-xnewb+12While,
a=Steepness parameter in first MOC equationb=Steepness parameter in second MOC equationxnew’=Element density generated by MOC methodxnew=Element density generated by OC methodUsing the steepness parameter, the higher the value, the steeper the graph is. This is as shown in the figures below ADDIN EN.CITE ;EndNote;;Cite;;Author;Du;/Author;;Year;2012;/Year;;RecNum;2;/RecNum;;DisplayText;40;/DisplayText;;record;;rec-number;2;/rec-number;;foreign-keys;;key app=”EN” db-id=”eef20vv9h99psxes2zox2fsk52pxsf9fss90″ timestamp=”1520762747″;2;/key;;/foreign-keys;;ref-type name=”Book”;6;/ref-type;;contributors;;authors;;author;Du, Yixian;/author;;author;Chen, De;/author;;/authors;;/contributors;;titles;;title;Suppressing Gray-Scale Elements in Topology Optimization of Continua Using Modified Optimality Criterion Methods;/title;;/titles;;pages;53-70;/pages;;volume;86;/volume;;dates;;year;2012;/year;;/dates;;urls;;/urls;;/record;;/Cite;;/EndNote;40.

Figure SEQ Figure * ARABIC 4 Different shapes of graphs when using different values of steepness parameter
As mentioned, different steepness parameter values could generate different shapes of graphs. It is noticed that when the steepness parameter a and b are increased, the graph will gradually become approximate to a smoothed Heaviside step function graph ADDIN EN.CITE ;EndNote;;Cite;;Author;Du;/Author;;Year;2012;/Year;;RecNum;2;/RecNum;;DisplayText;40;/DisplayText;;record;;rec-number;2;/rec-number;;foreign-keys;;key app=”EN” db-id=”eef20vv9h99psxes2zox2fsk52pxsf9fss90″ timestamp=”1520762747″;2;/key;;/foreign-keys;;ref-type name=”Book”;6;/ref-type;;contributors;;authors;;author;Du, Yixian;/author;;author;Chen, De;/author;;/authors;;/contributors;;titles;;title;Suppressing Gray-Scale Elements in Topology Optimization of Continua Using Modified Optimality Criterion Methods;/title;;/titles;;pages;53-70;/pages;;volume;86;/volume;;dates;;year;2012;/year;;/dates;;urls;;/urls;;/record;;/Cite;;/EndNote;40. A smoothed Heaviside function is more efficient in updating the element relative density into the value of 1 or 0. Low-relative-density elements are weakened and their stiffness matrixes are also weakened, which means that it does little effect on the global stiffness matrix ADDIN EN.CITE ;EndNote;;Cite;;Author;Du;/Author;;Year;2012;/Year;;RecNum;2;/RecNum;;DisplayText;40;/DisplayText;;record;;rec-number;2;/rec-number;;foreign-keys;;key app=”EN” db-id=”eef20vv9h99psxes2zox2fsk52pxsf9fss90″ timestamp=”1520762747″;2;/key;;/foreign-keys;;ref-type name=”Book”;6;/ref-type;;contributors;;authors;;author;Du, Yixian;/author;;author;Chen, De;/author;;/authors;;/contributors;;titles;;title;Suppressing Gray-Scale Elements in Topology Optimization of Continua Using Modified Optimality Criterion Methods;/title;;/titles;;pages;53-70;/pages;;volume;86;/volume;;dates;;year;2012;/year;;/dates;;urls;;/urls;;/record;;/Cite;;/EndNote;40.
On the other hand, the high-relative-density elements’ stiffness matrices are being enhanced, this means that the high-relative-density elements can contribute more to the global stiffness matrix ADDIN EN.CITE <EndNote><Cite><Author>Du</Author><Year>2012</Year><RecNum>2</RecNum><DisplayText>40</DisplayText><record><rec-number>2</rec-number><foreign-keys><key app=”EN” db-id=”eef20vv9h99psxes2zox2fsk52pxsf9fss90″ timestamp=”1520762747″>2</key></foreign-keys><ref-type name=”Book”>6</ref-type><contributors><authors><author>Du, Yixian</author><author>Chen, De</author></authors></contributors><titles><title>Suppressing Gray-Scale Elements in Topology Optimization of Continua Using Modified Optimality Criterion Methods</title></titles><pages>53-70</pages><volume>86</volume><dates><year>2012</year></dates><urls></urls></record></Cite></EndNote>40. All in all, this in turn suppresses the formation of gray-scale elements, as the MOC method enables the relative density of the elements be determined more clearly, into ‘0’ or ‘1’ values.
Again, this is particularly useful as it substantially reduces the possible error of having gray-scale elements during the topology optimisation process. It is worth looking into if there are too much grap-scale elements in the optimised solution. Of course, MOC method is a very efficient tool in eliminating the gray-scale elements in the problem should any of them exist in the design domain. However, if the problem has little effect on the solution produced, normal OC method will be applied.
Flow of the SIMP method

Figure SEQ Figure * ARABIC 5 SIMP flow ADDIN EN.CITE <EndNote><Cite><Author>Aremu</Author><Year>2010</Year><RecNum>1</RecNum><DisplayText>10</DisplayText><record><rec-number>1</rec-number><foreign-keys><key app=”EN” db-id=”eef20vv9h99psxes2zox2fsk52pxsf9fss90″ timestamp=”1520762454″>1</key></foreign-keys><ref-type name=”Book”>6</ref-type><contributors><authors><author>Aremu, Adedeji</author><author>Ashcroft, Ian</author><author>Hague, Richard</author><author>Wildman, Ricky</author><author>Tuck, Christopher</author></authors></contributors><titles><title>Suitability of SIMP and BESO topology optimization algorithms for additive manufacture</title></titles><pages>679-692</pages><dates><year>2010</year></dates><urls></urls></record></Cite></EndNote>10
The figure depicts the overall flow of the SIMP process for a typical TO process. Main process steps are as covered in the sections above. The FEA analysis is first carried out to illustrate the design domain in the software, as well as establishing necessary boundary and the loading conditions. The result file is then exported to the MATLAB software to carry out the further process steps. Of which, in this case, implementing the SIMP algorithms to the design problem. The algorithms are broken into many segments, which is shown in the sections above. Using the algorithms, the proposed design solution is then produced, and then imported into the ANSYS FEA software. The loop will then be carried out until the convergence criterion is fulfilled. The final results will then be shown in the ANSYS software.

