基于无网格径向点插值方法的简谐激励下的连续体结构拓扑优化  

Topology optimization of continuum structures subject to harmonic excitation based on meshless radial point interpolation method

作　　者：郑娟[1] 龙述尧[1] 李光耀[1] 丁灿辉[1] 

机构地区：[1]湖南大学汽车车身先进设计制造国家重点实验室,长沙410082

出　　处：《计算机辅助工程》2011年第1期50-55,共6页Computer Aided Engineering

基　　金：国家自然科学基金(10972075);国家重点基础研究发展计划("九七三"计划)(2010CB3228005);湖南省自然科学基金(10JJ3036);高等学校博士学科点专项科研基金(20090161110012);汽车先进设计和制造技术国家重点实验室建设基金(60870003)

摘　　要：针对用有限元法进行连续体结构拓扑优化时需不断重构网格来处理网格畸变和网格移动,且存在数值计算不稳定等问题,基于无网格径向点插值方法(Radial Point Interpolation Method,RPIM)对简谐激励下的连续体结构进行拓扑优化.选取节点的相对密度作为设计变量,以结构动柔度最小化为目标函数,基于带惩罚的各向同性固体微结构(Solid Isotropic Microstructure with Penalization,SIMP)模型建立简谐激励下的优化模型;采用伴随法求解得到目标函数的敏度分析公式;利用优化准则法求解优化模型.经典的二维连续体结构拓扑优化算例证明该方法的可行性和有效性.While using finite element method to perform topology optimization of continuum structures,there exists the continuous mesh reconstruction problem in dealing with mesh distortion and moving,and the numerical computation is not stable.The meshless Radial Point Interpolation Method（RPIM） is used to carry out the topology optimization of continuum structures subjected to a harmonic excitation.Taking the relative density of nodes as design variables and the dynamic compliance minimization of structures as objective function,the topology optimization model is established using Solid Isotropic Microstructures with Penalization（SIMP） model.The sensitivity analysis of the objective function is derived by the adjoint method.The optimization model is solved by the optimization criteria method.The classical 2D structure topology optimization examples show that the method is feasible and efficient.

关 键 词：连续体结构 拓扑优化 径向点插值方法 简谐激励 带惩罚的各向同性固体微结构模型 优化准则方法 

分 类 号：TB115[理学—数学]