Variational principles of laminated plates considering interlayer slip

Abstract

A model for analyzing laminated plates is proposed, considering the interlayer slip. The proposed model is suitable for civil engineering structures, such as undertrack structures and layered pavements. The interlayer slip at the interface was introduced in the model to reflect the effect of imperfect bonding between adjacent layers. The deformation of each layer follows the Kirchhoff–Love assumption of the classical plate theory. The principle of virtual work and the reciprocal theorem of laminated plates were established to account for interlayer slip, based on which the principles of minimum potential and complementary energy were derived and proven. Two- and three-field generalized variational principles were then developed by introducing the Lagrange multiplier method. Moreover, the variational principles for the free vibration and buckling of laminated plates were obtained. Finally, analytical solutions of the bending, free vibration and buckling responses of a simply supported laminated plate were obtained, and they were consistent with the numerical results.