Three dimensional analysis of functionally graded plates up to yielding, using full layer-wise finite element method

In this paper, full layer-wise method is employed to analyze the elastic bending of functionally graded plates up to yielding. The solution procedure is presented in two steps. Firstly, the elastic bending of simply supported FG plates is studied to find the deflection and stress distribution. Until this step, the mechanical properties are assumed to vary through the thickness following the rule of mixture. The numerical results are compared with those obtained from quasi 3D elasticity and various shear deformation theories and there has been an excellent agreement between them. In the next step, the mechanical properties of FG plates are determined by using TTO model as the modified rule of mixture. The volume fraction of material constituents is assumed to vary via a power-law function through the thickness in both steps. Finally, Tresca and Von Mises' yield criteria are utilized to predict the onset of yielding. The results obtained for four different boundary conditions and demonstrated that boundary conditions has a remarkable influence on the region in which yielding initiates. The effect of power-law index has been depicted on the onset of yielding as well.