Three-dimensional analysis of simply supported functionally graded plate with arbitrary distributed elastic modulus

Three-dimensional bending analysis is presented for a simply supported orthotropic functionally graded rectangular plate in this paper. Assuming that material properties have arbitrary variations along the plate-thickness direction, Peano-Baker series solution is obtained for the elastic fields of the functionally graded plate subjected to mechanical loads on its upper and lower surfaces by means of state space method. The correctness of the obtained series solution is validated through numerical examples. The influence of the structural response of the plate is also studied when material properties have different dependence on the thickness-coordinate. The results show that the solution is valid for the material properties of arbitrary dependence on the thickness-coordinate of the plate.