The Aboudi micromechanical model for topology design of structures

The micromechanical approach to topology design consists of defining a doma in of porous material, including the loads and supports, and finding an opt imal distribution of the densities. The usual method is to mesh the structu re and assign a different density and material orientation to every element . Optimal topologies emerge when using the densities and orientations as de sign variables in a mathematical programming formulation in conjunction wit h a finite element analysis program. This paper presents the Aboudi method of cells, an analytical method to compute the elastic properties of composi te material, and applies it to determine the mechanical properties of porou s material as a function of the density of material. It is shown that the r esults 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 r edesign scheme. (C) 1999 Civil-Comp Ltd and Elsevier Science Ltd, All right s reserved.