多载荷工况下无网格Galerkin法的拓扑优化  

Topology Optimization under Multi-load Cases Based on Element-free Galerkin Method

作　　者：龚曙光[1] 刘翔[1] 谢桂兰[1] 张建平[1] 

机构地区：[1]湘潭大学机械工程学院,湘潭411105

出　　处：《机械工程学报》2009年第12期137-142,共6页Journal of Mechanical Engineering

基　　金：国家自然科学基金(50875223);湖南省青年项目(06B096);湘潭大学博士启动基金(06QDZ16)资助项目

摘　　要：连续体结构拓扑优化位于产品的概念设计阶段,能够为产品结构的创新提供可能。基于此,提出以节点相对密度作为设计变量,以多载荷工况下结构柔度的加权平均值为目标函数,建立多载荷工况下基于无网格迦辽金法的连续体结构拓扑优化模型,利用Lagrange乘子法来施加本质边界条件,推导出相应的灵敏度计算公式。结合固体各向同性惩罚插值模型编写程序完成两个多工况的拓扑优化算例,并对单、多工况的优化结果进行了比较。所得结果表明,多工况的优化结果并不是单工况结果的简单迭加。同时利用节点密度的最大优势是影响域中的密度与位移具有相同的逼近策略,从而使所建立的模型能有效地提高密度场的连续性,并从模型上抑制了棋盘格现象,该方法的可行性得到验证。As a conceptual design of product structure, continuum structural topology optimization can provide presumption for innovation of product. The nodal relative density is chosen as the design variable, and a novel model of continuum structural topology optimization based on element-free Galerkin method under multiple loading conditions is presented, in which the model proposed takes the weighted mean of structure compliance under every loading condition as the objective function. The essential boundary conditions are imposed by Lagrange multipliers. Its sensitivity algorithm is deduced. Integrating with SIMP interpolation model, the two examples of topology optimization under multi-load cases are solved successfully by programming. The optimal results of multi-load cases and single loading condition are investigated. The results obtained show that a multi-case result is not assembled simply by optimal ones under single loading. The uppermost advantage of using nodal density is that the displacement and density in influence domain have the same approximation scheme, and the continuity of density fields is improved. The checkerboard phenomenon occurred frequently in topology optimization can be effectively eliminated in the optimal model proposed. The resulls of example also validate the effectiveness of the model.

关 键 词：拓扑优化 多载荷工况 无网格GALERKIN法 灵敏度分析 

分 类 号：TH122[机械工程—机械设计及理论]