Stiffness-based approach
Stiffness of the interconnections are very important as they are the measurement of degree of deformations when they are subjected to load. The stiffness of a material is directly related to its young modulus. A structure must be stiff enough to fulfil its applications without exceeding the prescribed deflection limit, and ensuring that there are no failures during the process ADDIN EN.CITE <EndNote><Cite><Author>Chu</Author><Year>1996</Year><RecNum>10</RecNum><DisplayText>44</DisplayText><record><rec-number>10</rec-number><foreign-keys><key app=”EN” db-id=”eef20vv9h99psxes2zox2fsk52pxsf9fss90″ timestamp=”1521344567″>10</key></foreign-keys><ref-type name=”Journal Article”>17</ref-type><contributors><authors><author>Chu, D. Nha</author><author>Xie, Y. M.</author><author>Hira, A.</author><author>Steven, G. P.</author></authors></contributors><titles><title>Evolutionary structural optimization for problems with stiffness constraints</title><secondary-title>Finite Elements in Analysis and Design</secondary-title></titles><periodical><full-title>Finite Elements in Analysis and Design</full-title></periodical><pages>239-251</pages><volume>21</volume><number>4</number><dates><year>1996</year><pub-dates><date>1996/04/01/</date></pub-dates></dates><isbn>0168-874X</isbn><urls><related-urls><url>http://www.sciencedirect.com/science/article/pii/0168874X9500043S</url></related-urls></urls><electronic-resource-num>https://doi.org/10.1016/0168-874X(95)00043-S</electronic-resource-num></record></Cite></EndNote>44.

In the article published by Chu et al., the stiffness constraints approach is done using ESO ADDIN EN.CITE <EndNote><Cite><Author>Chu</Author><Year>1996</Year><RecNum>10</RecNum><DisplayText>44</DisplayText><record><rec-number>10</rec-number><foreign-keys><key app=”EN” db-id=”eef20vv9h99psxes2zox2fsk52pxsf9fss90″ timestamp=”1521344567″>10</key></foreign-keys><ref-type name=”Journal Article”>17</ref-type><contributors><authors><author>Chu, D. Nha</author><author>Xie, Y. M.</author><author>Hira, A.</author><author>Steven, G. P.</author></authors></contributors><titles><title>Evolutionary structural optimization for problems with stiffness constraints</title><secondary-title>Finite Elements in Analysis and Design</secondary-title></titles><periodical><full-title>Finite Elements in Analysis and Design</full-title></periodical><pages>239-251</pages><volume>21</volume><number>4</number><dates><year>1996</year><pub-dates><date>1996/04/01/</date></pub-dates></dates><isbn>0168-874X</isbn><urls><related-urls><url>http://www.sciencedirect.com/science/article/pii/0168874X9500043S</url></related-urls></urls><electronic-resource-num>https://doi.org/10.1016/0168-874X(95)00043-S</electronic-resource-num></record></Cite></EndNote>44. Where in the paper, a sensitivity number is computed by running iterations in the FEA program ADDIN EN.CITE <EndNote><Cite><Author>Chu</Author><Year>1996</Year><RecNum>10</RecNum><DisplayText>44</DisplayText><record><rec-number>10</rec-number><foreign-keys><key app=”EN” db-id=”eef20vv9h99psxes2zox2fsk52pxsf9fss90″ timestamp=”1521344567″>10</key></foreign-keys><ref-type name=”Journal Article”>17</ref-type><contributors><authors><author>Chu, D. Nha</author><author>Xie, Y. M.</author><author>Hira, A.</author><author>Steven, G. P.</author></authors></contributors><titles><title>Evolutionary structural optimization for problems with stiffness constraints</title><secondary-title>Finite Elements in Analysis and Design</secondary-title></titles><periodical><full-title>Finite Elements in Analysis and Design</full-title></periodical><pages>239-251</pages><volume>21</volume><number>4</number><dates><year>1996</year><pub-dates><date>1996/04/01/</date></pub-dates></dates><isbn>0168-874X</isbn><urls><related-urls><url>http://www.sciencedirect.com/science/article/pii/0168874X9500043S</url></related-urls></urls><electronic-resource-num>https://doi.org/10.1016/0168-874X(95)00043-S</electronic-resource-num></record></Cite></EndNote>44. This approach can be useful in the thesis project, as SIMP method also has a sensitivity analysis process step, where this method could be implemented.
The discretised elements in the design domain will be assigned with a computed sensitivity values, where elements with lowest sensitivity numbers are filtered an eliminated from the design domain ADDIN EN.CITE <EndNote><Cite><Author>Chu</Author><Year>1996</Year><RecNum>10</RecNum><DisplayText>44</DisplayText><record><rec-number>10</rec-number><foreign-keys><key app=”EN” db-id=”eef20vv9h99psxes2zox2fsk52pxsf9fss90″ timestamp=”1521344567″>10</key></foreign-keys><ref-type name=”Journal Article”>17</ref-type><contributors><authors><author>Chu, D. Nha</author><author>Xie, Y. M.</author><author>Hira, A.</author><author>Steven, G. P.</author></authors></contributors><titles><title>Evolutionary structural optimization for problems with stiffness constraints</title><secondary-title>Finite Elements in Analysis and Design</secondary-title></titles><periodical><full-title>Finite Elements in Analysis and Design</full-title></periodical><pages>239-251</pages><volume>21</volume><number>4</number><dates><year>1996</year><pub-dates><date>1996/04/01/</date></pub-dates></dates><isbn>0168-874X</isbn><urls><related-urls><url>http://www.sciencedirect.com/science/article/pii/0168874X9500043S</url></related-urls></urls><electronic-resource-num>https://doi.org/10.1016/0168-874X(95)00043-S</electronic-resource-num></record></Cite></EndNote>44. Again, this can be done in the filtering process step in the SIMP method.
