A simple quasi-3D sinusoidal shear deformation theory for functionally graded plates

This paper presents a simple quasi-3D theory for the bending analysis of functionally graded plates. This theory accounts for both shear deformation and thickness stretching effects by a sinusoidal variation of all displacements through the thickness. By dividing the transverse displacement into bending and shear parts, the number of unknowns and governing equations of the present theory is reduced, and hence, makes it simple to use. The governing equations and boundary conditions are derived using the principle of virtual displacements. Analytical solutions are obtained for simply supported plates. The accuracy of the present theory is verified by comparing the obtained results with 3D and quasi-3D solutions and those predicted by higher-order shear deformation theories. The comparison studies show that the obtained results are not only more accurate than those obtained by higher-order shear deformation theories, but also comparable with those predicted by quasi-3D theories with a greater number of unknowns.