A General Nonlinear Third-Order Theory of Functionally Graded Plates

A general third-order plate theory that accounts for geometric nonlinearity and twoconstituent material variation through the plate thickness (i.e., functionally graded plates) is presented using the dynamic version of the principle of virtual displacements. The formulation is based on power-law variation of the material through the thickness and the von Karman nonlinear strains. The governing equations of motion derived herein for a general third-order theory with geometric nonlinearity and material gradation through the thickness are specialized to the existing classical and shear deformation plate theories in the literature. The theoretical developments presented herein can be used to develop finite element models and determine the effect of the geometric nonlinearity and material grading through the thickness on the bending, vibration, and buckling and postbuckling response of elastic plates.