Comptes Rendus
A direct approach for continuous topology optimization subject to admissible loading
[Une approche directe pour l'optimisation de la topologie continue sous chargement admissible]
Comptes Rendus. Mécanique, Volume 342 (2014) no. 9, pp. 520-531.

Dans le présent article, une méthode est proposée pour l'optimisation de la topologie des milieux continues soumis à des conditions d'admissibilité statique et plastique relativement à un chargement imposé. Une propriété essentielle de la méthode est qu'en utilisant une discrétisation par éléments finis, la forme du problème d'optimisation de la topologie résultant est similaire à celle du problème direct de l'analyse limite formulé selon l'approche statique. La méthode proposée est formulée en déformations planes en utilisant un matériau de Tresca. Elle est illustrée à travers des exemples de problèmes issus de la littérature.

In the present paper, a method is proposed for topology optimization of continuum structures subject to static and plastic admissibility conditions relative to a prescribed load. A key feature of the method is that, using a finite-element discretization, the form of the resulting topology optimization problem is similar to that of the direct static approach of the limit analysis problem. The proposed method is formulated in plane strain using Tresca materials and is illustrated on example problems taken from the literature.

Reçu le :
Accepté le :
Publié le :
DOI : 10.1016/j.crme.2014.06.003
Keywords: Plastic, Topology, Optimization, Continuum, Limit analysis
Mots-clés : Plastique, Topologie, Optimisation, Continuum, Analyse limite

Zied Kammoun 1 ; Hichem Smaoui 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 Salman bin Abdulaziz University, College of Engineering, P.O. Box 655, Al-Kharj 11942, Saudi Arabia
@article{CRMECA_2014__342_9_520_0,
     author = {Zied Kammoun and Hichem Smaoui},
     title = {A direct approach for continuous topology optimization subject to admissible loading},
     journal = {Comptes Rendus. M\'ecanique},
     pages = {520--531},
     publisher = {Elsevier},
     volume = {342},
     number = {9},
     year = {2014},
     doi = {10.1016/j.crme.2014.06.003},
     language = {en},
}
TY  - JOUR
AU  - Zied Kammoun
AU  - Hichem Smaoui
TI  - A direct approach for continuous topology optimization subject to admissible loading
JO  - Comptes Rendus. Mécanique
PY  - 2014
SP  - 520
EP  - 531
VL  - 342
IS  - 9
PB  - Elsevier
DO  - 10.1016/j.crme.2014.06.003
LA  - en
ID  - CRMECA_2014__342_9_520_0
ER  - 
%0 Journal Article
%A Zied Kammoun
%A Hichem Smaoui
%T A direct approach for continuous topology optimization subject to admissible loading
%J Comptes Rendus. Mécanique
%D 2014
%P 520-531
%V 342
%N 9
%I Elsevier
%R 10.1016/j.crme.2014.06.003
%G en
%F CRMECA_2014__342_9_520_0
Zied Kammoun; Hichem Smaoui. A direct approach for continuous topology optimization subject to admissible loading. Comptes Rendus. Mécanique, Volume 342 (2014) no. 9, pp. 520-531. doi : 10.1016/j.crme.2014.06.003. https://comptes-rendus.academie-sciences.fr/mecanique/articles/10.1016/j.crme.2014.06.003/

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

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

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

[4] R. Zakhama; M.M. Abdalla; H. Smaoui; Z. Gürdal Multigrid implementation of cellular automata for topology optimization of continuum structures, Comput. Model. Eng. Sci., Volume 51 (2009) no. 1, p. 1

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

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

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

[8] T.H. Woo; L.A. Schmit Decomposition in optimal plastic design of structures, Int. J. Solids Struct., Volume 17 (1981) no. 1, pp. 39-56

[9] K. Maute; S. Schwarz; E. Ramm Adaptive topology optimization of elastoplastic structures, Struct. Optim., Volume 15 (1998) no. 2, pp. 81-91

[10] K. Yuge; N. Kikuchi Optimization of a frame structure subjected to a plastic deformation, Struct. Optim., Volume 10 (1995) no. 3–4, pp. 197-208

