A simple and accurate sandwich plate theory accounting for transverse normal strain and interfacial stress continuity

Abstract

This paper presents a simple and accurate sandwich plate theory accounting for the transverse normal strain and interfacial stress continuity. A refined cubic polynomial is used for the transverse shear function and a linear function is adopted for the transverse normal strain. The Heaviside step function and stress continuity coefficients are employed respectively to enforce the interfacial continuity of the in-plane displacements and transverse stresses. By the enforcement of the traction conditions on the plate surfaces, there are only five independent field variables in the present sandwich plate theory. The variational consistent equilibrium equations and boundary conditions in terms of both displacements and stress resultants are derived by utilizing the variational principle. The analytical solutions of the bending analyses of sandwich plates with different aspect ratios and stiffness ratios are solved to demonstrate the accuracy of this new sandwich plate theory. The resulting analytical solutions of deflections, normal stresses and transverse shear stresses are compared with the 3D elasticity solutions, the numerical results and the results given by other sandwich plate theories. The comparison study shows that this equivalent single layer sandwich plate theory is not only simple, but also capable of achieving the accuracy of layerwise sandwich plate theories.