Stress analysis a functionally graded quadrangle plate using second order shear deformation theory

The theoretical equation of bending analysis of functionally graded (FG) quadrangle plates based on second order shear deformation theory (SSDI~ are presented Full-ceramic at upper surface material and full-metal at lower surface is considered and material properties between upper and lower surface are assumed to be graded by a power law distribution in terms of the volume fractions of the constituents. The complete form of governing equations are derived by the energy method and then solved analytically by applying Navier's method to obtain the displacement and stress components. The results are given under four types of mechanical loading for a quadrangle plate with simply supported boundary conditions. The effects of the material grading index of the plate on the stresses and displacements are thoroughly investigated The mechanical responses of homogeneous and FG plates are compared and verified with the known results in the literature. It is found that the neutral axes for FG plates move to upper surface (full-ceramic) and not at the mid-surface as predicted in the homogeneous plates. It can be concluded that, the gradation of the metal-ceramic components of the plate is the signifieant parameter in evaluating the mechanical responses of the FG plate. The SSDT has computed acceptable results for in-plane stresses and displacement fields.

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