Nonlinear bending analysis of thick functionally graded plates based on third-order shear deformation plate theory

Abstract

In this paper the nonlinear bending analysis of thick functionally graded plates subjected to mechanical loading is studied. The formulation is derived based on the third-order shear deformation plate theory and Von Kármán type non-linearity. Young’s modulus is assumed to vary according to a power law distribution in terms of the volume fractions of the constituents. The principle of virtual work is used to obtain the weak form of the governing differential equations. The most important advantage of employed numerical solution in this work is that the whole plate is considered as one element and the components of displacement field are interpolated over the entire domain, then a hierarchical finite-element scheme is developed. The validity and the accuracy of the method are verified by comparisons made with other solutions. In addition; the effect of numbers of interpolation functions on the accuracy of results is studied. It is concluded that accurate results are obtained even by few numbers of interpolation functions.