All in all, this method is proved to be simple and robust, as seen in the article by Chu et al. ADDIN EN.CITE <EndNote><Cite><Author>Chu</Author><Year>1996</Year><RecNum>10</RecNum><DisplayText>44</DisplayText><record><rec-number>10</rec-number><foreign-keys><key app=”EN” db-id=”eef20vv9h99psxes2zox2fsk52pxsf9fss90″ timestamp=”1521344567″>10</key></foreign-keys><ref-type name=”Journal Article”>17</ref-type><contributors><authors><author>Chu, D. Nha</author><author>Xie, Y. M.</author><author>Hira, A.</author><author>Steven, G. P.</author></authors></contributors><titles><title>Evolutionary structural optimization for problems with stiffness constraints</title><secondary-title>Finite Elements in Analysis and Design</secondary-title></titles><periodical><full-title>Finite Elements in Analysis and Design</full-title></periodical><pages>239-251</pages><volume>21</volume><number>4</number><dates><year>1996</year><pub-dates><date>1996/04/01/</date></pub-dates></dates><isbn>0168-874X</isbn><urls><related-urls><url>http://www.sciencedirect.com/science/article/pii/0168874X9500043S</url></related-urls></urls><electronic-resource-num>https://doi.org/10.1016/0168-874X(95)00043-S</electronic-resource-num></record></Cite></EndNote>44, and its relevancy to the current thesis project is essential and worth look into.

Frequency-based approach
As covered in the last section, the stiffness of the structural interconnections plays an important role when comes to assemble the structural members together. However, frequency is also another key factor that could cause devastating failure to a structure. And in the industry, many design analysis are done to prevent such incidents from happening. In short, natural frequency is something that every material has. In any kind of application, it there will always be presence of vibrations. When the object is excited by external forced vibrations, and its produced frequency is the same as its own natural frequency, resonance will occur. The resonance thereby causes drastic effect on the members by causing large amplitude, although the forced vibrations in the structure can be small. Which in this case, creating a bigger effect of vibrations in the members in the structure, which could result in failure of the structure, machines, and in this case, interconnection between members.

As such, it is best to set up frequency constraints in the interconnection members when doing a TO analysis, so as to ensure that resonance will have lesser chance of happening as due to the external load of vibrations. Thereby, preventing the failure of the interconnections in the members.
Thus, through frequency-based optimisation, the best way of the layout and the quantity of the interconnections can be optimised to prevent resonance failure. It is noted that the article published by Grandhi ADDIN EN.CITE <EndNote><Cite><Author>Grandhi</Author><Year>1993</Year><RecNum>78</RecNum><DisplayText>45</DisplayText><record><rec-number>78</rec-number><foreign-keys><key app=”EN” db-id=”eef20vv9h99psxes2zox2fsk52pxsf9fss90″ timestamp=”1525954339″>78</key></foreign-keys><ref-type name=”Journal Article”>17</ref-type><contributors><authors><author>Grandhi, Ramana</author></authors></contributors><titles><title>Structural optimization with frequency constraints – A review</title><secondary-title>AIAA Journal</secondary-title></titles><periodical><full-title>AIAA Journal</full-title></periodical><pages>2296-2303</pages><volume>31</volume><number>12</number><dates><year>1993</year><pub-dates><date>1993/12/01</date></pub-dates></dates><publisher>American Institute of Aeronautics and Astronautics</publisher><isbn>0001-1452</isbn><urls><related-urls><url>https://doi.org/10.2514/3.11928</url></related-urls></urls><electronic-resource-num>10.2514/3.11928</electronic-resource-num><access-date>2018/05/10</access-date></record></Cite></EndNote>45 discuss the importance of frequency TO process, and the article features about the method used, as well as the applications of the TO process. Normally, to alter the frequency, the size and the thickness of the structure changed. Up to today, there still no general method in optimising for frequency problem in interconnection problem. It is thus worth to look into the past work to create a general method for interconnection TO for frequency based problems. Articles from PEVuZE5vdGU+PENpdGU+PEF1dGhvcj5Ew61hYXo8L0F1dGhvcj48WWVhcj4xOTkyPC9ZZWFyPjxS
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L0NpdGU+PC9FbmROb3RlPgB=
ADDIN EN.CITE.DATA 39, 46, 47 depicts the usage of homogenisation method on solving frequency based problems.

