A semi-analytical solution of three dimensional elasticity theory for functionally graded rectangular plates

The rectangular plates made of functionally graded materials (FGM) are analyzed by three-dimensional linear elasticity theory. For the functionally graded rectangular plates, some displacement and stress components are acted as the basic variables. Firstly, these basic variables are expressed as the sums of the double trigonometric function expansions in the plane of the plates. Then, they are substituted into the governing differential equations of three-dimensional linear elasticity theory. Consequently, it leads to a series of two point boundary problems of ordinary differential equations with the basic variables. Finally, the interpolating matrix method is applied to directly solve the set of ordinary differential equations. All displacement and stress components of the FGM plate can be obtained. Two examples are given to demonstrate the accuracy and effectiveness of the computed results for the FGM plate by the comparisons with the solutions of the finite element method and state space method.