基于无单元Galerkin方法的受迫振动下的连续体结构拓扑优化  

TOPOLOGY OPTIMIZATION OF CONTINUUM STRUCTURES SUBJECTED TO FORCED VIBRATION BASED ON THE ELEMENT-FREE GALERKIN METHOD

作　　者：郑娟[1] 龙述尧[1] 李光耀[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：《固体力学学报》2011年第5期527-533,共7页Chinese Journal of Solid Mechanics

基　　金：国家自然科学基金(10972075);国家973计划(2010CB3228005);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)资助

摘　　要：基于无单元Galerkin法(EFG)对受迫振动下的连续体结构进行拓扑优化设计.选取节点的相对密度作为设计变量,以动柔度最小化为目标函数,基于带惩罚的各向同性固体材料模型(SIMP)建立了受迫振动下的连续体结构拓扑优化模型,采用伴随法求解得到目标函数的敏度分析公式,利用优化准则法对优化模型进行求解.通过经典的二维连续体结构拓扑优化算例证明了该方法的可行性和有效性.In this paper,the element-free Galerkin method （EFG） is applied to carry out the topology optimization of the continuum structures subjected to a forced vibration. Considering the relative density of nodes as design variables,the minimization of dynamic compliance as an objective function,the mathemati- cal formulation of the topology optimization is developed using the SIMP （solid isotropic microstructures with penalization） interpolation scheme. Sensitivity of the objective function is derived based on the adjoint method. The optimization formulation is solved by the optimality criteria method. Numerical examples show that the proposed approach is feasible and efficient for the topology optimization of the continuum structures subjected to a forced vibration.

关 键 词：无单元Galerkin方法(EFG) 受迫振动 SIMP插值模型 优化准则方法 连续体结构拓扑优化设计 

分 类 号：O321[理学—一般力学与力学基础]