基于无网格局部Petrov-Galerkin法的板结构拓扑优化

Topology optimization of plate structure based on meshless local Petrov-Galerkin method

为将无网格法的优势集成到结构拓扑优化中,基于无网格局部Petrov-Galerkin(MeshlessLocal Petrov-Galerkin,MLPG)法进行板结构的拓扑优化.基于带惩罚的各向同性固体微结构(Solid Isotropic Microstructure with Penalization,SIMP)的拓扑优化模型和优化准则法建立设计变量的优化修正方案.位移场和相对密度场均采用自然邻接点插值形函数进行离散插值.几种典型的拓扑优化算例证明该数值算法的正确性和有效性.

To apply the advantage of meshless method into the structural topology optimization,the topology optimization of plate structure is performed by using the Meshless Local Petrov-Galerkin（MLPG） method.The optimization correction program of the design variables is built by the topology optimization model based on Solid Isotropic Microstructures with Penalization（SIMP） and the optimality criteria method.The natural neighbour interpolation shape function is used to discretize both displacement field and relative density field.Several typical topology optimization examples are used to verify the validity and effectiveness of the numerical method.