Analytical and numerical solutions for a class of optimization problems in elasticity

Pages: 1013 - 1032, Volume 4, Issue 4, November 2004      doi:10.3934/dcdsb.2004.4.1013

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G. Machado - Department of Mathematics for Science and Technology, Officina Mathematica, University of Minho, 4800-058 Guimarães, Portugal (email)
L. Trabucho - Department of Mathematics, University of Lisbon, 1649-003 Lisboa, Portugal (email)

Abstract: The subject of topology optimization methods in structural design has increased rapidly since the publication of [5], where some ideas from homogenization theory were put into practice. Since then, several engineering applications have been developed successfully. However, in the literature, there is a lack of analytical solutions, even for simple cases, which might help in the validation of the numerical results. In this work, we develop analytical solutions for simple minimum compliance problems, in the framework of elasticity theory. We compare these analytical solutions with numerical results obtained via an algorithm proposed in [4].

Keywords:  Elasticity, homogenization theory, optimality conditions.
Mathematics Subject Classification:  74Q05, 74P05.

Received: December 2002;      Revised: January 2004;      Published: August 2004.