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Stiffness and Strength Optimization of the Anisotropy Distribution for Laminated Structures

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Abstract

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 lay-up 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.

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Acknowledgments

FNR of Luxembourg, supporting the first author through Aides à la Formation Recherche Grant PHD-09-184, is gratefully acknowledged.

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Author notes

  1. Anita Catapano

    Present address: I2M, UMR 5295 - CNRS and Université de Bordeaux, Talence, France

Authors and Affiliations

  1. Institut d’Alembert, UMR 7190 - CNRS and Université Paris 6, Paris, France

    Anita Catapano

  2. Centre de Recherche Public H. Tudor, Esch-sur-Alzette, Luxembourg

    Anita Catapano

  3. Institut Jean Le Rond d’Alembert, Sorbonne Universités, UPMC Univ Paris 06, CNRS, UMR 7190,, Paris, F-75005, France

    Boris Desmorat

  4. LMV, UMR 8100 - CNRS and Université de Versailles et Saint Quentin en Yvelines, Versailles, France

    Paolo Vannucci

  5. Université Paris-Saclay, Saclay, France

    Paolo Vannucci

Authors
  1. Anita Catapano
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  2. Boris Desmorat
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  3. Paolo Vannucci
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Correspondence to Paolo Vannucci.

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Catapano, A., Desmorat, B. & Vannucci, P. Stiffness and Strength Optimization of the Anisotropy Distribution for Laminated Structures. J Optim Theory Appl 167, 118–146 (2015). https://doi.org/10.1007/s10957-014-0693-5

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  • DOI: https://doi.org/10.1007/s10957-014-0693-5

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