多相材料结构拓扑优化：体积约束还是质量约束？  

TOPOLOGY OPTIMIZATION OF STRUCTURES DESIGNED WITH MULTIPHASE MATERIALS:VOLUME CONSTRAINT OR MASS CONSTRAINT?

作　　者：高彤[1,2] 张卫红[1] Duysinx Pierre 

机构地区：[1]西北工业大学现代设计与集成制造技术教育部重点实验室,西安710072 [2]列日大学汽车工程系,比利时列日4000

出　　处：《力学学报》2011年第2期296-305,共10页Chinese Journal of Theoretical and Applied Mechanics

基　　金：国家自然科学基金(10925212,90405016);高等学校博士学科点专项科研基金(20106102110018);高等学校学科创新引智计划(G07050)资助项目~~

摘　　要：针对拓扑优化设计中多年沿用的体积约束作为控制材料用量的思路,研究了采用质量约束开展多相材料结构拓扑优化的新方法,提出了相应的质量约束结构优化问题模型和材料插值模型.通过研究广义SIMP模型和对等混合模型两类多相材料属性插值方法,发现广义SIMP插值模型导致质量约束具有复杂的非线性特征,给优化问题的全局寻优和数值求解带来困难;采用的线性对等混合材料插值策略保证质量约束函数具有线性和变量可分离特征,为拓扑设计问题的数值求解,特别是凸规划寻优提供了极大便利.算例表明多相材料插值策略和结构优化模型的正确性和有效性;优化设计结果的比较说明了使用质量约束相对于体积约束的合理性和必要性,阐述了质量约束在解决结构轻量化布局设计问题的有效性以及所带来的显著收益.Instead of adopting the common idea of using volume constraint in topology optimization,this work is focused on the topology optimization of structures designed with multiphase materials and mass constraint. Related structural optimization models involving mass constraint and material interpolation model are proposed. Based on the study of two types of material interpolation models,i.e.GSIMP and UIM,the former is found to introduce the nonlinearity into the mass constraint which brings numerical difficulties in searching the global optimum of the optimization problem.The adopted UIM model,however,makes the mass constraint linear and design variable separable,which favors the mathematical programming approaches,especially the convex programming methods.Numerical examples show that the presented scheme is reliable and efficient to deal with the structural topology design problems of multiple materials with mass constraint.The mass constraint is proved to be more significant and important than the volume constraint in structural topology optimization.

关 键 词：结构拓扑优化 多相材料 质量约束 体积约束 

分 类 号：TU318[建筑科学—结构工程]