Three-dimensional modelling of laminated glass bending on two-dimensional in-plane mesh

The article presents an analysis of bending of a laminated glass (LG) plate. The analysis uses a 3D physical model in which only a 2D in-plane mesh is applied for numerical analysis. The LG consists of glass panes bonded by films of polymers, so the LG is layered structure. The approach in which the 3D spatial approximation in each layer is a combination of a 2D in-plane approximation with a 1D transverse approximation (along the plate thickness) is used. In consequence, the final numerical model is based on a 2D in-plane finite element mesh. A special postprocessing procedure, devised specially to be used in this method, has been developed which enables visualization of a full 3D deformation as well as all six stress components. The method is relatively simple, robust and effective, and it gives correct 3D results. The accuracy of the method has been tested with the use of some known solutions as well as by comparison with analytical solution, well established FEM procedures and with experimental results. In the examples the two-, three- and four-paned laminated glass is analysed. In spite of the fact that the numerical model is 2D, the full 3D results are obtained. For the sake of clarity, this paper is limited to elastic plate bending, but the method can be directly applied for LG subjected to thermal or thermo-mechanical load.