Multiple objective topology optimal design of multiphase microstructures

The overall behavior of an elastic material with a periodic microstructure is governed by the microstructure, whose effective properties may be computed using a homogenization method. Improvements in materials performance can be obtained by designing new topologies of microstructures of these materials. The topology and volume fraction of the microstructure determines the effective properties of the materials. A multiple objective function model is presented to optimize the topology of the periodic microstructure with two or three-phase materials. The combined value of effective elastic properties is maximized. Constraints on the material volume fraction and the perimeter control are considered for eliminating the checkerboard without the restriction of prescribed microstructure symmetry. By means of the finite element method and convex programming techniques, several cases of optimal design of multiphase microstructures are solved. Influences of volume fraction, mesh and elastic modulus ratio of three-phase materials on the optimal microstructures are discussed.