A new higher-order shear deformation theory for static, buckling and free vibration analysis of functionally graded sandwich beams

This paper presents a new higher-order shear deformation theory for static, buckling and free vibration analysis of functionally graded sandwich beams. In this theory, the axial displacement accounts for a third-order and inverse trigonometric distribution, and the transverse shear stress satisfies the traction-free boundary conditions on the top and bottom surfaces of the beams. Governing equations of motion are derived from the Hamilton's principle for sandwich beams with homogeneous hardcore and softcore. Navier-type solution for simply-supported beams is developed to solve the problem. Numerical results are obtained to investigate effects of the power-law index, span-to-height ratio and thickness ratio of layers on the displacements, stresses, critical buckling load and frequencies.