Finite Elements for the One Variable Version of Mindlin-Reissner Plate

Abstract

To analyze thin and thick plates, the paper presents two rectangular finite elements with high accuracy. In these elements, the proposed formulations of the displacement field utilize the Bergan-Wang approach, which depends only on one variable: the plate lateral deflection. This approach ensures that shear-locking problem will not happen as thickness decreases. The degrees of freedom of the proposed elements are twenty-four for the first element and it is named BWRE24, while the second one has thirty-six degrees of freedom and is named BWRE36. To evidence the efficiency of the two elements, a series of numerical examples for an isotropic plate subjected to various loadings and with different boundary conditions have been analyzed. Very good results are obtained suffering no numerical difficulties in case of very thin plates.