Three-dimensional elasticity solution of transversely isotropic rectangular plates with variable thickness



This paper studies the stress and displacement distributions of transversely isotropic rectangular plates with continuously varying thickness and 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 edge conditions of the plate, are analytically derived. The unknown coefficients in the solutions are approximately determined by using the double Fourier sinusoidal series expansions to the upper surface and lower surface conditions of the plate. Convergence and comparison studies demonstrate the correctness and effectiveness of the proposed method