动力学自然单元法的谐波激励下的连续体结构拓扑优化

Topology optimization of continuum structures under frequency excitation load based on dynamic natural element method

自然单元法是一种基于Voronoi图构造形函数的无网格方法,根据自然单元法的优点,提出了动力学自然单元法频率激励载荷下连续体的结构拓扑优化计算。采用各向同性固体微结构惩罚(SIMP)模型,将节点相对密度作为设计变量,建立以动柔度最小为目标函数,频率激励载荷作用下的拓扑优化模型。采用伴随分析法进行灵敏度分析并利用优化准则法对优化模型进行求解。通过数值算例计算,不仅得到了无棋盘格现象的优化结果,而且相比其它无网格方法提高了计算效率,说明该方法具有可行性和优越性。

The natural element method is a meshless one with shape function formed using Voronoi diagram. According to advantages of the natural element method, topology optimization method of continuum structures under frequency excitation load based on dynamic natural element method was proposed. Using isotropic solid micro-structure penalty(ISMP) model, taking relative density of nodes as design variables and the dynamic flexibility being the minimum as the objective, a topology optimization model was built under frequency excitation load. The adjoint analysis method was used to perform sensitivity analysis, and the optimization criteria method was used to solve the optimization model. The numerical example computation results showed that this method can be used not only to obtain the optimization results with chess-free phenomenon, but also has a higher computational efficiency compared with other meshless methods to verify its feasibility and effectiveness.