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

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.

Abstract
Résumé

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.

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.

Received: 2016-05-13
Accepted: 2016-08-09
Published online: 2016-08-29

DOI: 10.1016/j.crme.2016.08.002

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

Author's affiliations:

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

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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/

References
Cited by

[1] F. Duddeck New approaches for shape and topology optimization for crashworthiness, NAFEMS World Congress, École centrale de Lille, France, May 2011

[2] G.I.N. Rozvany A critical review of established methods of structural topology optimization, Struct. Multidiscip. Optim., Volume 37 (2009), pp. 217-237

[3] M.P. Bendsøe; O. Sigmund Material interpolation schemes in topology optimization, Arch. Appl. Mech., Volume 69 (1999) no. 9–10, pp. 635-654

[4] H.A. Eschenauer; N. Olhoff Topology optimization of continuum structures: a review, Appl. Mech. Rev., Volume 54 (2001) no. 4, pp. 331-390

[5] G. Allaire Conception optimale de structures, Math. Appl., vol. 58, Springer, Berlin, 2007

[6] P.A. Browne Topology optimization of linear elastic structures, Department of Mathematical Sciences, University of Bath, UK, May 2013 (PhD thesis)

[7] M.P. Bendsøe Optimal shape design as a material distribution problem, Struct. Optim., Volume 1 (1989) no. 4, pp. 193-202

[8] R.J. Yang; C.J. Chen Stress-based topology optimization, Struct. Optim., Volume 12 (1996) no. 2–3, pp. 98-105

[9] P. Duysinx; M.P. Bendsøe Topology optimization of continuum structures with local stress constraints, Int. J. Numer. Methods Eng., Volume 43 (1998) no. 8, pp. 1453-1478

[10] C.Y. Kiyono; S.L. Vatanabe; E.C.N. Silva; J.N. Reddy A new multi-p-norm formulation approach for stress-based topology optimization design, Compos. Struct. (2016) (in press) | DOI

[11] D. Gao; D. Wang; G. Wang; L. Hao Topology optimization of conditioner suspension for mower conditioner considering multiple loads, Math. Comput. Model., Volume 58 (2013) no. 3, pp. 489-496

[12] W. Li; Q. Li; G.P. Steven; Y.M. Xie An evolutionary shape optimization for elastic contact problems subject to multiple load cases, Comput. Methods Appl. Mech. Eng., Volume 194 (2005) no. 30, pp. 3394-3415

[13] A.R. Diaz; M.P. Bendsøe Shape optimization of structures for multiple loading conditions using a homogenization method, Struct. Optim., Volume 4 (1992) no. 1, pp. 17-22

[14] Y.M. Xie; G.P. Steven Optimal design of multiple load case structures using an evolutionary procedure, Eng. Comput., Volume 11 (1994) no. 4, pp. 295-302

[15] Z. Kammoun, H. Smaoui, A direct method formulation for topology plastic design of continua, in: 4th International Workshop on Direct Methods – DM2013, University Mediterranea of Reggio Calabria, Italy, 1–2 October 2013.

[16] Z. Kammoun; H. Smaoui A direct approach for continuous topology optimization subject to plastically admissible loading, Volume 342 (2014) no. 9, pp. 520-531

[17] Z. Kammoun; H. Smaoui A direct method formulation for topology plastic design of continua, Direct Methods for Limit and Shakedown Analysis of Structures, Springer, 2015, pp. 47-63

[18] J. Lysmer Limit analysis of plane problems in soil mechanics, J. Soil Mech. Found. Div., Volume 96 (1970), pp. 1311-1334

[19] J. Pastor; S. Turgeman Mise en oeuvre numérique des méthodes de l'analyse limite pour les matériaux de Von Mises et de Coulomb standards en déformation plane, Mech. Res. Commun., Volume 3 (1976), pp. 469-474

[20] J. Pastor Analyse limite: détermination numérique de solutions statiques complètes. Application au talus vertical, J. Méc. Appl., Volume 2 (1978), pp. 167-196

[21] R. Negre; J. Pastor; A. Bottero; S. Turgemen Finite element method and limit analysis theory for soil mechanics problems, Comput. Methods Appl. Mech. Eng., Volume 22 (1980), pp. 131-149

[22] J. Pastor; E. Loute; T.H. Thai On the efficiency of the limit analysis methods via the new techniques of optimization (P. Mesta, ed.), Vth Eur. Conf. Num. Methods in Geotechnical Engineering, Presses des Ponts et Chaussées, Paris, 2002

[23] J. Pastor; E. Loute; T.H. Thai Interior point optimization and limit analysis: an application, Commun. Numer. Methods Eng., Volume 19 (2003), pp. 779-785

[24] F. Pastor; M. Trillat; J. Pastor; E. Loute; P. Thoré Convex optimization and stress-based lower/upper bound methods for limit analysis of porous polymer materials, EMMC9 ( May 2006 )

[25] K. Krabbenhoft; L. Damkilde A general non-linear optimization algorithm for lower bound limit analysis, Int. J. Numer. Methods Eng., Volume 56 (2003), pp. 165-184

[26] A.V. Lyamin; S.W. Sloan Lower bound limit analysis using nonlinear programming, Int. J. Numer. Methods Eng., Volume 55 (2002), pp. 573-611

[27] S.W. Sloan; A.V. Lyamin Lower bound limit analysis using nonlinear programming, ECCOMAS-2000, Barcelona (2000)

[28] Z. Kammoun; F. Pastor; H. Smaoui; J. Pastor Large static problem in numerical limit analysis: a decomposition approach, Int. J. Numer. Anal. Methods Geomech., Volume 34 (2010) no. 18, pp. 1960-1980

[29] J. Salençon Théorie des charges limites: poinçonnement d'une plaque par deux poinçons symétriques en déformation plane, C. R. Acad. Sci. Paris, Volume 265 (1967), pp. 869-872

[30] J. Salençon Théorie de la plasticité pour les applications à la mécanique des sols, Eyrolles, Paris, 1974

[31] MOSEK ApS, C/O Symbion Science Park, Fruebjergvej 3, Box 16, 2100 Copenhagen ϕ, Denmark, www.mosek.com, 2002.

[32] Z. Kammoun; J. Pastor; H. Smaoui Limit analysis of a soil reinforced by micropile group: a decomposition approach, Limit State of Materials and Structures, Springer, 2013, pp. 179-195

[33] F. Pastor; Z. Kammoun; E. Loute; J. Pastor; H. Smaoui Large problems in numerical limit analysis: a decomposition approach, Limit States of Materials and Structures, Springer, 2009, pp. 23-43

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