Post-buckling analysis of functionally graded rectangular plates

The post-buckling response of the functionally graded materials plate, subjected to thermal and mechanical loadings, is obtained analytically, using fast converging finite double Chebyshev polynomials. A functionally graded plate made of aluminum and alumina is considered for different kinds of boundary conditions. The volume fraction of the material constituents follows a simple power law distribution. The mathematical formulation is based on the first-order shear deformation theory and von-Karman nonlinear kinematics. Numerical results indicate that the critical temperature and buckling loads decrease with increase in volume fraction exponent of the FGM plate. It is observed that effect of the volume fraction exponent k up to 2 on the buckling and post-buckling response of the plate is more significant. The effects of plate aspect ratio on the post-buckling response of the plate for different volume fraction of the constituents of the materials are presented. It is observed that the buckling load and post-buckling response of the FGM plate is almost same for a plate aspect ratio more than or equal to 3.