基频约束下的桁架结构半定规划法拓扑优化  

TRUSS TOPOLOGY OPTIMIZATION WITH FUNDAMENTAL FREQUENCY CONSTRAINTS VIA SEMI-DEFINITE PROGRAMMING

作　　者：李东泽[1] 于登云[2] 马兴瑞[2] 

机构地区：[1]中国空间技术研究院通信卫星事业部,北京100094 [2]中国航天科技集团公司,北京100037

出　　处：《工程力学》2011年第2期181-185,共5页Engineering Mechanics

摘　　要：大型复杂结构出现重频时该频点处不具有通常意义下的导数信息,基于灵敏度分析的优化算法遇到很大困难。若优化模型存在平衡方程等式约束,则为非凸优化,很难找到全局最优解。对此该文以桁架结构为研究对象,采用半定规划法建立了以结构系统体积和基频为约束,以柔度最小为目标的凸优化模型。通过将柔度和基频构造成半定矩阵的形式,将传统优化模型转化为半定规划模型。该模型将杆件横截面积和柔度均视为优化变量,模型的特点是在求解过程中不必计算特征值的灵敏度,对有无重频问题均适用。数值算例表明采用半定规划法处理重频优化问题是正确可行的。It is difficult to calculate the sensitivity coefficients of multiple eigenvalues for large complex structures due to lack of usual differentiability with respect to a design variable,and the equilibrium equation constraints if exists in the model will lead to nonconvex programming.Consequently the global optimum is difficult to find.To avoid this intractable issue,this paper presents a new optimization model for truss structures.The optimized problem is formulated as compliance minimization with volume and fundamental frequency constraints via semidefinite programming（SDP）,and the compliance and fundamental frequency in traditional models are casted as semidefinite matrix constraints,both the cross section and compliance are viewed as variables.In this way,the sensitivity coefficients of multiple eigenvalues are circumvented.The SDP model is applicable both to single and multiple eigenvalues.The theoretical results and the practical use of this model are illustrated by examples at the end of the paper.

关 键 词：桁架 重频 柔度 拓扑优化 半定规划 

分 类 号：O327[理学—一般力学与力学基础]