Topology description function based method for material design

Abstract

The purpose of this paper is to investigate the application of topology description function (TDF) in material design. Using TDF to describe the topology of the microstructure, the formulation and the solving technique of the design problem of materials with prescribed mechanical properties are presented. By presenting the TDF as the sum of a series of basis functions determined by parameters, the topology optimization of material microstructure is formulated as a size optimization problem whose design variables are parameters of TDF basis functions and independent of the mesh of the design domain. By this method, high quality topologies for describing the distribution of constituent material in design domain can be obtained and checkerboard problem often met in the variable density method is avoided. Compared with the conventional level set method, the optimization problem can be solved simply by existing optimization techniques without the process to solve the ‘Hamilton-Jacobi-type’ equation by the difference method. The method proposed is illustrated with two 2D examples. One gives the unit cell with positive Poisson’s ratio, the other with negative Poisson’s ratio. The examples show the method based on TDF is effective for material design.