多相材料结构拓扑优化的周长控制方法研究

Investigation of Perimeter Control Methods for Structural Topology Optimization with Multiphase Materials

针对多相材料结构的拓扑优化出现的棋盘格问题,研究了周长约束控制方法。根据多相材料组分情况下结构有限单元密度变量的定义特点,拓展了周长约束的原始定义概念并提出了相应的4种周长控制约束新格式。以结构最大刚度优化设计问题为例,结合凸规划对偶求解方法验证了4种格式的有效性。计算结果表明:独立控制各类变量周长的方式能更有效地实现多相材料结构的拓扑优化设计,获得消除棋盘格和中间变量值的清晰结果。

The development of perimeter control of the checkerboard involved in structure topology optimization of multiphase materials is presented. Based on the characteristics of density design variables associated with multiphase materials, the general concept of perimeter control is extended and four kinds of perimeter constraints are proposed in this paper. A comparative study of these perimeter constraints is carried out based on several 2D topology optimization examples that are extensively used in the literature for the compliance minimization. Design optimization problems are solved by convex linear programming. Numerical experiences show that the perimeter control using each kind of design variables separately is effective and can be directly extended to problems of multiphase materials. Checkerboards and intermediate values of density variables are able to be eliminated efficiently.