Revisiting Kirchhoff–Love plate theories for thin laminated configurations and the role of transverse loads

Abstract

The present article aims to re-derive a (de-)homogenization model for particularly investigating the behavior of thin laminated plates withstanding transverse loads. Instead of starting with Kirchhoff-type of assumptions, we directly apply perturbation analysis, in terms of the small parameter introduced by the thinness of composite plates, to the original three-dimensional governing elastostatic equations. The present article sees its intriguing points in the following three aspects. First, it is shown that transverse loads applied on a thin laminated plate induce an in-plane stress response, which essentially differs from the case of single-layered homogenous plates. A scaling law estimating the magnitude of the in-plane stresses due to transverse loads is then given, and a size effect in such induced in-plane stresses arises. Second, the stress state at any position of interest in the original three-dimensional configuration can be asymptotically estimated following a (de-)homogenization scheme, and the (de-homogenization) accuracy is shown, both theoretically and numerically, to be at a same order of magnitude as the thickness-to-size ratio. Third, the asymptotic analysis here identifies the right order of magnitude for the transverse normal strain, which is often set to vanish, leading to the so-called Poisson’s locking problem in classical thin plate theories.