拓扑优化中基于图论的邻接熵过滤方法

Abuttal entropy numerical filter method by graph theory in topology optimization

在拓扑优化中提出一种基于图论的邻接熵过滤方法,通过分析单元的邻接信息,对无效单元进行过滤,从而有效消除棋盘格现象并降低优化结构的网格依赖性.该方法具有数值实现简单、计算量小、适应复杂网格划分、兼容多种有限元求解器等优点.给出了采用邻接熵过滤法的拓扑优化程序流程,用Matlab程序和ANSYS参数化设计语言实现了算法,并通过典型算例证明了该方法的有效性.

An abuttal entropy method to solve the numerical filters in topology optimization is developed,in which the checkerboard pattern and mesh-dependency problem could be solved effectively through analyzing the adjacency information of the structure and filtering the invalid unit.Owing to its less computational complexity,this method could be implemented easily and adapted to the complex mesh and be compared with multiple finite element method solvers.A topology optimization procedure is also given by using the abuttal entropy method and be implemented through Matlab and ANSYS parametric design language.Finally,the validity of this methods is proved through several numerical applications.