Three-dimensional elasticity solution of functionally graded rectangular plates with variable thickness

This paper studies the stress and displacement distributions of continuously varying thickness functionally graded rectangular plates simply supported at four edges. Young’s modulus is graded through the thickness following the exponential-law and Poisson’s ratio keeps constant. 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 plates. The effect of Young’s modulus varying rules on the displacements and stresses of functionally graded rectangular plates is investigated. The proposed three-dimensional elasticity solution can be used to assess the validity of various approximate solutions and numerical methods for functionally graded plates.