A von Kármán-type model for two-layer laminated glass plates, with applications to buckling and free vibration under in-plane edge loads

Abstract

This article presents a layerwise geometrically nonlinear two-dimensional model for the undamped dynamical response of thin two-layer plates with partial shear interaction. The model is tailored for the analysis of laminated glass plates of the type most commonly used in building structures (two glass layers bonded by a polymeric interlayer). The geometrical nonlinearities are introduced via the so-called von Kármán strains. The process of dimensional reduction is based on Podio-Guidugli’s method of internal constraints. An unconventional choice of generalised displacements highlights several direct similarities with the single-layer plate theories of von Kármán and Mindlin.The model is used to study the flexural buckling and free vibration of two-layer plates under in-plane edge loads. Analytical solutions are obtained for rectangular plates with (i) all edges simply supported without shear restraint and (ii) a two-parameter system of uniform in-plane normal edge loads. These solutions degenerate into those of single-layer von Kármán plates in the two limiting cases of zero and full shear interaction. A conforming rectangular finite element is formulated and shown to perform effectively. When using uniform meshes, the observed asymptotic rate of convergence for the finite element approximation of the lowest buckling load and vibration frequency is quadratic.