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  

A LEVEL SET METHOD FOR TOPOLOGY OPTIMIZATION USING AOS SCHEME

作　　者：罗俊召[1] 陈立平[1] 罗震[1] 

机构地区：[1]华中科技大学机械学院CAD中心,武汉430074

出　　处：《固体力学学报》2008年第2期175-180,共6页Chinese Journal of Solid Mechanics

摘　　要：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.This paper presents an extended level set method for topology optimization in which a semiimplicit 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 mechaaccor being included to creating new holes inside the material domain in the conventional level set method is dingly resolved. A typical example is applied to demonstrate the availability of the present method.

关 键 词：拓扑优化 水平集法 加性算子分裂 有限差分法 

分 类 号：TP301.6[自动化与计算机技术—计算机系统结构]