In the paper published by Xie et al. ADDIN EN.CITE <EndNote><Cite><Author>Xie</Author><Year>1994</Year><RecNum>79</RecNum><DisplayText>48, 49</DisplayText><record><rec-number>79</rec-number><foreign-keys><key app=”EN” db-id=”eef20vv9h99psxes2zox2fsk52pxsf9fss90″ timestamp=”1525954419″>79</key></foreign-keys><ref-type name=”Journal Article”>17</ref-type><contributors><authors><author>Xie, Y. M.</author><author>Steven, G. P.</author></authors></contributors><titles><title>A simple approach to structural frequency optimization</title><secondary-title>Computers &amp; Structures</secondary-title></titles><periodical><full-title>Computers &amp; Structures</full-title></periodical><pages>1487-1491</pages><volume>53</volume><number>6</number><dates><year>1994</year><pub-dates><date>1994/12/17/</date></pub-dates></dates><isbn>0045-7949</isbn><urls><related-urls><url>http://www.sciencedirect.com/science/article/pii/0045794994904146</url></related-urls></urls><electronic-resource-num>https://doi.org/10.1016/0045-7949(94)90414-6</electronic-resource-num></record></Cite><Cite><Author>Xie</Author><Year>1996</Year><RecNum>80</RecNum><record><rec-number>80</rec-number><foreign-keys><key app=”EN” db-id=”eef20vv9h99psxes2zox2fsk52pxsf9fss90″ timestamp=”1525956487″>80</key></foreign-keys><ref-type name=”Journal Article”>17</ref-type><contributors><authors><author>Xie, Y. M.</author><author>Steven, G. P.</author></authors></contributors><titles><title>Evolutionary structural optimization for dynamic problems</title><secondary-title>Computers &amp; Structures</secondary-title></titles><periodical><full-title>Computers &amp; Structures</full-title></periodical><pages>1067-1073</pages><volume>58</volume><number>6</number><dates><year>1996</year><pub-dates><date>1996/03/17/</date></pub-dates></dates><isbn>0045-7949</isbn><urls><related-urls><url>http://www.sciencedirect.com/science/article/pii/0045794995002359</url></related-urls></urls><electronic-resource-num>https://doi.org/10.1016/0045-7949(95)00235-9</electronic-resource-num></record></Cite></EndNote>48, 49, who used ESO method for TO frequency problem, who illustrate the design problem into an eigenvalue problem. Each elements are then assigned with a sensitivity number, similar to stiffness based approach. Of which the sensitivity number is the indicator of the change of frequency. As according to the paper, the sensitivity values of the elements can be categorised into 3 regions. By removing elements in a specific region, one can increase or reduce the frequency of the structure. While doing so, it fulfils the required frequency as set by the user, while removing elements from the design domain, thereby TO is achieved. Thus, there are number of ways in solving the frequency based problem, depending on the user, whether he wants to increase, reduce, maintain the chosen frequency. These steps are all detailed in the article published by Xie et al. ADDIN EN.CITE <EndNote><Cite><Author>Xie</Author><Year>1996</Year><RecNum>80</RecNum><DisplayText>49</DisplayText><record><rec-number>80</rec-number><foreign-keys><key app=”EN” db-id=”eef20vv9h99psxes2zox2fsk52pxsf9fss90″ timestamp=”1525956487″>80</key></foreign-keys><ref-type name=”Journal Article”>17</ref-type><contributors><authors><author>Xie, Y. M.</author><author>Steven, G. P.</author></authors></contributors><titles><title>Evolutionary structural optimization for dynamic problems</title><secondary-title>Computers &amp; Structures</secondary-title></titles><periodical><full-title>Computers &amp; Structures</full-title></periodical><pages>1067-1073</pages><volume>58</volume><number>6</number><dates><year>1996</year><pub-dates><date>1996/03/17/</date></pub-dates></dates><isbn>0045-7949</isbn><urls><related-urls><url>http://www.sciencedirect.com/science/article/pii/0045794995002359</url></related-urls></urls><electronic-resource-num>https://doi.org/10.1016/0045-7949(95)00235-9</electronic-resource-num></record></Cite></EndNote>49.

It is noted that the normal OC method might not work well with the frequency-based problem, as explained from Ma et al. article ADDIN EN.CITE <EndNote><Cite><Author>Ma</Author><Year>1993</Year><RecNum>83</RecNum><DisplayText>47</DisplayText><record><rec-number>83</rec-number><foreign-keys><key app=”EN” db-id=”eef20vv9h99psxes2zox2fsk52pxsf9fss90″ timestamp=”1526214928″>83</key></foreign-keys><ref-type name=”Journal Article”>17</ref-type><contributors><authors><author>Ma, Z. D.</author><author>Kikuchi, N.</author><author>Hagiwara, I.</author></authors></contributors><titles><title>Structural topology and shape optimization for a frequency response problem</title><secondary-title>Computational Mechanics</secondary-title></titles><periodical><full-title>Computational Mechanics</full-title></periodical><pages>157-174</pages><volume>13</volume><number>3</number><dates><year>1993</year></dates><isbn>0178-7675</isbn><urls><related-urls><url>http://usyd.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwtV07T8MwELagLDDwRjwlS4xVkBPnOTAgBKpUdaGFgaVy7AtUqC2ilRD_nnNsp6ZdYGCJIiuJlNyX83f23XeE8OiKBUs-IUUOl2ciLRlGRGVUCKaYTLmKuW6IlC6vbLtMosXYvxoex9D0upD2D8ZvHooDeI4QwCOCAI-_gkG_1oettTXmph-CEVyavYp3aE_RYYxtJabJp2xXHya5-qv9YdJndSVV3XTG57GmGYRbSOyBrh_28uZ7NSV9vmoHTUJxd_Sm-6782P3piJfRp6g7HdnVW2UL8riXy2GXJDEO1ZIwZkYxbjTmeFFhqqMbP8s9PHHPaYZGotrOv6Hp2rPi2plLWGc8Q97KFxOY27RfmteabEOnzOzdq3XVx2ok59cwCR7762QDeW6kHftD56nZhUpy06DVveFPeVv7LI_QeMxksEu2bUhBb4zx98gaTPbJjg0vqHXes32y5WlPHpDuAhnUIYMiMmiNDOojgyIyqKANMqhDBrXIOCT9-7vBbSewnTUCWSQ8SEQskLvJNIQc6XxYiizLBZNZGAPIMq-YEFGMwWTB8U_VCnlQZVUKMpGKFcCPSGsyncAxoSBiSEtQsQIdqcu8KqIMpCoSyYVI1Am5dB9n-G7kU4ar5jj91VVnZHOBv3PSwq8EF0Y98xvKbl_h</url></related-urls></urls><electronic-resource-num>10.1007/BF00370133</electronic-resource-num></record></Cite></EndNote>47. Again, MOC method will be used if necessary should there be any gray-scale element problem in the optimised solution.
