Research of the Checkerboard Pattern Suppression Method in Structural Topological Optimization

DOU Lin-long; YIN Yi-hui; LIU Yuan-dong

doi:10.3879/j.issn.1000-0887.2014.08.010

Volume 35 Issue 8

Turn off MathJax

Article Contents

Article Navigation > Applied Mathematics and Mechanics > 2014 > 35(8): 920-929

DOU Lin-long, YIN Yi-hui, LIU Yuan-dong. Research of the Checkerboard Pattern Suppression Method in Structural Topological Optimization[J]. Applied Mathematics and Mechanics, 2014, 35(8): 920-929. doi: 10.3879/j.issn.1000-0887.2014.08.010

Citation:

PDF( 3735 KB)

Research of the Checkerboard Pattern Suppression Method in Structural Topological Optimization

doi: 10.3879/j.issn.1000-0887.2014.08.010

Institute of Systems Engineering, China Academy of Engineering Physics, Mianyang, Sichuan 621900, P.R.China

Received Date: 2014-01-03
Publish Date: 2014-08-15

Abstract

Abstract

Aimed at the calculation of elements’weight coefficients in the checkerboard pattern filtering technique, a previous checkerboard pattern suppression method was improved, and a more generalized weight coefficient formula with more specific physical meanings was proposed. The topological optimization model, in which the material elastoplastic deformation was considered, was established under stress constraint conditions, and the improved checkerboard pattern suppression method was employed in the structural topological optimization process with the ESO method. Two numerical examples were implemented. The results show that the improved checkerboard pattern suppression method has better suppression effects than the previous one, and is applicable to the topological optimization of not only linearmaterial structures, but also nonlinearmaterial structures.
- weight coefficient,
- checkerboard pattern,
- structural topological optimization,
- elasto-plastic material,
- ESO method

FullText(HTML)

References(17)

References

[1]	Jog C S, Haber R B. Stability of finite element models for distributed-parameter optimization and topology design[J].Computer Methods in Applied Mechanics and Engineering,1996, 130(3/4): 203-226.
[2]	Rodrigues H, Fernandes P. A material based model for topology optimization of thermoelastic structures[J].International Journal for Numerical Methods in Engineering,1995, 38(12): 1951-1965.
[3]	Haber R B, Jog C S, Bendse M P. Variable-topology shape optimization with a constraint on perimeter[C]//Gilmore B J, Hoeltzel D A, Dutta D, Eschenauer H A eds.Advances in Design Automation.New York: ASME , 1994: 261-272.
[4]	Borrvall T. Topology optimization of elastic continua using restriction[J].Archives of Computational Methods in Engineering, 2001,8(4): 351-385.
[5]	Petersson J, Sigmund O. Slope constrained topology optimization[J].International Journal for Numerical Methods in Engineering,1998,41(8): 1417-1434.
[6]	Zhou M, Shyy Y K, Thomas H L. Checkerboard and minimum member size control in topology optimization[J].Structural and Multidisciplinary Optimization,2001,21(2): 152-158.
[7]	Bruns T E, Tortorelli D A. Topology optimization of nonlinear elastic structures and compliant mechanisms[J].Computer Methods in Applied Mechanics and Engineering,2001,190(26/27): 3443-3459.
[8]	Bourdin B. Filters in topology optimization [J].International Journal for Numerical Methods in Engineering,2001,50(9): 2143-2158.
[9]	Sigmund O, Petersson J. Numerical instabilities in topology optimization: a survey on procedures dealing with checkerboards, mesh-dependencies and local minima[J].Structural optimization,1998,16(1): 68-75.
[10]	Sigmund O. Morphology-based black and white filters for topology optimization[J].Structural and Multidisciplinary Optimization,2007,33(4/5): 401-424.
[11]	Hu S B, Chen L P, Zhang Y Q, Yang J Z, Wang S T. A crossing sensitivity filter for structural topology optimization with chamfering, rounding, and checkerboard-free patterns[J].Structural and Multidisciplinary Optimization,2009,37(5): 529-540.
[12]	Huang X, Xie Y M. Topology optimization of nonlinear structures under displacement loading[J].Engineering Structures,2008,30(7): 2057-2068.
[13]	Li Q, Steven G P, Xie Y M. A simple checkerboard suppression algorithm for evolutionary structural optimization[J].Structural and Multidisciplinary,2001,22(3): 230-239.
[14]	郭中泽, 陈裕泽, 张卫红, 邓克文. 渐进优化法的一种高阶棋盘格式抑制方法[J]. 机械设计, 2006,23(5): 1-4.(GUO Zhong-ze, CHEN Yu-ze, ZHANG Wei-hong, DENG Ke-wen. A kind of high ordered checkerboard pattern suppressing algorithm of progressive optimization method [J].Journal of Machine Design,2006,23(5): 1-4.(in Chinese))
[15]	Querin O M, Steven G P, Xie Y M. Topology optimization of structures with material and geometric nonlinearities[C]//AIAA Meeting Papers on Disc,1996: 1812-1818.
[16]	谢亿民, 杨晓英, Steven G P, Querin O M. 渐进结构优化法的基本理论及应用[J]. 工程力学, 1999,16(16): 70-81.(XIE Yi-min, YANG Xiao-ying, Steven G P, Querin O M. The basic theory and application of evolutionary structural optimization method[J].Engineering Mechanics,1999,16(16): 70-81.(in Chinese))
[17]	Poulsen T A. A simple scheme to prevent checkerboard patterns and one-node connected hinges in topology optimization[J].Structural and Multidisciplinary Optimization,2002,24(5): 396-399.