Abstract

The discretization of the Reissner-Mindlin model for plates requires finite elements of class only C 0. This is perhaps the main advantage respect to the Kirchhoff formulation, where C 1 finite elements need to be used for a conforming approximation. However, despite its simple approach, the numerical approximation of the Reissner-Mindlin plate is not straightforward. The inclusion of transverse shear strain effect in standard finite element models introduces undesirable numerical effects. Standard low order finite elements are not able to meet the Kirchhoff constraint enforced when the thickness becomes smaller and therefore are subject to the locking phenomenon. The approximate solution is very sensitive to the plate thickness and unsatisfactory results are obtained for small thickness. We have solved the Reissner-Mindlin plate problem in its plain formulation with the use of high order finite elements. We have developed a hierarchic family of finite elements and have performed several numerical tests to analyze the behavior with respect to the thickness. In this paper we are particularly interested in the investigation of the robustness properties of the family of finite elements. In this direction we analyse the performance of the elements when very small values of the thickness of the plate are considered. The numerical results indicate a large range of robustness for the higher order elements.

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