Um Algoritmo de Restauração Inexata para a Otimização Topológica de Treliças

Authors

  • T. Ando Jr.
  • F.A.M. Gomes

DOI:

https://doi.org/10.5540/tema.2006.07.02.0179

Abstract

Treliças são estruturas compostas por barras delgadas e ligadas entre si por meio de rótulas, geralmente sujeitas somente a cargas nos nós, apresentando, neste caso, apenas esforços axiais. Neste trabalho, determinamos a geometria ótima de uma treliça sujeita a um conjunto de forças, obtendo a estrutura mais rígida possível que obedece a restrições de material e de domínio. A abordagem escolhida engloba os problemas de dimensionamento geométrico e topológico, resultando num modelo de programação não linear. Resolvemos esse problema adaptando um algoritmo do tipo restauração inexata, para o qual propomos especializações levando em conta as particularidades do modelo e o objetivo de resolver problemas de grande porte.

References

[1] M.P. Bendsøe, O. Sigmund, “Topology Optimization: Theory, Methods and Applications”, Springer, Berlin, 2003.

A. Ben-Tal, A. Nemirovski. Potential reduction polynomial time method for truss topology design, SIAM J. Optimization, 7 (1994), 596-612.

A. Ben-Tal, A. Nemirovski. “Lectures on Modern Convex Optimization: Analysis, Algorithms and Engineering Applications”, SIAM, Philadelphia, 2001.

A. Ben-Tal, M. Zibulevsky. Penalty/Barrier multiplier methods for convex programming problems, SIAM J. Optimization, 7 (1997), 347-366.

F. Jarre, M. Koˇcvara, J. Zowe, Optimal truss design by interior point methods, SIAM Journal of Optimization, 8 (1998), 1084-1107.

J.M. Martínez, E.A. Pilota, Inexact restoration algorithm for constrained optimization, Journal of Optimization Theory and Applications, 104 (2000), 135-163.

G.I.N. Rozvany, “Structural design via optimality criteria”, Kluwer, Dordrecht, 1989.

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Published

2006-06-01

How to Cite

Ando Jr., T., & Gomes, F. (2006). Um Algoritmo de Restauração Inexata para a Otimização Topológica de Treliças. Trends in Computational and Applied Mathematics, 7(2), 179–188. https://doi.org/10.5540/tema.2006.07.02.0179

Issue

Vol. 7 No. 2 (2006)

Section

Original Article

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