Research of the Checkerboard Pattern Suppression Method in Structural Topological Optimization
摘要: 针对棋盘格过滤技术中单元权重系数的计算，对已有文献中的棋盘格抑制方法进行改进，提出了物理意义明确且更具一般性的公式.建立含应力约束的弹塑性拓扑优化模型，将改进的棋盘格抑制方法用于弹塑性结构拓扑优化，采用ESO(evolutionary structural optimization)法进行优化.编程实现了两个数值算例，对算例结果分析表明：改进的棋盘格抑制方法具有更好的抑制效果，且该方法并不局限于材料线性范围的拓扑优化，也适用于进行材料非线性的拓扑优化时棋盘格的抑制.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 elastoplastic 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 linearmaterial structures, but also nonlinearmaterial structures.
 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.  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.  Haber R B, Jog C S, Bendse 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.  Borrvall T. Topology optimization of elastic continua using restriction[J].Archives of Computational Methods in Engineering, 2001,8(4): 351-385.  Petersson J, Sigmund O. Slope constrained topology optimization[J].International Journal for Numerical Methods in Engineering,1998,41(8): 1417-1434.  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.  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.  Bourdin B. Filters in topology optimization [J].International Journal for Numerical Methods in Engineering,2001,50(9): 2143-2158.  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.  Sigmund O. Morphology-based black and white filters for topology optimization[J].Structural and Multidisciplinary Optimization,2007,33(4/5): 401-424.  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.  Huang X, Xie Y M. Topology optimization of nonlinear structures under displacement loading[J].Engineering Structures,2008,30(7): 2057-2068.  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.  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))  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.  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))  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.
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