Aboudi micromechanical model for topology design of structures

The micromechanical approach to topology design consists of defining a domain of porous material, including the loads and supports, and finding an optimal distribution of the densities. The usual method is to mesh the structure and assign a different density and material orientation to every element. Optimal topologies emerge when using the densities and orientations as design variables in a mathematical programming formulation in conjunction with a finite element analysis program. This paper presents the Aboudi method of cells, an analytical method to compute the elastic properties of composite material, and applies it to determine the mechanical properties of porous material as a function of the density of material. It is shown that the results are similar to those obtained by special finite element analysis set up to compute the elasticity matrix. The procedure is visualized on simple cantilever design problems and used within the content of a stress-ratio redesign scheme.