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Optimal Orthotropy for Minimum Elastic Energy by the Polar Method

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Abstract

The polar method is a minimal invariant representation in plane elasticity. A plane orthotropic elastic behaviour is expressed by five polar invariants related to the elastic symmetries. In this paper, considering the orthotropy orientation and the polar invariants as optimisation parameters, we discuss the problem of minimising the elastic energy for a given state of stress. The minimisation with respect to the orientation is solved in order to find the associated optimal elastic energy for given polar invariants. Then, this quantity is minimised with respect to the polar invariants which characterise the magnitude of the anisotropic components of the elastic stiffness tensor. Optimal uncoupled composite laminates corresponding to this optimum are presented for membrane and bending loadings.

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Authors and Affiliations

  1. UMR 7190, Institut Jean Le Rond d’Alembert, UPMC Univ. Paris 6, Case 161, 4 place jussieu, 75252, Cedex Paris, France

    A. Vincenti & B. Desmorat

  2. Univ. Paris Sud 11, 91405, Orsay, France

    B. Desmorat

Authors
  1. A. Vincenti
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  2. B. Desmorat
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Correspondence to A. Vincenti.

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Vincenti, A., Desmorat, B. Optimal Orthotropy for Minimum Elastic Energy by the Polar Method. J Elast 102, 55–78 (2011). https://doi.org/10.1007/s10659-010-9262-9

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  • DOI: https://doi.org/10.1007/s10659-010-9262-9

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