Solving topology optimization problems by the Guide-Weight method

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.

Key words： Guide-Weight method; topology optimization; SIMP method

Acknowledgments

The authors gratefully acknowledge the discussion on the paper with professor Jianbin Du (Institute of Dynamics and Control, School of Aerospace, Tsinghua University).

This work was supported in part by the National Natural Science Foundation of China (Grant No. 51075222), High Technology Research and Development Program (863 Program) of China (No. 2010AA101404), and the Program for New Century Excellent Talents in University of China (No. NCET-08-0323).

References

1 Bendsoe M P, Kikuchi N. Generating optimal topologies in structural design using homogenization method. Computer Methods in Applied Mechanics and Engineering, 1988, 71(2): 197-224

2 Grujicic M, Arakere G, Pisu P, Ayalew B, Seyr N, Erdmann M, Holzleitner J. Etc. Application of topology, size and shape optimization methods in polymer metal hybrid structural lightweight engineering. Multidiscipline Modeling in Materials and Structures, 2008, 4(4): 305-330

3 Bendsoe M P, Sigmund O. Topology Optimization: Theory,Methods and Applications. Springer Berlin, 2003

4 Eschenauer H A, Olhoff N. Topology optimization of continuum structure: a review. Applied Mechanics Reviews, 2001, 54(4): 331-390

5 Sigmund O. Manufacturing tolerant topology optimization. Acta Mechanica Sinica, 2009, 25(2): 227-239

6 Xie Y M, Steven G P. A Simple evolutionary procedure for structural optimization. Computers & Structures, 1993, 49(5): 885-896

7 Bendsoe M P, Sigmund O. Material interpolation schemes in topology optimization. Archive of Applied Mechanics, 1999, 69(9-10): 635-654

8 Rozvany G I N. A critical review of established methods of structural topology optimization. Structural and Multidisciplinary Optimization, 2009, 37(3): 217-237

9 Sui Y K, Yang D Q. etc. Uniform ICM theory and method on optimization of structural topology for skeleton and continuum structures. Chinease Journal of Computational Mechanics, 2000, 17(1): 28-33

10 Peng X R, Sui Y K. Topological optimization of continuum structure with static and displacement and frenquency constraints by ICM method. Chinease Journal of Computational Mechanics, 2006, 23(4): 391-396

11 Rozvany G I N, Zhou M. The COC algorithm, part I: cross-section optimization or sizing. Computer Methods in Applied Mechanics and Engineering, 1991, 89(1-3): 281-308

12 Rozvany G I N, Zhou M. The COC algorithm, part II: topological, geometrical and generalized shape optimization. Computer Methods in Applied Mechanics and Engineering, 1991, 89(1-3): 309-336

13 Zhou M, Rozvany G I N. DCOC: an optimality criteria method for large systems part I: theory. Structural Optimization, 1992, 5(1-2): 12-25

14 Zhou M, Rozvany G I N. DCOC: an optimality criteria method for large systems part II: algorithm. Structural Optimization, 1992, 6(3): 250-262

15 Schmit L A Jr, Farshi B. Some approximation concepts for structural synthesis. AIAA Journal, 1974, 12(5): 692-699

16 Barthelemy JFM, Haftka RT. Approximation concepts for optimum structural design-a review. Structural and Multidisciplinary Optimization, 1993, 5(3)

17 Fleury C. A unified approach to structural weight minimization. Computer Methods in Applied Mechanics and Engineering, 1979, 20(1): 17-38

18 Chen S, Ye S A. Guide-Weight criterion method for the optimal design of antenna structures. Engineering Optimization, 1986, 10(3): 199-216

19 Chen S. Some modern design methods of precise and complex structures (In Chinese). Press of Beijing University of Aeronautics and Astronautics, Beijing, 1992

20 Chen S.Analysis, Synthesis and Optimization of Engineering Structural Systems (In Chinese). China Science Culture Publishing House, Hongkong, 2008

21 Beckers M. Topology optimization using a dual method with discrete variables. Structural Optimization, 1999, 17(1): 14-24

22 Jog C S. A dual algorithm for the topology optimization of non-linear elastic structures. International Journal for Numerical Methods in Engineering, 2009, 77(4): 502-517

23 Hammer V B, Olhoff N. Topology optimization of continuum structures subjected to pressure loading. Structural and Multidisciplinary Optimization, 2000, 19(2): 85-92

24 Levy R. Fixed point theory and structural optimization. Engineering Optimization, 1991, 17(4): 251-261

25 Svanberg K. The method of moving asymptotes-a new method for structural optimization. International Journal for Numerical Methods in Engineering, 1987, 24(2): 359-373

26 Bruyneel M, Duysinx P, Fleury C. A family of MMA approximations for structural optimization. Structural and Multidisciplinary Optimization., 2002, 24(4): 263-276

27 Duysinx P. Layout optimization: a mathematical programming approach. Danish Center for Applied Mathematics and Mechanics, DCAMM Report No. 540 (<month>March</month>1997)

28 Chang H. Research of auto-solving Guide-Weight functions and develop of auto-optimization software SOGA1 (In Chinese). University of Guangxi, Guangxi China, 2008