There are little articles that incorporates frequency-based method into SIMP method. In the article published by Tcherniak ADDIN EN.CITE <EndNote><Cite><Author>Tcherniak</Author><Year>2002</Year><RecNum>84</RecNum><DisplayText>50</DisplayText><record><rec-number>84</rec-number><foreign-keys><key app=”EN” db-id=”eef20vv9h99psxes2zox2fsk52pxsf9fss90″ timestamp=”1526471355″>84</key></foreign-keys><ref-type name=”Journal Article”>17</ref-type><contributors><authors><author>Tcherniak, Dmitri</author></authors></contributors><titles><title>Topology optimization of resonating structures using SIMP method</title><secondary-title>International Journal for Numerical Methods in Engineering</secondary-title></titles><periodical><full-title>International Journal for Numerical Methods in Engineering</full-title></periodical><pages>1605-1622</pages><volume>54</volume><number>11</number><dates><year>2002</year></dates><isbn>0029-5981</isbn><urls><related-urls><url>http://usyd.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwtV07T8MwELagXWDgUUA8Je9ViuM4Dw9IICgCiSKktnPkJI6UISmi7cC_5xznYdIBGFii9FRHSe7L5_PZ_g4hh46I1eEEP3CiKHCJEHYMHTRP4Yw7JOYJ0CMRcSezXc-7t7Z_dTzYwPVqI-0fnN9cFAxwDhCAI4AAjr-DgS6C8DlcADfk1aZLFSHCMFslznU6QWnIrsEyXJepg-nz5K2qLW0Gr5vZw0Jvfxy-rvXEj1olq1qVi2wNqcMmP6AgUmSipOCHPFt9ZN_SDlTlUSkxqZRyy-W63spIavYkStqV6jK2Nb1qjegaRrZBlrZHXKPjtT29Q3mD1CuR2FyOtO5pRza70501iwy1IDMNoWGoGiot9TzJ4tWNLKz5dBv1IbalrIf6L_PZeNrMPUGI7NQLg9QD6q3W6lLX1T0YMYwRjMwO0F716vGd9vch2pLFAO1XIwpc8fVygHYNH8CvSaPRuzxCtzU0sAkNvEhxCw3cQgOX0MAKGlhD4xjNH8ez-yerqqdhxTCMZFbks5inEr48GfFEzbdR-Ci5BJvH3ChIeJRK6rnUi2zoCAJHpsynRLDAZoLErnOCesWikKcIC4fR1KXA_jAedUUQsIB4Uth-4kF4Q-0zhOs3FL5r2ZSw44_zn_9ygXZa6F2iHjyyvNJ6mV9KnmAu</url></related-urls></urls><electronic-resource-num>10.1002/nme.484</electronic-resource-num></record></Cite></EndNote>50, which uses SIMP method in frequency problems, uses mode acceleration method to illustrate the dynamic response of the structure. Due to the fact that dynamic problem might generate multiple eigenvalues as describe in article ADDIN EN.CITE <EndNote><Cite><Author>Yaghoobi</Author><Year>2017</Year><RecNum>86</RecNum><DisplayText>51</DisplayText><record><rec-number>86</rec-number><foreign-keys><key app=”EN” db-id=”eef20vv9h99psxes2zox2fsk52pxsf9fss90″ timestamp=”1526473046″>86</key></foreign-keys><ref-type name=”Journal Article”>17</ref-type><contributors><authors><author>Yaghoobi, N.</author><author>Hassani, B.</author></authors></contributors><titles><title>TOPOLOGICAL OPTIMIZATION OF VIBRATING CONTINUUM STRUCTURES FOR OPTIMAL NATURAL EIGENFREQUENCY</title><secondary-title>International Journal of Optimization in Civil Engineering</secondary-title></titles><periodical><full-title>International Journal of Optimization in Civil Engineering</full-title></periodical><pages>1-12</pages><volume>7</volume><number>1</number><section>1</section><keywords><keyword>topology optimization, SIMP, multiple eigenvalues, bound formulation, MMA</keyword></keywords><dates><year>2017</year></dates><isbn>2228-7558</isbn><call-num>A-10-66-122</call-num><work-type>Technical note</work-type><urls><related-urls><url>http://ijoce.iust.ac.ir/article-1-280-en.html</url></related-urls><pdf-urls><url>http://ijoce.iust.ac.ir/article-1-280-en.pdf</url></pdf-urls></urls><language>eng</language><access-date>2017</access-date></record></Cite></EndNote>51, in article from Tcherniak, it uses adjoint method as a way to calculate the sensitivities. While in article from Yaghoobi et al. ADDIN EN.CITE <EndNote><Cite><Author>Yaghoobi</Author><Year>2017</Year><RecNum>86</RecNum><DisplayText>51</DisplayText><record><rec-number>86</rec-number><foreign-keys><key app=”EN” db-id=”eef20vv9h99psxes2zox2fsk52pxsf9fss90″ timestamp=”1526473046″>86</key></foreign-keys><ref-type name=”Journal Article”>17</ref-type><contributors><authors><author>Yaghoobi, N.</author><author>Hassani, B.</author></authors></contributors><titles><title>TOPOLOGICAL OPTIMIZATION OF VIBRATING CONTINUUM STRUCTURES FOR OPTIMAL NATURAL EIGENFREQUENCY</title><secondary-title>International Journal of Optimization in Civil Engineering</secondary-title></titles><periodical><full-title>International Journal of Optimization in Civil Engineering</full-title></periodical><pages>1-12</pages><volume>7</volume><number>1</number><section>1</section><keywords><keyword>topology optimization, SIMP, multiple eigenvalues, bound formulation, MMA</keyword></keywords><dates><year>2017</year></dates><isbn>2228-7558</isbn><call-num>A-10-66-122</call-num><work-type>Technical note</work-type><urls><related-urls><url>http://ijoce.iust.ac.ir/article-1-280-en.html</url></related-urls><pdf-urls><url>http://ijoce.iust.ac.ir/article-1-280-en.pdf</url></pdf-urls></urls><language>eng</language><access-date>2017</access-date></record></Cite></EndNote>51, they uses mathematical perturbation analysis to carry out the process ADDIN EN.CITE <EndNote><Cite><Author>Seyranian</Author><Year>1994</Year><RecNum>87</RecNum><DisplayText>52</DisplayText><record><rec-number>87</rec-number><foreign-keys><key app=”EN” db-id=”eef20vv9h99psxes2zox2fsk52pxsf9fss90″ timestamp=”1526473683″>87</key></foreign-keys><ref-type name=”Journal Article”>17</ref-type><contributors><authors><author>Seyranian, A. P.</author><author>Lund, E.</author><author>Olhoff, N.</author></authors></contributors><titles><title>Multiple eigenvalues in structural optimization problems</title><secondary-title>Structural optimization</secondary-title></titles><periodical><full-title>Structural optimization</full-title></periodical><pages>207-227</pages><volume>8</volume><number>4</number><dates><year>1994</year><pub-dates><date>1994/12/01</date></pub-dates></dates><isbn>1615-1488</isbn><urls><related-urls><url>https://doi.org/10.1007/BF01742705</url></related-urls></urls><electronic-resource-num>10.1007/BF01742705</electronic-resource-num></record></Cite></EndNote>52. Thus, using either of the two methods will simplify the sensitivity calculations and process.

