A Simple Model for Inflexed Multilayered Laminated Glass Beams Based on Refined Zig-Zag Theory

Laminated glass is a composite made of glass plies sandwiching polymeric interlayers, permanently bonded with a process at high pressure and temperature in autoclave. Within the quasi-elastic approximation, according to which the polymer is linear elastic material whose elastic modulus parametrically depends upon time and environmental temperature, we present a model for inflexed laminated-glass beams in the pre-glass-breakage phase. The approach relies on a modified version of the refined zig-zag theory for composites, in which the glass plies are treated as Euler-Bernoulli beams, whereas the interlayers can only provide a shear-stiffness contribution to the coupling of the glass plies. The kinematic description is greatly simplified and the governing equations can be solved analytically, for laminated packages of any type, when the beam is statically determined. A finite element implementation is proposed for the most general cases. The convergence analysis for the numerical approach and the comparison with the analytical solution in benchmark problems demonstrate the efficiency of the proposed method.