Finite element model based on refined plate theories for laminated glass units

TL;DR

This paper develops a refined finite element model for laminated glass units using advanced plate theories, enabling accurate nonlinear analysis of their complex mechanical behavior.

Contribution

It introduces a novel finite element formulation based on Mau's refined plate theory with layer compatibility enforced by Lagrange multipliers, suitable for nonlinear laminated glass analysis.

Findings

Model accurately reproduces laminated glass behavior

Verification confirms reliability of the formulation

First step towards comprehensive glass system modeling

Abstract

Laminated glass units exhibit complex response as a result of different mechanical behavior and properties of glass and polymer foil. We aim to develop a finite element model for elastic laminated glass plates based on the refined plate theory by Mau. For a geometrically nonlinear description of the behavior of units, each layer behaves according to the Reissner-Mindlin kinematics, complemented with membrane effects and the von K\'{a}rm\'{a}n assumptions. Nodal Lagrange multipliers enforce the compatibility of independent layers in this approach. We have derived the discretized model by the energy-minimization arguments, assuming that the unknown fields are approximated by bi-linear functions at the element level, and solved the resulting system by the Newton method with consistent linearization. We have demonstrated through verification and validation examples that the proposed formulation is reliable and accurately reproduces the behavior of laminated glass units. This study represents a first step to the development of a comprehensive, mechanics-based model for laminated glass systems that is suitable for implementation in common engineering finite element solvers.