A generalized notion of compliance

Cristian Barbarosie; Sérgio Lopes

doi:10.1016/j.crme.2011.07.002

A generalized notion of 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.

Abstract
Résumé

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.

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.

Received: 2011-06-09
Accepted: 2011-07-19
Published online: 2011-08-19

DOI: 10.1016/j.crme.2011.07.002

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

Author's affiliations:

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

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     title = {A generalized notion of compliance},
     journal = {Comptes Rendus. M\'ecanique},
     pages = {641--648},
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     volume = {339},
     number = {10},
     year = {2011},
     doi = {10.1016/j.crme.2011.07.002},
     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/

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