Efficient analysis of laminated composite and sandwich plates with interfacial imperfections

Abstract

An enhanced first-order shear deformation theory is developed for laminated composite plates that have interfacial imperfections. The proposed methodology is as follows: First, higher-order zigzag displacements are introduced to account for the interfacial imperfections, which are modeled as spring-layers. This makes it possible to describe such imperfections as a five-degree-of-freedom problem, which makes the proposed theory efficient yet accurate. Second, the relationship between the derived displacements and the Reissner–Mindlin displacements are systematically established by using the least square approximation, which renders a so-called ‘effective shear modulus’ via strain energy transformation. Finally, the governing equations based on the transformed strain energy, which are the same as the Reissner–Mindlin equations except in the case of the transverse shear modulus, are solved either analytically or numerically. Once the governing equations are solved, the displacements of the Reissner–Mindlin-like theory can be improved by using the derived relationships. In other words, the higher-order in-plane zigzag displacements are recovered in terms of the obtained solutions. One advantage of the proposed theory is that it has the same number of degrees of freedom as the Reissner–Mindlin theory, which implies that any finite elements developed for such a theory can be used without any modifications. The accuracy of the present theory is assessed by comparing its analytical solutions with available data from the literature. The effects of interfacial imperfections on stresses and shear correction factors are also explored via numerical examples.