An original four-variable quasi-3D shear deformation theory for the static and free vibration analysis of new type of sandwich plates with both FG face sheets and FGM hard core

This paper presents an original high-order shear and normal deformation theory for the static and free vibration of sandwich plates. The number of unknowns and governing equations of the present theory is reduced, and hence makes it simple to use. Unlike any other theory, the number of unknown functions involved in displacement field is only four, as against five or more in the case of other shear and normal deformation theories. New types of functionally graded materials (FGMs) sandwich plates are considered, namely, both FG face sheets which the properties vary according to power-law function and exponentially graded hard core. The equations of motion for the present problem are derived from Hamilton's principle. For simply-supported boundary conditions, Navier's approach is utilized to solve the motion equations. The accuracy of the present theory is verified by comparing the obtained results with three-dimensional elasticity solutions and other quasi-3D higher-order theories reported in the literature. Other numerical examples are also presented to show the influences of the volume fraction distribution, geometrical parameters and power law index on the bending and free vibration responses of the FGM sandwich plates are studied. It can be concluded that present formulation which takes into account both the transverse shear and normal deformation, predicts the natural frequencies with the same degree of accuracy as that of 3D elasticity solutions and gives a good results of displacements and stress compared with others Quasi-3D theories. It can be also deduced that the central deflection is in direct correlation relation with inhomogeneity parameter and the natural frequency is in inverse relation with this parameter.