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 引用本文: 荣见华 梁清泉 杨端生. 基于结构拓扑随机变异的水平集优化方法[J]. 力学学报, 2007, 23(6): 796-803.
Jianhua Rong, Qingquan Liang, Duansheng Yang. A level set method for structural topology optimization based on topology random mutations[J]. Chinese Journal of Theoretical and Applied Mechanics, 2007, 23(6): 796-803.
 Citation: Jianhua Rong, Qingquan Liang, Duansheng Yang. A level set method for structural topology optimization based on topology random mutations[J]. Chinese Journal of Theoretical and Applied Mechanics, 2007, 23(6): 796-803.

## A level set method for structural topology optimization based on topology random mutations

• 摘要: 基于结构拓扑导数的水平集优化方法, 利用结构拓扑导数信息和通过不断减少结构体积的方式来确定需开孔的结构位置,需选用最大设计区域结构作为初始优化结构. 该方法不适合求解结构体积等式约束的优化问题. 为了解决上述问题和克服水平集方法不能在结构内产生新孔洞的困难,提出了一种基于结构拓扑随机变异的水平集优化方法. 引进了以小概率随机方式进行结构拓扑变异的结构优化方案. 设计了变异算子,讨论了提出方法的收敛性情况. 最后,结合考虑结构最大设计区域限制的结构拓扑优化的水平集方法,建立了一套新的涉及结构柔顺度作为目标函数,体积作约束条件的水平集演化算法. 给出的算例验证了该方法的正确性和有效性.

Abstract: The level set method was firstly introduced into the structuraltopology optimization by Sethian et al. Wang et al. studied structuraltopology optimization by incorporating the shape derivative or sensitivityanalysis with the level set model. In essence, the method employs theimplicit moving material interface models or the level set vector torepresent complex interfaces, and the movement of the material interfaces isgoverned by a Hamilton--Jacobi type partial differential equation, whoserobust numerical algorithm can handle topology merging or breaking naturallyduring the topology optimization process. In order to consider limitedmaximum design domain etc. practical requirements, Rong proposed an improvedlevel set method for topology optimization of continuum structures. However,the level set based topology optimization method is unable to nucleate holeswithin the structural material, which is far from the structural boundaries.In order to overcome the difficulty generating new material holes, thematerial topological derivative analysis was incorporated into the level setmethod.The level set method based on topological derivatives employs topologicalderivative information and the structural volume reduction quantity toidentify hole nucleation sites. And the initial structure must be set to themaximum design domain structure for this method. Moreover, it is not fit tosolving the topology optimization problem with an equality volumeconstraint. In order to solve this problem and overcome the difficulty ofthat the level set based topology optimization method is unable to nucleateholes within the structural material, this paper proposes a new level setmethod for structural topology optimization based on random topologymutations. At first, this paper introduces a new optimization scheme withtopology mutations in the optimization iteration process in a smallpossibility random way. Second, a mutation operator is given and theproposed algorithm convergence is discussed. Finally, a new topologyoptimization method, which incorporates topology mutations into the levelset method for structural topology optimization with maximum design domainlimits, is proposed. The algorithm of the objective function of the problembeing the strain energy with a material volume constraint is implemented.The benefit and advantages of the proposed method are illustrated withexamples.

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