The dynamic problem will then be solved and updated by method of moving asymptotes (MMA) ADDIN EN.CITE <EndNote><Cite><Author>Svanberg</Author><Year>1987</Year><RecNum>85</RecNum><DisplayText>53</DisplayText><record><rec-number>85</rec-number><foreign-keys><key app=”EN” db-id=”eef20vv9h99psxes2zox2fsk52pxsf9fss90″ timestamp=”1526472608″>85</key></foreign-keys><ref-type name=”Journal Article”>17</ref-type><contributors><authors><author>Svanberg, Krister</author></authors></contributors><titles><title>The method of moving asymptotes—a new method for structural optimization</title><secondary-title>International Journal for Numerical Methods in Engineering</secondary-title></titles><periodical><full-title>International Journal for Numerical Methods in Engineering</full-title></periodical><pages>359-373</pages><volume>24</volume><number>2</number><dates><year>1987</year></dates><isbn>0029-5981</isbn><urls><related-urls><url>http://usyd.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwtV07T-QwELZ4NFBwsIAO7pDcUaAsiR3nUVDcnUAICSiAeuX4IVFsFmmhoDnxI_iF_BLGGTtrWAooaKxdy7GSzKfPE3vmG0I4G6bJO06whdWmgZbzomGysSqHlUnb0uaVVl3JpXhn-783_KzvWw0PfWB6l0j7BeP3k0IH_AYIQAsggPbTMMAq0d1JOu4fyOnj-O5-Al5miHXIpastHka60EMUlu1EOSZAK2Ofrxk7s_O7iS2mQx5cPOBBkIuadTN2QbeR9GG_rwN-fAgw6-jGxwprzMsDZkr7kI6QFlAnosb6K0ODbJo6qVeGZW0D3WLKtIcVi7iTe2lwXIY5VjiZY3ivGDs2w6xgTqAtTP9GSvvdEtcHHqJIMxvB9aPoeiezPta36v7ItMnN1SJZBreXuVIM2eXf_lAKfGceIobckwYN0JQdvr2fyMeJnJXrdbLmTUH_IB42yIJpB-SH_-Kgns-nA7Ia2QT-nfcavtNNcgbQoQgIOrEUoUNn0Hl5epYUQBPGgN3pDDQ0Bs0WuTk5vv53mvjKG4nKWCGSTFhltWKqqatKKG4qZmtZpgpeiywbrUVhlK5qVVZNqTIhueHwoe7ooMysrvk2WWonrflJqHHLhNWl0I3IeSVkLrPaSFao3Cou-Q7ZD-9qdIcCK6OPrbT76ZG_yMoMor_JEjy72UOdzVfogHJX</url></related-urls></urls><electronic-resource-num>10.1002/nme.1620240207</electronic-resource-num></record></Cite></EndNote>53. All in all, there are little research on dynamic problems using SIMP method, that includes the interconnection TO problems.
Interfacing MATLAB and ANSYS
It is important to integrate the MATLAB and ANSYS into the TO process. Of which MATLAB serve as the key to create the necessary algorithms for the SIMP method. On the other hand, ANSYS creates the design domain, as well as implementing the loading and boundary conditions to the members, in order for the necessary algorithms to work.

In the past few years, there are already several articles published based on using the Matlab to carry out the TO process. In the most early stage of TO using MATLAB, Sigmund uses 99-line program for a two dimensional TO process ADDIN EN.CITE <EndNote><Cite><Author>Sigmund</Author><Year>2001</Year><RecNum>53</RecNum><DisplayText>41</DisplayText><record><rec-number>53</rec-number><foreign-keys><key app=”EN” db-id=”eef20vv9h99psxes2zox2fsk52pxsf9fss90″ timestamp=”1524993428″>53</key></foreign-keys><ref-type name=”Book”>6</ref-type><contributors><authors><author>Sigmund, Ole</author></authors></contributors><titles><title>Sigmund, O.: A 99 Line Topology Optimization Code Written in MATLAB. Structural and Multidisciplinary Optimization 21, 120-127</title></titles><pages>120-127</pages><volume>21</volume><dates><year>2001</year></dates><urls></urls><electronic-resource-num>10.1007/s001580050176</electronic-resource-num></record></Cite></EndNote>41. However, Sigmund method is proved to be slow on solving larger problems. Therefore, Andreassen et al. created a 88-line program with improved assembly and filtering strategies, which tends to solve the design problem more reliable and faster, of which, using the SIMP method as well ADDIN EN.CITE <EndNote><Cite><Author>Andreassen</Author><Year>2011</Year><RecNum>56</RecNum><DisplayText>54</DisplayText><record><rec-number>56</rec-number><foreign-keys><key app=”EN” db-id=”eef20vv9h99psxes2zox2fsk52pxsf9fss90″ timestamp=”1524995456″>56</key></foreign-keys><ref-type name=”Journal Article”>17</ref-type><contributors><authors><author>Erik Andreassen</author><author>Anders Clausen</author><author>Mattias Schevenels</author><author>Boyan S. Lazarov</author><author>Ole Sigmund</author></authors></contributors><titles><title>Efficient topology optimization in MATLAB using 88 lines of code</title><secondary-title>Struct. Multidiscip. Optim.</secondary-title></titles><periodical><full-title>Struct. Multidiscip. Optim.</full-title></periodical><pages>1-16</pages><volume>43</volume><number>1</number><dates><year>2011</year></dates><isbn>1615-147X</isbn><urls></urls><custom1>1922470</custom1><electronic-resource-num>10.1007/s00158-010-0594-7</electronic-resource-num></record></Cite></EndNote>54. By using the past articles as mentioned, in 2014 Liu et al. uses 169 lines of MATLAB codes, focusing on the topology optimisation on density-based approach, which is also known as the SIMP method ADDIN EN.CITE <EndNote><Cite><Author>Liu</Author><Year>2014</Year><RecNum>52</RecNum><DisplayText>55</DisplayText><record><rec-number>52</rec-number><foreign-keys><key app=”EN” db-id=”eef20vv9h99psxes2zox2fsk52pxsf9fss90″ timestamp=”1524993219″>52</key></foreign-keys><ref-type name=”Journal Article”>17</ref-type><contributors><authors><author>Liu, Kai</author><author>Tovar, Andrés</author></authors></contributors><titles><title>An efficient 3D topology optimization code written in Matlab</title><secondary-title>Structural and Multidisciplinary Optimization</secondary-title></titles><periodical><full-title>Structural and Multidisciplinary Optimization</full-title></periodical><pages>1175-1196</pages><volume>50</volume><number>6</number><dates><year>2014</year><pub-dates><date>2014/12/01</date></pub-dates></dates><isbn>1615-1488</isbn><urls><related-urls><url>https://doi.org/10.1007/s00158-014-1107-x</url></related-urls></urls><electronic-resource-num>10.1007/s00158-014-1107-x</electronic-resource-num></record></Cite></EndNote>55.
