A refined laminated plate theory accounting for the third-order shear deformation and interlaminar transverse stress continuity

Abstract

A variational consistent third-order shear laminated plate theory accounting for the transverse shear stress continuity at the interlaminar interfaces of laminated plates is developed in this paper. The transverse shear function used in this new laminated plate theory is based on the kinematics in the third-order shear deformation plate theory proposed by Shi (2007). The variational principle is employed to derive the variational consistent equilibrium equations in terms of displacements and the variational boundary conditions in terms of displacements and equivalent stress resultants. The continuity conditions of the in-plane displacements and transverse shear stresses at the interlaminar interfaces of laminated plates are enforced by the Heaviside step functions and continuity coefficients. The resulting new laminated composite plate theory accounting for interlaminar continuity has only five independent field variables. Furthermore, the number of the field variables in the present third-order shear laminated plate theory is the same as that used in the first-order shear deformation plate theory. The refined laminated plate theory is applied to solve the bending problems of four laminated composite plates with different lamination schemes and different aspect ratios to evaluate its reliability and accuracy. The resulting analytical solutions of both deflections and stresses agree well with the 3D elasticity solutions and the numerical results of finite element analysis. The result comparison with other laminated plate theories shows that new laminated plate theory accounting for the interlaminar continuity proposed in this paper yields more accurate displacements and stresses than other laminated plate theories with five global variables. Because only five field variables are used in this new laminated plate theory with interlaminar continuity, this refined laminated plate theory can be used as an accurate and efficient theoretical model for the finite element analysis of laminated composite plates.