Analytical layerwise stress and deformation analysis of laminated composite plates with arbitrary shapes of interfacial imperfections and discontinuous lateral deflections

Abstract

In the present article, a double power series analytical layerwise model is proposed for analysis of multilayer orthotropic plates with arbitrary shapes of interfacial bond defects. In contrast to the previous models, the discontinuity in the lateral deflections of the successive layers is also considered. The adhesive bonding layers are modeled by elastic elements with normal and shear stiffness coefficients; so that, the continuity conditions of the transverse shear and normal stresses are met at the layer interfaces. It is the first time that an analytical solution rather than the data-dependent finite element method is proposed for stress and displacement analysis of multilayer rectangular plates with arbitrary shapes of interfacial bond damages, including the discontinuity in the transverse displacements of the successive layers. Results of the transverse displacement and stresses are then refined according to the 3D theory of elasticity. Results reveal that even small violations in the bonding between layers, may increase the resulting stresses, lateral deflections, and the differences between lateral deflections of the successive layers to more than twice, thrice, and five times, respectively. Moreover, in contrast to the growth of the in-plane stresses, redistribution of the transverse shear stress is governed by the equilibrium rather than the constitutive-law-based conditions.