The articles mentioned above used SIMP approach for their algorithms. In the year of 2012, Cameron et al. uses polygonal mesh in the design domain, which proves to be robust and the many problems in SIMP method, such as the checkerboard pattern, is significantly reduced ADDIN EN.CITE <EndNote><Cite><Author>Talischi</Author><Year>2012</Year><RecNum>54</RecNum><DisplayText>56</DisplayText><record><rec-number>54</rec-number><foreign-keys><key app=”EN” db-id=”eef20vv9h99psxes2zox2fsk52pxsf9fss90″ timestamp=”1524994693″>54</key></foreign-keys><ref-type name=”Journal Article”>17</ref-type><contributors><authors><author>Talischi, Cameron</author><author>Paulino, Glaucio H.</author><author>Pereira, Anderson</author><author>Menezes, Ivan F. M.</author></authors></contributors><titles><title>PolyMesher: a general-purpose mesh generator for polygonal elements written in Matlab</title><secondary-title>Structural and Multidisciplinary Optimization</secondary-title></titles><periodical><full-title>Structural and Multidisciplinary Optimization</full-title></periodical><pages>309-328</pages><volume>45</volume><number>3</number><dates><year>2012</year><pub-dates><date>2012/03/01</date></pub-dates></dates><isbn>1615-1488</isbn><urls><related-urls><url>https://doi.org/10.1007/s00158-011-0706-z</url></related-urls></urls><electronic-resource-num>10.1007/s00158-011-0706-z</electronic-resource-num></record></Cite></EndNote>56. This can be a way of eliminating the problem in the SIMP method, that is, if the TO is done on the MATLAB software alone. On the other hand, Wang et al. also uses MATLAB to solve for TO problems by using 199-line program, through using level-set method ADDIN EN.CITE <EndNote><Cite><Author>Wang</Author><Year>2006</Year><RecNum>55</RecNum><DisplayText>57</DisplayText><record><rec-number>55</rec-number><foreign-keys><key app=”EN” db-id=”eef20vv9h99psxes2zox2fsk52pxsf9fss90″ timestamp=”1524995274″>55</key></foreign-keys><ref-type name=”Journal Article”>17</ref-type><contributors><authors><author>Wang, Michael Yu</author></authors></contributors><titles><title>Structural Topology Optimization Using Level Set Method</title></titles><dates><year>2006</year></dates><urls></urls></record></Cite></EndNote>57. All in all, MATLAB proves to be very versatile when comes to creating algorithms for the TO process.

One big constraint of using the MATLAB coding solely to solve for TO problem is somewhat inefficient in some ways. This is because for the past work, the design problems are fairly simple, using simple cantilever problem as the design problem. MATLAB has proved itself to be an efficient tool to implement the algorithms for the TO process, but the software is not as proficient enough as using the ANSYS program to illustrate a more complex and harder problem. This is particularly difficult in this current project, where the TO is done on the interconnections, but not on the structures. That said, it is worth to look into the ways and algorithms from the past work, as some of them use the SIMP approach in their solving algorithms ADDIN EN.CITE <EndNote><Cite><Author>Allaire</Author><Year>2005</Year><RecNum>49</RecNum><DisplayText>36</DisplayText><record><rec-number>49</rec-number><foreign-keys><key app=”EN” db-id=”eef20vv9h99psxes2zox2fsk52pxsf9fss90″ timestamp=”1523932368″>49</key></foreign-keys><ref-type name=”Conference Proceedings”>10</ref-type><contributors><authors><author>Allaire, G.</author></authors><secondary-authors><author>Castañeda, P. Ponte</author><author>Telega, J. J.</author><author>Gambin, B.</author></secondary-authors></contributors><titles><title>Topology Optimization with the Homogenization and the Level-Set Methods</title><secondary-title>Nonlinear Homogenization and its Applications to Composites, Polycrystals and Smart Materials</secondary-title></titles><pages>1-13</pages><dates><year>2005</year><pub-dates><date>2005//</date></pub-dates></dates><pub-location>Dordrecht</pub-location><publisher>Springer Netherlands</publisher><isbn>978-1-4020-2623-2</isbn><urls></urls></record></Cite></EndNote>36.
Now, as mentioned above, MATLAB proved to be a sufficient tool to generate necessary algorithms and coding in order for the TO process to work. ANSYS is proficient in establishing the design domain, discretising the domain into fine meshes, as well as implementing necessary boundary and loading conditions for the design problem. Thus, to make the best out of these two software, it is possible to interface them and carry out the TO problems as a whole.
