基于无网格数值求解技术的二维连续体结构拓扑优化设计

将无网格径向点插值法(RPIM)引入到连续体结构拓扑优化设计中。在优化问题中,选取节点的相对密度作为设计变量,以结构的柔度最小化作为目标函数,基于带惩罚的各向同性固体材料模型(SIMP)建立了结构拓扑优化的数学模型,推导了目标函数和体积约束的灵敏度,利用优化准则法进行求解。算例表明了应用无网格径向点插值法进行结构拓扑优化设计的可行性和有效性,同时表明选取节点的相对密度作为设计变量可以有效地克服拓扑优化中的棋盘格现象。

The topology optimization design of the continuum structure based on the meshless numerical technique

In this paper,the meshless radial point interpolation method(RPIM) is applied to carry out the topology optimization of the continuum structure.Considering the relative density of nodes as design variables,and the minimization of compliance as an objective function,the mathematical formulation of the topology optimization is developed using the SIMP(solid isotropic micro-structures with penalization) interpolation scheme.The optimization formulation is solved by the optimality criteria method.Numerical exam...