A refined higher order shear and normal deformation theory for E-, P-, and S-FGM plates on Pasternak elastic foundation

Here, a refined higher order shear and normal deformation theory is presented for exponential (E), power-law (P) and sigmoid (S) functionally graded material (FGM) plates on elastic foundation. In this study, the displacement field of the 4-variable plate theory is modified by considering a thickness stretching effect. The number of unknown functions involved in the present theory is only five, as opposed to six or even greater numbers in the case of other shear and normal deformation theories. The present theory accounts for both shear deformation and thickness stretching effects by a parabolic variation of all displacements across the thickness, and satisfies the stress-free boundary conditions on the upper and lower surfaces of the plate. The equations of motion are derived from minimum total potential energy principle. Analytical solutions for the bending analysis are obtained for simply supported plates. It is assumed that the elastic medium is modeled as Pasternak elastic foundation. The obtained results are compared with 3-dimensional and quasi-3-dimensional solutions and those predicted by other plate theories. Verification studies show that the present theory is not only more accurate than the 4-variable plate theory but also simple in predicting the bending response of E-, P-, and S-FGM plates.