Combining hierarchic high order and mixed-interpolated finite elements for Reissner—Mindlin plate problems

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The Reissner—Mindlin plate bending model describes the deformation of a plate subject to a transverse loading when transverse shear deformation is taken into account. Despite its simple approach, the discretization of the Reissner—Mindlin model is not straightforward. The inclusion of the transverse shear strain effect in standard finite element models introduces undesirable numerical effects. The approximate solution is very sensitive to the plate thickness and, for small thickness, it is very far from the true solution. The phenomenon is known as locking of the numerical solution. The most common way to avoiding the locking problem is to use non-standard finite elements and/or modify the variational formulation. Recently, numerical experiences with high order finite elements applied to the plain Reissner—Mindlin formulation have shown a consistent improvement in the quality of the results. Meanwhile some mixed-interpolated finite elements have been suggested and shown to be locking free. In this paper we propose the combination of the two classes of elements introducing a family of hierarchic high order mixed-interpolated finite elements.