力学学报 ›› 2007, Vol. 23 ›› Issue (6): 796-803.doi: 10.6052/0459-1879-2007-6-2007-191

• 研究论文 • 上一篇    下一篇

基于结构拓扑随机变异的水平集优化方法

荣见华 梁清泉 杨端生   

  1. 长沙理工大学汽车与机械工程学院 Faculty of Engineering and Surveying, The University of Southern Queensland, Toowoomba, QLD 4350, Australia 长沙理工大学汽车与机械工程学院
  • 收稿日期:2007-04-17 修回日期:2007-06-04 出版日期:2007-11-18 发布日期:2007-11-18

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

Jianhua Rong Qingquan Liang Duansheng Yang   

  • Received:2007-04-17 Revised:2007-06-04 Online:2007-11-18 Published:2007-11-18

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.

关键词: 固体力学, 结构优化, 拓扑优化, 水平集方法, 随机变异

Abstract: The level set method was firstly introduced into the structural topology optimization by Sethian et al. Wang et al. studied structural topology optimization by incorporating the shape derivative or sensitivity analysis with the level set model. In essence, the method employs the implicit moving material interface models or the level set vector to represent complex interfaces, and the movement of the material interfaces is governed by a Hamilton--Jacobi type partial differential equation, whose robust numerical algorithm can handle topology merging or breaking naturally during the topology optimization process. In order to consider limited maximum design domain etc. practical requirements, Rong proposed an improved level set method for topology optimization of continuum structures. However, the level set based topology optimization method is unable to nucleate holes within the structural material, which is far from the structural boundaries. In order to overcome the difficulty generating new material holes, the material topological derivative analysis was incorporated into the level set method. The level set method based on topological derivatives employs topological derivative information and the structural volume reduction quantity to identify hole nucleation sites. And the initial structure must be set to the maximum design domain structure for this method. Moreover, it is not fit to solving the topology optimization problem with an equality volume constraint. In order to solve this problem and overcome the difficulty of that the level set based topology optimization method is unable to nucleate holes within the structural material, this paper proposes a new level set method for structural topology optimization based on random topology mutations. At first, this paper introduces a new optimization scheme with topology mutations in the optimization iteration process in a small possibility random way. Second, a mutation operator is given and the proposed algorithm convergence is discussed. Finally, a new topology optimization method, which incorporates topology mutations into the level set method for structural topology optimization with maximum design domain limits, is proposed. The algorithm of the objective function of the problem being the strain energy with a material volume constraint is implemented. The benefit and advantages of the proposed method are illustrated with examples.

Key words: Solid Mechanics, Structural Optimization, topology optimization, level set method, random mutation