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Civil-Comp Proceedings
ISSN 1759-3433
CCP: 40
ADVANCES IN OPTIMIZATION FOR STRUCTURAL ENGINEERING
Edited by: B.H.V. Topping
Paper VIII.5

The Aboudi Micromechanical Model for Shape Design of Structures

M. Paley, M.B. Fuchs and Y. Miroshnik

Department of Solid Mechanics, Materials and Structures, Tel Aviv University, Ramat Aviv, Israel

Full Bibliographic Reference for this paper
M. Paley, M.B. Fuchs, Y. Miroshnik, "The Aboudi Micromechanical Model for Shape Design of Structures", in B.H.V. Topping, (Editor), "Advances in Optimization for Structural Engineering", Civil-Comp Press, Edinburgh, UK, pp 221-226, 1996. doi:10.4203/ccp.40.8.5
Abstract
The micromechanical approach to topology design consists in 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 context of a stress-ratio redesign scheme.

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