Solving topology optimization problems by the Guide-Weight method

doi:10.1007/s11465-010-0126-6

Front Mech Eng

2011, Vol. 6

Issue (1) : 136-150 https://doi.org/10.1007/s11465-010-0126-6

RESEARCH ARTICLE

Solving topology optimization problems by the Guide-Weight method

Xinjun LIU(

), Zhidong LI, Liping WANG, Jinsong WANG

Institute of Manufacturing Engineering, Department of Precision Instruments and Mechanology, Tsinghua University, Beijing 100084, China

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Abstract

Finding a good solution method for topology optimization problems is always paid attention to by the research field because they are subject to the large number of the design variables and to the complexity that occurs because the objective and constraint functions are usually implicit with respect to design variables. Guide-Weight method, proposed first by Chen in 1980s, was effectively and successfully used in antenna structures’ optimization. This paper makes some improvement to it so that it possesses the characteristics of both the optimality criteria methods and the mathematical programming methods. When the Guide-Weight method is applied into topology optimization, it works very well with unified and simple form, wide availability and fast convergence. The algorithm of the Guide-Weight method and the improvement on it are described; two formulations of topology optimization solved by the Guide-Weight method combining with SIMP method are presented; subsequently, three numerical examples are provided, and comparison of the Guide-Weight method with other methods is made.

Keywords Guide-Weight method topology optimization SIMP method

Corresponding Author(s): LIU Xinjun,Email:xinjunliu@mail.tsinghua.edu.cn

Issue Date: 05 March 2011

Cite this article:

Xinjun LIU,Zhidong LI,Liping WANG, et al. Solving topology optimization problems by the Guide-Weight method[J]. Front Mech Eng, 2011, 6(1): 136-150.

URL:

https://academic.hep.com.cn/fme/EN/10.1007/s11465-010-0126-6
https://academic.hep.com.cn/fme/EN/Y2011/V6/I1/136

Fig.1 Calculation procedure

Fig.2 Design domain with working conditions for the (a) 2D problem and (b) 3D problem

Tab.1 Parameters for topology optimization for problem in Fig. 2

Fig.3 Process of compliance variation for the (a) 2D problem and (b) 3D problem

Fig.4 Process of weight variation for the (a) 2D problem and (b) 3D problem

Fig.5 Optimal topologies for the 2D problem of Fig. 2(a) at iterations (a) 2, (b) 6, (c) 10, (d) 20, (e) 30, and (f) 40 solved by the Guide-Weight method

Fig.6 Optimal topology for the 3D problem of Fig. 2(b)

Fig.7 Design domain with working conditions for problem with multiple displacement constraints

Tab.2 Parameters for topology optimization for problems in Fig. 7

Fig.8 Convergence process of the problem in Fig. 7

Fig.9 Optimal topology for the problem of Fig. 7

Tab.3 Parameters for topology optimization solved by the fixed point method

Fig.10 Process of compliance variation for the problem in Fig. 2(a) solved by fixed point method

Fig.11 Process of weight variation for the problem in Fig. 2(a) solved by fixed point method

Fig.12 Optimal topologies for the problem in Fig. 2(a) at iterations (a) 2, (b) 6, (c) 10, (d) 20, (e) 30, and (f) 40 solved by the fixed point method

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