An Analytical Approach for Buckling Analysis of Functionally Graded Rectangular Mindlin Plates

A Levy solution for buckling analysis of moderately thick functionally graded (FG) rectangular plates has been presented in this paper. Based on the first order shear deformation plate theory, the stability equations are obtained for a plate subjected to in-plane compressive loads. Since the plate is made of functionally graded materials (FGMs) and the material properties vary through the thickness, the stability equations are coupled. In order to remove the existing coupling, a new analytical method has been presented. Introducing four new analytical functions (which are thefunction of displacement components) and doing some mathematical calculations, five coupled stability equations are converted to five independent equations. Focusing on these equations, some expressions are suggested for the in-plane components of the displacement field. Therefore, it is concluded that in FG plates, the mid-plane does not coincide with the neutral surface. It is assumed that the plate is simply supported in x direction and has arbitrary boundary conditions along the other edges. Therefore, the Levy solution is considered as the solution. Imposing the boundary conditions on the solution, the buckling loads which are the eigen values of the problem are obtained. Finally, the critical buckling load for plates with different boundary conditions, various FGM properties and some aspect ratios and thickness to side ratios has beenpresented in tables and figures. Also, the effect of boundary conditions, thickness ratio and aspect ratio on the critical buckling load and mode is investigated in details.

Keywords:

Buckling analysis , Functionally graded , Levy Solution , Mindlin Theory