Investigation of perimeter control methods for structural topology optimization with multiphase materials

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. 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.