A formulation for multiple loading cases in plastic topology design of continua

Zied Kammoun

doi:10.1016/j.crme.2016.08.002

A formulation for multiple loading cases in plastic topology design of continua
[Une formulation pour la conception topologique des milieux plastiques sous cas de chargement multiples]

Zied Kammoun ^1,²

¹ Université de Tunis El Manar, École nationale d'ingénieurs de Tunis, LR11ES16, Laboratoire de matériaux, optimisation et énergie pour la durabilité, B.P. 37, 1002 Tunis-Belvédère, Tunisia
² Université de Carthage, Institut supérieur des technologies de l'environnement de l'urbanisme et du bâtiment, 2, rue de l'Artisanat-Charguia 2, 2035 Tunis, Tunisia

Comptes Rendus. Mécanique, Volume 344 (2016) no. 10, pp. 725-735.

Résumé
Abstract

Dans la vie réelle, la majorité des structures industrielles sont soumises à des cas de charges multiples. Le présent article propose une formulation pour l'optimisation de la topologie des structures soumises à plusieurs cas de chargement. Il est basé sur une technique récente développée en utilisant une méthode directe d'analyse limite pour la conception topologique des structures plastiques (LADM). Dans cette formulation, un seul problème mathématique est généré pour optimiser les structures soumises à des cas de chargements multiples, chaque cas agissant indépendamment à différents moments. Pour le problème continu, comme dans la LADM, une seule itération est nécessaire. Pour le problème discret, l'approche utilisée dans la méthode LADM est conservée, avec l'utilisation d'une séquence de problèmes de programmation de coniques de même forme que le problème de conception continue. La méthode proposée est illustrée par des problèmes continus et discrets. Les exemples de topologie avec plusieurs cas de chargement montrent la conservation des caractéristiques de la méthode LADM.

In the real life, most industrial structures are subject to multiple load cases. The present paper proposes a topology optimization formulation for multiple loading cases. It is based on the recently developed Direct Method of Limit Analysis for plastic topology Design (LADM). In this formulation, a single mathematical problem is considered to optimize structures under multiple loading cases; each case acts independently at a different time. For the continuous design problem, as in LADM, a unique iteration is considered. For the discrete, i.e. black and white, topology optimization problem, the same approach used in LADM is conserved with the use of a sequence of conic programming problems of the same form as the continuous design problem. The proposed method is illustrated with continuous and discrete example design problems. Examples with multiple loading cases confirm the conservation of the LADM features.

Reçu le : 2016-05-13
Accepté le : 2016-08-09
Publié le : 2016-08-29

DOI : 10.1016/j.crme.2016.08.002

Keywords: Plastic, Topology, Optimization, LADM, Limit analysis, Loading cases
Mot clés : Plastique, Topologie, Optimisation, Analyse limite, Cas de chargement

Affiliations des auteurs :

Zied Kammoun ^{1, 2}

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Zied Kammoun. A formulation for multiple loading cases in plastic topology design of continua. Comptes Rendus. Mécanique, Volume 344 (2016) no. 10, pp. 725-735. doi : 10.1016/j.crme.2016.08.002. https://comptes-rendus.academie-sciences.fr/mecanique/articles/10.1016/j.crme.2016.08.002/

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