Stiffness and Strength Optimization of the Anisotropy Distribution for Laminated Structures

In this paper, we deal with the problem of optimizing the anisotropy distribution of a laminated structure in order to maximize, simultaneously, its stiffness and strength. For these two objectives, two functionals are considered: the compliance as a measure of the plate stiffness and a laminate-level failure index as a measure of the strength. To solve this optimization problem we used a two-step hierarchical strategy: in the first step the aim is to find the best distribution of the stiffness and strength anisotropic tensors of an equivalent homogenized plate, while in the second one the objective is to find at least one laminate layup satisfying the optimal properties obtained as result of the first step. The polar formalism has been used to represent both the stiffness and strength tensors and allowed us to find analytical solutions to the local minimizations of the two functionals. A test case is finally presented to show the effectiveness of the proposed strategy. Anita Catapano Institut d’Alembert, UMR 7190 CNRS and Université Paris 6, Paris (F) and Centre de Recherche Public H. Tudor, Luxembourg (L) (at present at I2M, UMR 5295 CNRS and Université de Bordeaux) E-mail: [email protected] Boris Desmorat Institut d’Alembert, UMR 7190 CNRS and Université Paris 6, Paris (F) and Université Paris Sud 11, Orsay (F) E-mail: [email protected] Paolo VannucciB LMV, UMR 8100 CNRS and Université de Versailles et Saint Quentin en Yvelines, Versailles (F) and Université Paris-Saclay, Saclay (F) E-mail: [email protected] 2 A. Catapano et al.