Abstract
The problem of formulating the design of laminated composite plates as a global optimization problem is discussed. In the paper, a general procedure, based upon the polar formalism for the use of tensor invariants as design variables is presented, along with a wide discussion of its peculiarities and of some numerical issues. An outlook about some open problems is also given, with a perspective on possible future issues and further developments.
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References
Abrate, S.: Optimal design of laminated plates and shells. Compos. Struct. 29, 269–286 (1994)
Ghiasi, H., Pasini, D., Lessard, L.: Optimum stacking sequence design of composite materials part 1: Constant stiffness design. Compos. Struct. 90, 1–11 (2009)
Ghiasi, H., Fayazbakhsh, D., Pasini, D., Lessard, L.: Optimum stacking sequence design of composite materials part 2: Variable stiffness design. Compos. Struct. 93, 1–13 (2010)
Jones, R.M.: Mechanics of Composite Materials, 2nd edn. Taylor and Francis, Philadelphia (1999)
Gurtin, M.E.: an Introduction to Continuum Mechanics. Academic Press, New York (1981)
Villaggio, P.: Mathematical Models for Elastic Structures. Cambridge University Press, Cambridge (1997)
Vannucci, P.: On bending-tension coupling of laminates. J. Elast. 64, 13–28 (2001)
Banichuk, N.V.: Problems and Methods of Optimal Structural Design. Plenum Press, New York (1983)
Pedersen, P.: On optimal orientation of orthotropic materials. Struct. Multidiscip. Optim. 1, 101–106 (1989)
Sacchi Landriani, G., Rovati, M.: Optimal design of two-dimensional structures made of composite materials. J. Mech. Des. 113, 88–92 (1991)
Vincenti, A., Desmorat, B.: Optimal orthotropy for minimum elastic energy by the polar method. J. Elast. 102, 55–78 (2011)
Verchery, G.: Les invariants des tenseurs d’ordre 4 du type de l’élasticité. In: Proc. of Colloque Euromech, VIllard-de-Lans, France, vol. 115 (1979)
Vannucci, P.: Plane anisotropy by the polar method. Meccanica 40, 437–454 (2005)
Vannucci, P.: Influence of invariant material parameters on the flexural optimal design of thin anisotropic laminates. Int. J. Mech. Sci. 51, 192–203 (2009)
Vannucci, P.: A special planar orthotropic material. J. Elast. 67, 81–96 (2002)
Vannucci, P.: On special orthotropy of paper. J. Elast. 99, 75–83 (2012)
Vannucci, P.: Designing the elastic properties of laminates as an optimisation problem: a unified approach based on polar tensor invariants. Struct. Multidiscip. Optim. 31, 378–387 (2006)
Vincenti, A., Vannucci, P.: Optimal design of smart composite laminates by the polar method and the genetic algorithm BIANCA. In: Mota Soares, C.A. et al. (eds.) Proc. of III European Conference on Computational Mechanics—Solids, Structures and Coupled Problems in Engineering, Lisbon (2006)
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)
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)
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)
Vannucci, P.: ALE-PSO: an adaptive swarm algorithm to solve design problems of laminates. Algorithms 2, 710–734 (2009)
Trelea, I.C.: The particle swarm optimization algorithm: convergence analysis and parameter selection. Inf. Process. Lett. 85, 317–325 (2003)
Jiang, M., Luo, Y.P., Yang, S.Y.: Stochastic convergence analysis and parameter selection of the standard particle swarm optimization algorithm. Inf. Process. Lett. 102, 8–16 (2007)
Le Riche, R., Haftka, R.T.: Optimization of laminate stacking sequence for buckling load maximization by genetic algorithms. AIAA J. 31, 951–956 (1993)
Nagendra, S., Jestin, D., Gürdal, Z., Hatfka, R.T., Watson, L.T.: Improved genetic algorithm for the design of stiffened composite panels. Comput. Struct. 58, 543–555 (1996)
Kogiso, N., Watson, L.T., Gurdal, Z., Haftka, R.T.: Genetic algorithms with local improvement for composite laminate design. Struct. Optim. 7, 207–218 (1994)
Gürdal, Z., Haftka, R.T., Hajela, P.: Design and Optimization of Laminated Composite Materials. Wiley, New York (1999)
Soremekun, G., Gurdal, Z., Haftka, R.T., Watson, L.T.: Composite laminate design optimization by genetic algorithm with generalized elitist selection. Comput. Struct. 79, 131–143 (2001)