[11] 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

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

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

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

[15] 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

[16] 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

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

[18] M.P. Bendsøe; N. Kikuchi Generating optimal topologies in structural design using a homogenization method, Comput. Methods Appl. Mech. Eng., Volume 71 (1988) no. 2, pp. 197-224

[19] G. Rozvany; M. Zhou; T. Birker Generalized shape optimization without homogenization, Struct. Optim., Volume 4 (1992) no. 3–4, pp. 250-252

[20] O. Sigmund; J. Petersson Numerical instabilities in topology optimization: a survey on procedures dealing with checkerboards, mesh-dependencies and local minima, Struct. Optim., Volume 16 (1998) no. 1, pp. 68-75

[21] E. Holmberg; B. Torstenfelt; A. Klarbring Stress constrained topology optimization, Struct. Multidiscip. Optim., Volume 48 (2013) no. 1, pp. 33-47

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

[23] 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), pp. 1960-1980

[24] M.M. Abdalla; Z. Gürdal Structural design using optimality based cellular automata, Proceedings of 43rd AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics, and Materials Conference, 2002

[25] K. Suzuki; N. Kikuchi A homogenization method for shape and topology optimization, Comput. Methods Appl. Mech. Eng., Volume 93 (1991) no. 3, pp. 291-318

  • Changxiong Huang; Geng Chen; Konstantinos V. Spiliopoulos; Lele Zhang A shakedown oriented topology optimization algorithm utilizing second-order cone programming (SOCP) and its application in spacecraft structure design, Computational Mechanics, Volume 75 (2025) no. 2, p. 897 | DOI:10.1007/s00466-024-02537-6
  • Hichem Smaoui; Zied Kammoun Convergence of the direct limit analysis design method for discrete topology optimization, Optimization and Engineering, Volume 23 (2022) no. 1, p. 1 | DOI:10.1007/s11081-020-09543-6
  • Mohamed Fourati; Zied Kammoun; Jamel Neji; Hichem Smaoui Large-scale smooth plastic topology optimization using domain decomposition, Comptes Rendus. Mécanique, Volume 349 (2021) no. 2, p. 323 | DOI:10.5802/crmeca.88
  • Jeremy Bleyer; Ghazi Hassen Automated formulation and resolution of limit analysis problems, Computers Structures, Volume 243 (2021), p. 106341 | DOI:10.1016/j.compstruc.2020.106341
  • Mathilde Boissier; Joshua D. Deaton; Philip A. Beran; Natasha Vermaak Elastoplastic topology optimization of cyclically loaded structures via direct methods for shakedown, Structural and Multidisciplinary Optimization, Volume 64 (2021) no. 1, p. 189 | DOI:10.1007/s00158-021-02875-6
  • Leyla Mourad; Jeremy Bleyer; Romain Mesnil; Joanna Nseir; Karam Sab; Wassim Raphael Topology optimization of load-bearing capacity, Structural and Multidisciplinary Optimization, Volume 64 (2021) no. 3, p. 1367 | DOI:10.1007/s00158-021-02923-1
  • Zied Kammoun; Mohamed Fourati; Hichem Smaoui Direct limit analysis based topology optimization of foundations, Soils and Foundations, Volume 59 (2019) no. 4, p. 1063 | DOI:10.1016/j.sandf.2019.05.003
  • Morten A. Herfelt; Peter N. Poulsen; Linh C. Hoang Strength-based topology optimisation of plastic isotropic von Mises materials, Structural and Multidisciplinary Optimization, Volume 59 (2019) no. 3, p. 893 | DOI:10.1007/s00158-018-2108-y
  • Juliano Fin; Lavinia Alves Borges; Eduardo Alberto Fancello Structural topology optimization under limit analysis, Structural and Multidisciplinary Optimization, Volume 59 (2019) no. 4, p. 1355 | DOI:10.1007/s00158-018-2132-y
  • N. Vermaak; M. Boissier; L. Valdevit; R. M. McMeeking Some Graphical Interpretations of Melan’s Theorem for Shakedown Design, Advances in Direct Methods for Materials and Structures (2018), p. 179 | DOI:10.1007/978-3-319-59810-9_11

Cité par 10 documents. Sources : Crossref

Commentaires - Politique