Relationships between axisymmetric bending and buckling solutions of FGM circular plates based on third-order plate theory and classical plate theory

The third-order shear deformation plate theory (TPT) is employed to solve the axisymmetric bending and buckling problems of functionally graded circular plates. Relationships between the TPT solutions of axisymmetric bending and buckling of functionally graded circular plates and those of isotropic circular plates based on the classical plate theory (CPT) are presented, from which one can easily obtain the TPT solutions for the axisymmetric bending and buckling of functionally graded plates. It is assumed in analysis that the mechanical properties of the functionally graded plates vary continuously through the thickness of the plate and obey a power law distribution of the volume fraction of the constituents. Effects of material gradient property and shear deformation on the bending and buckling of functionally graded plates are discussed in the frameworks of the first-order plate theory (FPT) and third-order plate theories. Also, comparisons of the TPT solutions to the FPT and CPT solutions are presented, which show that the first-order shear deformation plate theory is enough to consider the effect of shear deformation on the axisymmetric bending and buckling of functionally graded circular plate, a much higher order and more complex plate theory (say TPT) is not necessary for such a kind of problem.