Three-dimensional elasticity solution for simply supported rectangular plates with variable thickness

This paper studies the stress and displacement distributions of rectangular plates with a continuously varying thickness that are simply supported at four edges. On the basis of three-dimensional elasticity theory, the general expressions for the displacements and stresses of the plate under static loads, which exactly satisfy the governing differential equations and the simply supported boundary conditions at four edges of the plate, are analytically derived. The unknown coefficients in the general expressions of the stresses are approximately determined by using the double Fourier sinusoidal series expansions to the boundary conditions on the upper and lower surfaces of the plate. The present solution gives rapid convergence and accurate results which are in good agreement with those obtained from the commercial finite element software ANSYS.