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Design Problems of Anisotropic Structures: Some Recent Results

Conference paper
Part of the Springer Optimization and Its Applications book series (SOIA, volume 66)

Abstract

We show in this paper a general procedure to tackle the problem of designing anisotropic laminates corresponding to given criteria and optimizing a given objective function. The method is based, on one side, on the use of tensor invariants for the description of the anisotropic properties and, on the other side, on a free-material approach for the determination, first, of the optimal fields of anisotropic properties and, then, using numerical metaheuristics, of a suitable stacking sequence. Some general results concerning the method are introduced, along with a discussion of the influence of anisotropy on the optimal design of laminates. Some different problems are dealt with for showing the effectiveness of the approach.

Keywords

Particle Swarm Optimization Topology Optimization Polar Parameter Polar Formalism Elementary Layer 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

References

  1. 1.
    Allaire, G., Kohn, R.V.: Optimal design for minimum weight and compliance in plane stress using external micro structures. Eur. J. Mech. A, Solids 12, 839–878 (1993) MathSciNetMATHGoogle Scholar
  2. 2.
    Cheng, G., Pedersen, P.: On sufficiency conditions for optimal design based on extremum principles of mechanics. J. Mech. Phys. Solids 45, 135–150 (1997) MATHCrossRefGoogle Scholar
  3. 3.
    Gong, X.J., Vannucci, P., Verchery, G.: Effect of adjacent layer fiber orientation on the resistance of laminates to delamination fracture. In: Proc. of ICCM13—International Conference on Composite Materials 13, Beijing (2001) Google Scholar
  4. 4.
    Grédiac, M.: A procedure for designing laminated plates with required stiffness properties. Application to thin quasi-isotropic quasi-homogeneous uncoupled laminates. J. Compos. Mater. 33, 1939–1956 (1999) CrossRefGoogle Scholar
  5. 5.
    Hammer, V.B., Bendsoe, M., Lipton, R., Pedersen, P.: Parameterization in laminate design for optimal compliance. Int. J. Solids Struct. 34, 415–434 (1997) MATHCrossRefGoogle Scholar
  6. 6.
    Hammer, V.B.: Optimal laminate design subject to single membrane loads. Struct. Multidiscip. Optim. 17, 65–73 (1999) Google Scholar
  7. 7.
    Jibawy, A., Julien, C., Desmorat, B., Vincenti, A., Léné, F.: Optimisation de plaques stratifiées en représentation polaire. In: Proceedings of the 9th Colloque National en Calcul des Structures, Giens, France, vol. 1, pp. 499–504 (2009) Google Scholar
  8. 8.
    Jibawy, A.: Optimisation structurale de coques minces composites stratifiées. PhD Thesis, Université Pierre et Marie Curie (2010) Google Scholar
  9. 9.
    Jones, R.M.: Mechanics of Composite Materials. McGraw-Hill, New York (1975) Google Scholar
  10. 10.
    Julien, C.: Conception optimale de l’anisotropie dans les structures stratifées à rigidité variable par la méthode polaire-génétique. PhD Thesis, Université Pierre et Marie Curie (2010) Google Scholar
  11. 11.
    Kandil, N., Verchery, G.: New methods of design for stacking sequences of laminates. In: Proc. of CADCOMP88–Computer Aided Design in Composite Materials 88. Southampton, UK (1988) Google Scholar
  12. 12.
    Tsai, S.W., Hahn, T.: Introduction to Composite Materials. Technomic, Lancaster (1980) Google Scholar
  13. 13.
    Valot, E., Vannucci, P.: Some exact solutions for fully orthotropic laminates. Compos. Struct. 69, 157–166 (2005) CrossRefGoogle Scholar
  14. 14.
    Vannucci, P.: Designing the elastic properties of laminates as an optimisation problem: A unified approach based on polar tensor invariants. Int. J. Struct. Multidiscip. Optim. 31, 378–387 (2006) MathSciNetCrossRefGoogle Scholar
  15. 15.
