Stabilised finite element methods for a bending moment formulation of the Reissner-Mindlin plate model

Barrenechea, Gabriel R. and Barrios, Tomás P. and Wachtel, Andreas (2014) Stabilised finite element methods for a bending moment formulation of the Reissner-Mindlin plate model. Calcolo. ISSN 0008-0624

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    Abstract

    This work presents new stabilised finite element methods for a bending moments formulation of the Reissner-Mindlin plate model. The introduction of the bending moment as an extra unknown leads to a new weak formulation, where the symmetry of this variable is imposed strongly in the space. This weak problem is proved to be well-posed, and stabilised Galerkin schemes for its discretisation are presented and analysed. The finite element methods are such that the bending moment tensor is sought in a finite element space constituted of piecewise linear continuos and symmetric tensors. Optimal error estimates are proved, and these findings are illustrated by representative numerical experiments.