An Analytical Model to Predict Optimal Material Properties in the Context of Optimal Structural Design

[+] Author and Article Information
M. P. Bendsoe

Mathematical Institute, The Technical University of Denmark, DK-2800 Lyngby, Denmark

J. M. Guedes

CEMUL, Instituto Superior Tecnico, Av. Rovisco Pais, P-1096 Lisboa Codex, Portugal

R. B. Haber

Department of Theoretical and Applied Mechanics, University of Illinois at Urbana-Champaign, Urbana, IL 61801

P. Pedersen

Department of Solid Mechanics, The Technical University of Denmark, DK-2800 Lyngby, Denmark

J. E. Taylor

Department of Aerospace Engineering, University of Michigan, Ann Arbor, MI 48109-2140

J. Appl. Mech 61(4), 930-937 (Dec 01, 1994) (8 pages) doi:10.1115/1.2901581 History: Received December 22, 1992; Revised August 12, 1993; Online March 31, 2008


This paper deals with the simultaneous optimization of material and structure for minimum compliance. Material properties are represented in the most general form possible for a (locally) linear elastic continuum, namely the unrestricted set of elements of positive semi-definite constitutive tensors and cost measures based on certain invariants of the tensors. Analytical forms are derived for the optimized material properties. These results, which apply in general, indicate that the optimized material is orthotropic with the directions of orthotropy following the directions of principal strains. The analysis for optimization of the material leads to a reduced structural optimization problem, for which the existence of solutions can be shown and for which effective methods for computational solution can be devised.

Copyright © 1994 by The American Society of Mechanical Engineers
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