无网格径向点插值法在拓扑优化中的应用

论文基于无网格径向点插值法(RPIM)对连续体结构进行拓扑优化设计.以高斯点的相对密度为设计变量,以结构的柔度最小化为目标函数,利用带惩罚的各向同性固体材料模型(SIMP)和优化准则法,建立了设计变量的迭代格式.利用灵敏度过滤技术有效地消除了点状棋盘格现象.给出了相应的计算流程,并用Fortran程序语言实现其算法.算例证明,应用无网格径向点插值法能够有效地对连续体结构进行拓扑优化设计.

AN APPLICATION OF THE MESHLESS RADIAL POINT INTERPOLATION METHOD TO THE STRUCTURAL TOPOLOGY OPTIMIZATION DESIGN

In this paper, a structural topology optimization design is investigated based on the meshless radial point interpolation method (RPIM). Considering the relative density of Gauss quadrature points as a design variable, and the minimization of compliance as an objective function, the updating scheme for the design variable is created by using the solid isotropic microstructures with penalization (SIMP) and the optimality criteria method. The filter method is applied to eliminate the checkerboard pattern with the point state. The effects of different parameters on the topology optimization design are in detail discussed. Numerical examples show that the proposed approach is feasible and efficient for the topology optimization design.