Nonlinear Bending Analysis of Thick Functionally Graded Plates Based on Third-Order Shear Deformation Plate Theory

The nonlinear bending analysis of thick functionally graded plates subjected to mechanical loading is studied in this paper. The formulation was 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 the power law distribution in terms of the volume fractions of the constituents. The principle of virtual work was 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 was considered as one element and the components of displacement field were interpolated over the entire domain, then a hierarchical finite-element scheme was developed. The validity and accuracy of the method was verified by comparisons made with other solutions. In addition, the effect of numbers of interpolation functions on the accuracy of results was studied. It is concluded that accurate results are obtained even by few numbers of interpolation functions.