    Vannucci, P.: The polar analysis of a third order piezoelectricity-like plane tensor. Int. J. Solids Struct. 44, 7803–7815 (2007) MATHCrossRefGoogle Scholar
  16. 16.
    Vannucci, P.: ALE-PSO: an adaptive swarm algorithm to solve design problems of laminates. Algorithms 2, 710–734 (2009) MathSciNetCrossRefGoogle Scholar
  17. 17.
    Vannucci, P.: Influence of invariant material parameters on the flexural optimal design of thin anisotropic laminates. Int. J. Mech. Sci. 51, 192–203 (2009) CrossRefGoogle Scholar
  18. 18.
    Vannucci, P.: On special orthotropy of paper. J. Elast. 99, 75–83 (2010) MathSciNetMATHCrossRefGoogle Scholar
  19. 19.
    Vannucci, P.: A new general approach for optimising the performances of smart laminates. Mech Adv. Math. Struct. 15, 558–568 (2012) Google Scholar
  20. 20.
    Vannucci, P., Gong, X.J., Verchery, G.: Determination des stratifies quasi-homogènes par l’approche polaire. In: Proc. of JNC11—11 èmes Journées Nationales sur les Composites, Arcachon, France (1998) Google Scholar
  21. 21.
    Vannucci, P., Pouget, J.: Laminates with given piezoelectric expansion coefficients. Mech. Adv. Mat. Struct. 13, 419–427 (2006) CrossRefGoogle Scholar
  22. 22.
    Vannucci, P., Verchery, G.: A special class of uncoupled and quasi-homogeneous laminates. Compos. Sci. Technol. 61, 1465–1473 (2001) CrossRefGoogle Scholar
  23. 23.
    Vannucci, P., Verchery, G.: Stiffness design of laminates using the polar method. Int. J. Solids Struct. 38, 9281–9294 (2001) MATHCrossRefGoogle Scholar
  24. 24.
    Vannucci, P., Verchery, G.: A new method for generating fully isotropic laminates. Compos. Struct. 58, 75–82 (2002) CrossRefGoogle Scholar
  25. 25.
    Vannucci, P., Vincenti, A.: The design of laminates with given thermal/hygral expansion coefficients: A general approach based upon the polar-genetic method. Compos. Struct. 79, 454–466 (2007) CrossRefGoogle Scholar
  26. 26.
    Verchery, G.: Les invariants des tenseurs d’ordre 4 du type de l’élasticité. In: Proc. of Colloque Euromech 115, Editions du CNRS, Villard-de-Lans, France (1979) Google Scholar
  27. 27.
    Vincenti, A., Ahmadian, M.R., Vannucci, P.: BIANCA: A genetic algorithm to solve hard combinatorial optimisation problems in engineering. J. Glob. Optim. 48, 399–421 (2010) MathSciNetMATHCrossRefGoogle Scholar
  28. 28.
    Vincenti, A., Desmorat, B.: Optimal orthotropy for minimum elastic energy by the polar method. J. Elast. 102, 55–78 (2011) MathSciNetMATHCrossRefGoogle Scholar
  29. 29.
    Vincenti, A., Vannucci, P.: Optimal design of smart composite laminates by the polar method and the genetic algorithm BIANCA. In: Proc. of 3rd European Conference on Computational Mechanics—Solids, Structures and Coupled Problems in Engineering, Lisbon (2006) Google Scholar
  30. 30.
    Wu, K.M., Avery, B.L.: Fully isotropic laminates and quasi-homogeneous laminates. J. Compos. Mater. 26, 210–2117 (1992) CrossRefGoogle Scholar
  31. 31.
    York, C.B.: Characterization of nonsymmetric forms of fully orthotropic laminates. J. Aircr. 46, 1114–1125 (2009) CrossRefGoogle Scholar
  32. 32.
    York, C.B.: Unified approach to the characterization of coupled composite laminates: Benchmark configurations and special cases. J. Aerosp. Eng. 23, 219–242 (2010) CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media, LLC 2012

Authors and Affiliations

  • Paolo Vannucci
    • 1
  • Boris Desmorat
    • 2
  • Angela Vincenti
    • 3
  1. 1.Institut Jean Le Rond d’AlembertUniversité Versailles Saint Quentin, UMR7190, Université Paris 6 – CNRS, 4ParisFrance
  2. 2.Institut Jean Le Rond d’AlembertUniversité Paris Sud, UMR7190, Université Paris 6 – CNRS, 4ParisFrance
  3. 3.Institut Jean Le Rond d’AlembertUMR7190, Université Paris 6 – CNRS, 4ParisFrance

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