基于拓扑导数变化规律的快速水平集拓扑优化方法

A Rapid Level Set Method Based on Topological Derivative Change Law for Structural Topology Optimization

在基于水平集拓扑优化方法的优化过程中,孔洞的融合与分裂实现了边界与拓扑的演化,其本质就是设计区域内材料的增加或删除变化。这种材料的增加与删除变化,在其变化的同时,会对设计区域内相应拓扑导数产生不同的影响,进而得到不同的拓扑导数数值。考虑到拓扑导数数值的这种变化规律,建立新的基于拓扑导数数值变化规律的判断准则,在孔洞变化的同时,尽可能多的删除不必要存在材料。以多删除材料的方式实现减少迭代次数目的,因此提高了水平集优化方法的收敛速度、节约了计算时间、提高了计算效率,并通过典型算例验证了该方法的高效性和有效性。

A rapid level set method is proposed in the present work. The most prominent characteristic of the proposed method is acceleration optimization process for structural topology＂ optimization. In the optimization, the topological derivative can create new holes inside the material domain. On the other hand, when a new hole is created at the specific point, the corresponding topological derivative is changed by the changing simultaneously. So a new criterion is founded based on the changed law. During the optimization, the material is removed via the new criterion as much as possible. With the materials is removed quickly, the number of iterations is reduced, the computation time is saved and the calculation efficiency is improved obviously. Finally, the validity and high efficiency of the rapid level set method is proved by two widely researched examples.