The mixed finite element formulation for the thick plates on elastic foundations

A new functional has been constructed for Reissner plates on Winkler foundations through a systematic procedure based on the Gâteaux differential. In this functional there exists eight independent variables, such as deflection, internal forces and boundary condition terms (BC), which were included in the functional in a systematic way. The closed form mixed elements are created for a (6 x 8) triangular element (TR48) and a (4 x 8) rectangular element (REC32). The element does not suffer from shear locking. Various boundary conditions are analyzed and boundary values were included in the global system of equations by the Lagrange multiplier method. An interesting property of this formulation is that the numerical results converge from above and below, depending on whether odd or even numbers of elements are used in the mesh refinement. Numerical tests on the elements were applied in representative problems.