Investigation of the Static Bending Response of FGM Sandwich Plates

In the present work, a displacement-based high-order shear deformation theory is introduced for the static response of functionally graded plates. The present theory is variationally consistent and strongly similar to the classical plate theory in many aspects. It does not require the shear correction factor, and gives rise to the transverse shear stress variation so that the transverse shear stresses vary parabolically across the thickness to satisfy free surface conditions for the shear stress. By dividing the transverse displacement into the bending and shear parts and making further assumptions, the number of unknowns and equations of motion of the present theory is reduced a and hence makes them simple to use. The material properties of the plate are assumed to be graded in the thickness direction according to a simple power-law distribution in terms of volume fractions of material constituents. The equilibrium equations of a functionally graded plate are given based on the higher order shear deformation theory. The numerical results presented in the paper are demonstrated by comparing the results with solutions derived from other higher-order models found in the literature and the present numerical results of Finite Element Analysis (FEA). In the numerical results, the effects of the grading materials, lay-up scheme and aspect ratio on the normal stress, shear stress and static deflections of the functionally graded sandwich plates are presented and discussed. It can be concluded that the proposed theory is accurate, elegant and simple in solving the problem of the bending behavior of functionally graded plates.