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

[thumbnail of Barrenechea-etal-Calcolo2014-bending-moment-formulation-of-the-Reissner-Mindlin-plate-model] PDF (Barrenechea-etal-Calcolo2014-bending-moment-formulation-of-the-Reissner-Mindlin-plate-model)
Barrenechea_etal_Calcolo2014_bending_moment_formulation_of_the_Reissner_Mindlin_plate_model.pdf
Accepted Author Manuscript

Download (618kB)

    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.

    ORCID iDs

    Barrenechea, Gabriel R. ORCID logoORCID: https://orcid.org/0000-0003-4490-678X, Barrios, Tomás P. and Wachtel, Andreas;