基于半隐式格式的水平集法连续体结构形状和拓扑优化方法

提出一种改进的基于水平集方法的结构拓扑优化方法.将半隐式的加性算子分裂方法(AOS)引入传统的水平集方程求解,使得原来的Hamilton-Jacobi偏微分方程摆脱了差分法中CFL条件对时间步长的严格限制,差分格式变得高效且稳定.在求解水平集方程过程中不用再对高维的水平集函数进行耗时的周期性的初始化,这样解决了传统水平集方法在优化过程中不能生成新孔的问题.通过典型算例验证了该文算法的有效性.

A LEVEL SET METHOD FOR TOPOLOGY OPTIMIZATION USING AOS SCHEME

This paper presents an extended level set method for topology optimization in which a semi-implicit additive operator splitting (AOS) scheme is included to solve the Hamilton-Jacobi equation. Thus, the time step size to satisfy the CFL condition for the up-wind scheme is totally eliminated. The finite difference format is now unconditionally stable and without any step size restriction, which leads the present method to a higher efficiency and stability. In addition, the time-consuming procedure for regularly reinitializing the level set function is avoided. As a result, the well-recognized disadvantage of no mechanism being included to creating new holes inside the material domain in the conventional level set method is accordingly resolved. A typical example is applied to demonstrate the availability of the present method.