Development of a discrete Reissner–Mindlin element on Winkler foundation

Over the years several plate-bending elements have been developed by several researchers. Most of the developed elements have been either for thin plates or thick plates. Recently, a set of robust triangular and quadrilateral elements, which showed excellent performance for both thin and thick plates, had been developed. Among the series of the triangular elements developed is the Discrete Reissner–Mindlin (DRM) element. The main features of the DRM element are its mixed interpolation formulation and its discrete collocation constraints. In this paper the DRM element has been extended to solve problems of plates on elastic foundations. The Hu–Washizu variational principle is used to formulate the element stiffness matrix. Deflection, bending moment and shear force responses of plates on Winkler-type foundation and with various thicknesses, loading conditions and foundation elastic constants, using both the DRM finite element and the classical approach, are presented. It has been demonstrated that the DRM finite element solutions agree very well with the classical solutions, specifically, for deflection response in the case of both thin and thick plates. Therefore, it can be concluded that, the DRM plate element is both effective and reliable for solving problems of thin and thick plates on elastic foundations.