用ICM法拓扑优化静位移及频率约束下连续体结构  

Topological optimization of continuum structure with static displacement and frequency constraints by ICM method

作　　者：彭细荣[1] 隋允康[2] 

机构地区：[1]清华大学深圳研究生院,深圳518055 [2]北京工业大学工程数值模拟中心,100022

出　　处：《计算力学学报》2006年第4期391-396,共6页Chinese Journal of Computational Mechanics

基　　金：国家自然科学基金(10072005);北京市自然科学基金委(3042002);北京市教委(KM200410005019)项目资助和美国MSC公司支持的课题

摘　　要：用ICM方法建立了静位移及频率约束下、重量最小为目标的连续体结构拓扑优化模型。采用独立于截面及形状参数的连续拓扑变量,借助于过滤函数,位移约束用莫尔定理显式化,频率约束用瑞利商求导数借助模态动能及模态应变能近似显式化。用图形过滤处理的方法解决了棋盘格及网格依赖问题。通过构造适当的过滤函数有效地防止了局部模态问题。动态引入防止模态交换的频率约束条件,使迭代过程不发生振荡。算例表明:用ICM方法建立的模型在处理多工况静位移约束、多频率约束及解决局部模态及模态交换等问题上有优势。The topological optimization model of continuum structure that minimizes weight and subjects to static displacement and frequency constraints is established by ICM method. Continuous topological variables independent of cross-sectional or shape variables are adopted. Based on the filter function, the displacement constraints are expressed approximately by Mohr theorem. By differentiating the Rayleigh quotient with respect to design variables, the frequency constraints are expressed approximately by the modal elastic energy and kinetic energy of structure. Adopting image-filtering method, checkerboard patterns and mesh dependence problems are eliminated. Local modal problems are solved by constructing a suitable set of filter functions. By adding additional frequency constraints into optimization model to prevent modal switch from occurring, the oscillation is eliminated during the process of optimization. Several numerical examples reveal that it is convenient for dealing with multi-displacement and multi-frequency constraints and is also convenient for solving local modal and modal switch problems to establish optimization model by ICM method.

关 键 词：连续体结构 拓扑优化 位移约束 频率约束 

分 类 号：O343.1[理学—固体力学]