Gantovnik, V.B., Gurdal, Z., Watson, L.T.: A genetic algorithm with memory for optimal design of laminated sandwich composite panels. Compos. Struct. 58, 513–520 (2002)
Coello Coello, C.A.: Theoretical and numerical constraint-handling techniques used with evolutionary algorithms: a survey of the state of the art. Comput. Methods Appl. Mech. Eng. 191, 1245–1287 (2002)
Montemurro, M., Vincenti, A., Vannucci, P.: The automatic dynamic penalization method (ADP) for handling constraints with genetic algorithms. Comput. Methods Appl. Mech. Eng. (2012, submitted). Preprint in HAL Archives Ouvertes. hal-00721271. http://hal.archives-ouvertes.fr/docs/00/72/12/71/PDF/ADP.pdf
Irisarri, F.-X., Bassir, D.H., Carrere, N., Maire, J.-F.: Multiobjective stacking sequence optimization for laminated composite structures. Compos. Sci. Technol. 69, 983–990 (2009)
Sebaey, T.A., Lopes, C.S., Blanco, N., Costa, J.: Ant colony optimization for dispersed laminated composite panels under biaxial loading. Compos. Struct. 94, 31–36 (2011)
Vincenti, A., Vannucci, P., Ahmadian, M.R.: Optimization of laminated composites by using genetic algorithm and the polar description of plane anisotropy. Mech. Adv. Mat. Struct. (doi:10.1080/15376494.2011.563415) (2012, in press). Preprint in HAL Archives Ouvertes. hal-00718807. http://hal.archives-ouvertes.fr/docs/00/71/88/07/PDF/Article.pdf
Tsai, S.W., Hahn, T.: Introduction to Composite Materials. Technomic Publishing, Lancaster (1980)
Montemurro, M., Vincenti, A., Vannucci, P.: Design of elastic properties of laminates with minimum number of plies. Mech. Compos. Mater. 48, 369–390 (2012)
Miki, M.: Material design of composite laminates with required in-plane elastic properties. In: Proc. of ICCM 4 (Fourth International Conference on Composite Materials), Tokio, pp. 1725–1731 (1982)
Vannucci, P.: A note on the geometric and elastic bounds for composite laminates. J. Elast. (2012, in press). Preprint in HAL archives ouvertes, hal-00666598. http://hal.archives-ouvertes.fr/docs/00/66/65/98/PDF/article.pdf
Jibawy, A., Julien, C., Desmorat, B., Vincenti, A., Léné, F.: Hierarchical structural optimization of laminated plates using polar representation. Int. J. Solids Struct. 48, 2576–2584 (2011)
Vannucci, P.: A new general approach for optimizing the performances of smart laminates. Mech. Adv. Mat. Struct. 18, 558–568 (2011)
Vannucci, P., Verchery, G.: Anisotropy of plane complex elastic bodies. Int. J. Solids Struct. 47, 1154–1166 (2010)
Cross, R.J., Haynes, R.A., Armanios, E.A.: Families of hygrothermally stable asymmetric laminated composites. J. Compos. Mater. 42, 697–716 (2008)
Vannucci, P.: General theory of coupled thermally stable anisotropic laminates. J. Elast. (2012, submitted). Preprint in HAL archives ouvertes, hal-00718543. http://hal.archives-ouvertes.fr/docs/00/71/85/43/PDF/article.pdf
Montemurro, M., Vincenti, A., Vannucci, P.: A two-level procedure for the global optimum design of composite modular structures—application to the design of an aircraft wing. Part 1: Theoretical formulation. J. Optim. Theory Appl. 155, 1–23 (2012)
Montemurro, M., Vincenti, A., Vannucci, P.: A two-level procedure for the global optimum design of composite modular structures—application to the design of an aircraft wing. Part 2: Numerical aspects and examples. J. Optim. Theory Appl. 155, 24–53 (2012)
Vannucci, P., Verchery, G.: Stiffness design of laminates using the polar method. Int. J. Solids Struct. 38, 9281–9294 (2001)
Catapano, A., Desmorat, B., Vannucci, P.: Invariant formulation of phenomenological failure criteria for orthotropic sheets and optimization of their strength. Math. Methods Appl. Sci., doi:10.1002/mma.2530 (2012, in press)
Diaconu, C.G., Sato, M., Sekine, H.: Feasible region in general design space of lamination parameters for laminated composites. AIAA J. 40, 559–565 (2002)
Liu, S., Hou, Y., Sun, X., Zhang, Y.: A two-step optimization scheme for maximum stiffness design of laminated plates based on lamination parameters. Compos. Struct. 94, 3529–3537 (2012)
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Vannucci, P. The Design of Laminates as a Global Optimization Problem. J Optim Theory Appl 157, 299–323 (2013). https://doi.org/10.1007/s10957-012-0175-6
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DOI: https://doi.org/10.1007/s10957-012-0175-6