A locking-free Reissner-Mindlin quadrilateral element

Abstract

Abstract. On arbitrary regular quadrilaterals, a new finite element method for the Reissner-Mindlin plate is proposed, where both transverse displacement and rotation are approximated by isoparametric bilinear elements, with local bubbles enriching rotation, and a local reduction operator is applied to the shear energy term. This new method gives optimal error bounds, uniform in the thickness of the plate, for both transverse displacement and rotation with respect to H 1 and L 2 norms.

Locking free quadrilateral continuous/discontinuous finite element methods for the Reissner–Mindlin plate

“…For instance, the MITC element family of Bathe and co-workers [6] are based on this approach. For quadrilaterals, this type of approach has been used and analyzed in [2,14,15,21,22].…”

A Tool for Modal Analysis of Laminated Bending Plates

“…Though laminated structures are widely used, the theories of non-linear deformation and failure of modern layered composites as well as methods of mathematical modelling have not been fully developed and presented in detail yet. Because of anisotropic nature of laminated structures, all tensioncompression and bending effects as well as the interaction of bending-membrane and membrane-shear effects should be considered [1][2][3][4]. Therefore, only a few assumptions simplifying the stress-strain state for the problems associated with the analysis of thin-wall bending plates can be applied.…”