应力和位移约束下连续结构的有效拓扑优化方法  

An efficient structural topological optimization method for continuum structures with stress and displacement constraints

作　　者：李志强[1] 张运章[2] 宋艳丽[3] 

机构地区：[1]广西大学土木建筑工程学院,南宁530004 [2]河南科技大学数学与统计学院,洛阳471003 [3]河南质量工程职业学院经济与管理系,平顶山467001

出　　处：《应用力学学报》2013年第1期70-75,147-148,共6页Chinese Journal of Applied Mechanics

基　　金：国家自然科学基金(11171269)

摘　　要：为了解决在拥有位移与应力多个约束条件下,以减少结构重量为目标函数的拓扑优化中多约束难处理的问题,本文研究了以位移约束、应力约束、应变能约束重量最小化为目标的拓扑优化关系。通过对目标函数与约束函数的解析敏度推导,证明了它们之间的等价性。得到的准则方程表明:在最优结构中,单元质量与该单元应变能之比等于结构总质量与结构总应变能之比。由于迭代准则方程中的各项都可以在ANSYS有限元分析中直接提取,也不必计算乘子,从而减少了优化过程中的函数调用次数,加快了优化速度。两个算例说明了该方法的简单、高效与适用性。In order to deal with the multiple constraints problem for the topology optimization of elastic structures that aims at minimizing the structural weight subject to displacement and stress constraints,this paper studies the various relationship of the topology optimization theoretically,and proves their equivalence among the questions of topology optimization,in which displacement,stress and strain energy is constraint and weight is objective function.The criterion equations obtained reveal that the essence of them is the same:In optimum structure,the ratio of mass of element and strain energy of the element should be equal to the ratio of total mass of the structure and total strain energy of the structure.For every item can be extracted directly in analysis file of ANSYS and there is no need to calculate the Lagrange multiplier,the proposed method deduces the times of function call and expedites optimal velocity.The simplicity,effectiveness and applicability of the method are demonstrated through two topology optimization examples.

关 键 词：位移约束 应力约束 应变能约束 伪密度 拓扑优化 

分 类 号：O332[理学—一般力学与力学基础]