基于固有振型的非确定性振动结构稳健拓扑优化  

ROBUST TOPOLOGY OPTIMIZATION OF UNCERTAINTY VIBRATING STRUCTURES WITH SPECIFIED EIGENMODE SHAPES

作　　者：崔明涛[1] 陈建军[1] 宋宗凤[1] 张耀强[1] 

机构地区：[1]西安电子科技大学机电工程学院,西安710071

出　　处：《机械强度》2008年第2期212-218,共7页Journal of Mechanical Strength

基　　金：国防预研基金(51421060505DZ0155);陕西省自然科学基金(2005A09)资助项目~~

摘　　要：考虑结构材料弹性模量和质量密度的随机性,构建以期望固有振型为目标的振动结构稳健拓扑优化模型,其中引入加权系数构建包括原目标函数均值及其标准差的新目标函数,引入原约束函数的标准差及满足约束的概率指标作为稳健性约束条件。利用Monte Carlo模拟法求目标函数和约束函数的均值和方差。在计算目标函数和约束函数对设计变量灵敏度的基础上,采用序列线性规划方法进行优化求解。两个数值算例及其结果验证所建模型的合理性和方法的有效性。Considering the random uncertainties of elasticity modulus and mass density, the mathematical model of robust topology optimization of vibrating structures is proposed, in which the desired eigenmode shapes are utilized as objectives. The summation weighting coefficient is introduced to build the objective function including the mean value and the standard deviation of the original one, and the standard deviation of original constraints and the probability index of the constraints satisfaction are introduced to build the new constraint functions. The mean value and the standard deviation of objective function and constraints are obtained by Monte Carlo simulation. The sensitivities of objective function and constraints are calculated, based on which the sequential linear programming （SLP） method is used to solve the optimization. Two numerical examples and the results are presented to illustrate the validity of the model and method here.

关 键 词：随机参数 振动结构 固有振型 稳健性 拓扑优化 

分 类 号：O327[理学—一般力学与力学基础] TB114.3[理学—力学]