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Two-dimensional model for the combined bending, stretching and shearing of shells: A general approach and application to laminated cylindrical shells derived from three-dimensional elasticity

type de publication      article dans une revue internationale avec comité de lecture
date de publication 2014
auteur(s) Pruchnicki Erick
journal (abréviation) Mathematics and Mechanics of Solids (Math Mech Solid)
volume (numéro) 19 (5)
  
pages 491 – 501
résumé For laminated shells, the displacement field can be approximated in each layer by a third-order Taylor–Young expansion in thickness. Then we are motivated to consider a simplified theory based on the thickness-wise expansion of the potential energy truncated at third-order in thickness. The equilibrium equations imply local constraints on the through- thickness derivatives of the zero-order displacement field in each layer. These lead to an analytical expression for the two-dimensional potential energy of cylindrical shells in terms of the zero-order displacement field, and its derivatives, that includes non-standard transverse shearing and normal stress energy. As a consequence this potential energy satisfies the stability condition of Legendre–Hadamard which is necessary for the existence of a minimizer.
mots clés Laminated cylindrical shells, linear elasticity, strain gradients
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