EFG法在拓扑优化中的灵敏度分析与应用

针对传统拓扑优化过程中所出现的数值不稳定性现象,以节点相对密度为设计变量,结构的柔度最小化为目标函数,提出了一种以无网格Galerkin法为数值分析方法的结构拓扑优化数学模型。利用SIMP插值模型和优化准则法,推导出其灵敏度分析算法,并编写了相应的计算程序,完成了两个连续体结构的拓扑优化。所得结果与基于有限元法的拓扑优化结果对比显示,应用无网格Galerkin法对结构进行拓扑优化设计,不仅能有效抑制棋盘格现象,且具有较好的迭代收敛性。

Sensitivity analysis and applied research on topology optimization based on element-free Galerkin method

To prevent numerical instabilities occurring in the conventional topology optimization, we present a model of structural topology optimization based on the element-free Galerkin method （EFG）, in which the relative density of nodes is chosen as design variables and the minimized compliance as the objective function. The algorithm of sensitivity was derived and MATLAB programs were written to finish two topology optimization examples of continuum structures using Solid Isotropic Microstructure of Penalization （SIMP） and the optimality criteria method. Compared with the results obtained by the finite element method, the proposed method is not only effective on suppressing checkerboards but also has better convergence.