This method is used widely in the recent years, where many TO related articles successfully interface the two software and make the TO process easier and more efficient. This is as seen in the article from K. Atani et al. ADDIN EN.CITE <EndNote><Cite><Author>K. Atani</Author><Year>2016</Year><RecNum>57</RecNum><DisplayText>58</DisplayText><record><rec-number>57</rec-number><foreign-keys><key app=”EN” db-id=”eef20vv9h99psxes2zox2fsk52pxsf9fss90″ timestamp=”1525227988″>57</key></foreign-keys><ref-type name=”Journal Article”>17</ref-type><contributors><authors><author>K. Atani, A. Makrizi, B. Radi</author></authors></contributors><titles><title>Topology optimization of 3D structures using ANSYS and MATLAB</title></titles><dates><year>2016</year></dates><urls></urls></record></Cite></EndNote>58. They implement SIMP algorithms in MATLAB in conjunction with ANSYS to solve for the design problem. Of which, the method proves to be useful and reliable when comes to solving for cantilever problem, where the optimisation results in the last few iterations are similar ADDIN EN.CITE <EndNote><Cite><Author>K. Atani</Author><Year>2016</Year><RecNum>57</RecNum><DisplayText>58</DisplayText><record><rec-number>57</rec-number><foreign-keys><key app=”EN” db-id=”eef20vv9h99psxes2zox2fsk52pxsf9fss90″ timestamp=”1525227988″>57</key></foreign-keys><ref-type name=”Journal Article”>17</ref-type><contributors><authors><author>K. Atani, A. Makrizi, B. Radi</author></authors></contributors><titles><title>Topology optimization of 3D structures using ANSYS and MATLAB</title></titles><dates><year>2016</year></dates><urls></urls></record></Cite></EndNote>58. In the year of 2014, A Gauchía et al, published a book article, detailing the steps to interface both software, as well as the post processing needed for the TO process ADDIN EN.CITE <EndNote><Cite><Author>Gauchía</Author><Year>2014</Year><RecNum>58</RecNum><DisplayText>59</DisplayText><record><rec-number>58</rec-number><foreign-keys><key app=”EN” db-id=”eef20vv9h99psxes2zox2fsk52pxsf9fss90″ timestamp=”1525228990″>58</key></foreign-keys><ref-type name=”Book”>6</ref-type><contributors><authors><author>Gauchía, A.</author><author>Boada, Beatriz</author><author>Boada, María</author><author>Diaz, V.</author></authors></contributors><titles><title>Integration of MATLAB and ANSYS for Advanced Analysis of Vehicle Structures</title></titles><pages>1-22</pages><dates><year>2014</year></dates><isbn>978-953-51-1719-3</isbn><urls></urls><electronic-resource-num>10.5772/57390</electronic-resource-num></record></Cite></EndNote>59. It uses GA method for the TO process, however, it is still worth looking into and implement the necessary methods and steps into this current project, which uses SIMP method on interconnection TO.
It is noted that the ANSYS software that will be used is ANSYS Mechanical Advanced (MAPDL). This software can be particularly useful in analysing a typical TO problem. Instead of using the Graphical User Interface (GUI) in the program, a series of ANSYS Parametric Design Language (APDL) coding are used to generate the design domain, meshing, as well as loading and boundary conditions for the design program.

The advantage of using the APDL codes over GUI is that the process can be done fairly quickly in a shorter time. By importing the APDL codes into the MAPDL, which is written in the text file, geometry and the loading parameters of the design problem can be created in seconds. Of which, if GUI is used instead, the user will have to spend longer time to create the same outcome as described earlier. This is not particularly efficient, as the computational time is one of the main priorities in TO. Generating the design problem in the MAPDL should be done as quickly as possible.
After creating the geometry, MATLAB will then carry out the necessary algorithms for the TO process. Generated results from the MAPDL will then be exported to MATLAB for converging criterion or any other criterions. MATLAB will then decide to carry out the next iteration or none.
If another iteration is needed, the results file will be imported into the MAPDL to carry out another set of TO process, until certain requirement is met. All these steps are detailed in the article published by A Gauchía et al. ADDIN EN.CITE <EndNote><Cite><Author>Gauchía</Author><Year>2014</Year><RecNum>58</RecNum><DisplayText>59</DisplayText><record><rec-number>58</rec-number><foreign-keys><key app=”EN” db-id=”eef20vv9h99psxes2zox2fsk52pxsf9fss90″ timestamp=”1525228990″>58</key></foreign-keys><ref-type name=”Book”>6</ref-type><contributors><authors><author>Gauchía, A.</author><author>Boada, Beatriz</author><author>Boada, María</author><author>Diaz, V.</author></authors></contributors><titles><title>Integration of MATLAB and ANSYS for Advanced Analysis of Vehicle Structures</title></titles><pages>1-22</pages><dates><year>2014</year></dates><isbn>978-953-51-1719-3</isbn><urls></urls><electronic-resource-num>10.5772/57390</electronic-resource-num></record></Cite></EndNote>59. The methods that are used in the articles mentioned above will be used in this project, as it serves as a good reference that details the steps and procedures to interface the MATLAB and ANSYS software together.
Conclusion
Why SIMP is the best out of all
Efficiency, history, less problematic, robust, coding simpler and relevancy to the computational time
Why SIMP is good to use on interconnection problems, as compared to other methods
How can this interconnection optimisation benefit the industry, in major point!
GA method can be proved quite useful in TO but its concept takes longer time when comes to coding. The computational time for the method could be longer than any other methods mentioned above, as described in the GA method section of this literature review. LSM can be problematic as the generated boundary of the solution can be irregular, and this will pose great challenge in manufacturability and the relevancy in interconnections. For ESO, it has shown in many articles that BESO could be a better way for TO process. This is due to the fact that the BESO method can both add and remove elements in each iteration process, giving it an edge as compare to ESO method, which only remove elements in the design domain in the iterations.
SIMP solely consider the density of the elements used in the design domain, which are represented as 0 or other numerical values and finding out the minimal necessary material usage to support the loading conditions, the optimal solution are then considered through OC or MOC, arriving to the final solution through many iterations. This thus makes SIMP and BESO the more preferable approaches to solve for interconnection TO problem. as according to article from Aremu et al. ADDIN EN.CITE <EndNote><Cite><Author>Aremu</Author><Year>2010</Year><RecNum>1</RecNum><DisplayText>10</DisplayText><record><rec-number>1</rec-number><foreign-keys><key app=”EN” db-id=”eef20vv9h99psxes2zox2fsk52pxsf9fss90″ timestamp=”1520762454″>1</key></foreign-keys><ref-type name=”Book”>6</ref-type><contributors><authors><author>Aremu, Adedeji</author><author>Ashcroft, Ian</author><author>Hague, Richard</author><author>Wildman, Ricky</author><author>Tuck, Christopher</author></authors></contributors><titles><title>Suitability of SIMP and BESO topology optimization algorithms for additive manufacture</title></titles><pages>679-692</pages><dates><year>2010</year></dates><urls></urls></record></Cite></EndNote>10, BESO and SIMP are the most widely used method in the current industry, as due to their success in their practical TO solutions.
All in all, there are pros and cons in every TO methods as mentioned in this literature review. It is to say that the SIMP method is chosen for this interconnection TO thesis problem due to its simplicity in concept and the robustness in many TO analysis that had been done in the past.
It is noted that stiffness-based problems are widely analysed in many TO methods as seen in the many literature as listed in this review. However, only little studies are made on solving dynamic problems through SIMP method. That includes the interconnection topology optimisation as well.References
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