In the present study, an improved higher order theory in conjunction with finite element method (FEM) is presented and is applied to study the nonlinear vibration analysis of shear deformable functionally graded material (FGMs) plates. The present structural model kinematics assumes the cubically varying in-plane displacement over the entire thickness, while the transverse displacement varies quadratically to achieve the accountability of normal strain and its derivative in calculation of transverse shear strains. The theory also satisfies zero transverse strains conditions at the top and bottom faces of the plate, and the geometric nonlinearity is based on Green-Lagrange assumptions. All higher order terms appearing from nonlinear strain displacement relations are incorporated in the formulation. The material properties of the plates are assumed to vary smoothly and continuously throughout the thickness of the plate by a simple power-law distribution in terms of the volume fractions of the constituents. A C0 continuous isoparametric nonlinear FEM with 13 degrees of freedom per node is proposed for the accomplishment of the improved elastic continuum. Numerical results with different system parameters and boundary conditions are accomplished, to show the importance and necessity of the higher order terms in the nonlinear formulations.

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