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

G. Machado; L. Trabucho

doi:10.3934/dcdsb.2004.4.1013

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2004, Volume 4, Issue 4: 1013-1032. Doi: 10.3934/dcdsb.2004.4.1013

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

G. Machado^1, and
L. Trabucho^2,

1.
Department of Mathematics for Science and Technology, Officina Mathematica, University of Minho, 4800-058 Guimarães
2.
Department of Mathematics, University of Lisbon, 1649-003 Lisboa

Received: November 30, 2002

Revised: December 31, 2003

Published: October 2004

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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].

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Mathematics Subject Classification: 74Q05, 74P05.

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