On the analytical approach for the bending/stretching of linearly elastic functionally graded rectangular plates with two opposite edges simply supported

Abstract

In this article, a new analytical method for bending—stretching analysis of thick functionally graded (FG) rectangular plates is presented. Using this method, the governing equations of FG rectangular plates based on the first-order shear deformation or Mindlin plate theory are decoupled. Five coupled partial differential equations of the Mindlin FG plate are converted into two uncoupled partial differential equations in terms of transverse displacement and a new function. It is analytically shown that by introducing an equivalent flexural rigidity, the equations of FG rectangular plate become similar to those of the homogeneous isotropic plate. Solving these equations, the solutions are obtained for the FG rectangular plate with two opposite edges simply supported. A comparison of the present results with available solutions from previous studies is made and a good agreement can be seen. Also, the numerical results for stress and deflection of the FG rectangular plate with various boundary conditions are obtained.

Keywords

bending—stretching functionally graded thick rectangular plate analytical method

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