Accepted Paper

Inserted: 15 mar 2017
Last Updated: 9 oct 2017

Journal: Annali di Matematica Pura e Applicata
Year: 2017

Abstract:

In this paper we rigorously deduce a quasistatic evolution model for shallow shells by means of $\Gamma$-convergence. The starting point of the analysis is the three-dimensional model of Prandlt-Reuss elasto-plasticity. We study the asymptotic behaviour of the solutions, as the thickness of the shell tends to $0$. As in the case of plates, the limiting model is genuinely three-dimensional, limiting displacements are of Kirchhoff-Love type, and the stretching and bending components of the stress are coupled in the flow rule and in the stress constraint. However, in contrast with the case of plates, the equilibrium equations are not decoupled, because of the presence of curvature terms. An equivalent formulation of the limiting problem in rate form is also discussed.

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