A generalized notion of compliance

Cristian Barbarosie; Sérgio Lopes

doi:10.1016/j.crme.2011.07.002

A generalized notion of compliance
[Une notion généralisée de compliance]

Cristian Barbarosie ¹ ; Sérgio Lopes ^1,²

¹ Centro de Matemática e Aplicações Fundamentais, Universidade de Lisboa, Av. Prof. Gama Pinto, 2, 1649-003 Lisboa, Portugal
² Instituto Superior de Engenharia de Lisboa, Instituto Politécnico de Lisboa, Rua Conselheiro Emídio Navarro, 1, 1959-007 Lisboa, Portugal

Comptes Rendus. Mécanique, Volume 339 (2011) no. 10, pp. 641-648.

Résumé
Abstract

Il est un fait établi dans la littérature sur lʼoptimisation de structures que, pour mésurer la compliance de structures dont une partie de la frontière a un déplacement prescrit non nul, le travail effectué par les charges nʼest pas un critére correcte ; lʼenergie élastique emmagasiné dans le corps nʼen est non plus. Cette notte propose un critére alternative pour mésurer la compliance dʼune structure pour des conditions de frontière très générales. Les états adjoints (nécéssaires pour le calcul de la dérivée structurale) sont presentés pour les trois fonctionnelles considerées.

It is a known fact in structural optimization that for structures subject to prescribed non-zero displacements the work done by the loads is not a good measure of compliance, neither is the stored elastic energy. We briefly discuss a possible alternative measure of compliance, valid for general boundary conditions. We also present the adjoint states (necessary for the computation of the structural derivative) for the three functionals under consideration.

Reçu le : 2011-06-09
Accepté le : 2011-07-19
Publié le : 2011-08-19

DOI : 10.1016/j.crme.2011.07.002

Keywords: Computational solid mechanics, Optimization of structures, Linear elasticity, Stiff structures
Mot clés : Mécanique des solides numérique, Optimisation de structures, Élasticité linéaire, Structures raides

Affiliations des auteurs :

Cristian Barbarosie ¹ ; Sérgio Lopes ^{1, 2}

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     title = {A generalized notion of compliance},
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     language = {en},
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Cristian Barbarosie; Sérgio Lopes. A generalized notion of compliance. Comptes Rendus. Mécanique, Volume 339 (2011) no. 10, pp. 641-648. doi : 10.1016/j.crme.2011.07.002. https://comptes-rendus.academie-sciences.fr/mecanique/articles/10.1016/j.crme.2011.07.002/

Bibliographie
Cité par

[1] M.P. Bendsoe; O. Sigmund Topology Optimization – Theory, Methods and Applications, Springer, 2003

[2] S. Lopes, Optimização estrutural com escolha livre de materiais, Master Thesis, University of Lisbon, 2006.

[3] P. Pedersen; N.L. Pedersen Design objectives with non-zero prescribed support displacements, Structural and Multidisciplinary Optimization, Volume 43 (2011) no. 2, pp. 205-214

[4] C. Barbarosie; A.M. Toader Shape and topology optimization for periodic problems, Part I: The shape and the topological derivative, Structural and Multidisciplinary Optimization, Volume 40 (2010), pp. 381-391

[5] A.M. Toader The topological derivative for homogenized elastic coefficients of periodic microstructures, SIAM Journal on Control and Optimization, Volume 49 (2011), pp. 1607-1628 http://cmaf.ptmat.fc.ul.pt/preprints.html (see also Pre-Print CMAF Pre-2010-001 at)

[6] F. Niu; S. Xu; G. Cheng A general formulation of structural topology for maximizing structural stiffness, Structural and Multidisciplinary Optimization, Volume 43 (2011), pp. 561-572

[7] C. Barbarosie; S. Lopes A generalized notion of compliance http://cmaf.ptmat.fc.ul.pt/preprints.html (Preprint CMAF Pre-2011-002 at)

[8] G. Allaire Conception optimale de Structures, Springer, 2007

[9] J. Céa Optimisation, Théorie et Algorithmes, Dunod, 1971

[10] D. Chenais Optimal design of midsurface of shells: differentiability proofs and sensitivity computation, Applied Mathematics and Optimization, Volume 16 (1987), pp. 93-133

[11] C. Barbarosie; S. Lopes A gradient-type algorithm for optimization with constraints, submitted for publication http://cmaf.ptmat.fc.ul.pt/preprints.html (Preprint CMAF Pre-2011-001 at)

[12] C. Barbarosie Shape optimization of periodic structures, Computational Mechanics, Volume 30 (2003) no. 3, pp. 235-246

[13] O. Pironneau; F. Hecht; A. Le Hyaric FreeFem++ home page http://www.freefem.org/ff++/index.htm (URL:)

[14] F. Jouve xd3d home page http://www.cmap.polytechnique.fr/~jouve/xd3d/ (URL:)

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