Nonlinear analysis of composite shells with application to glass structures

Abstract

Laminated glass is a special composite material, which is characterised by an alternating stiff/soft lay-up owing to the significant stiffness mismatch between glass and PVB. This work is motivated by the need for an efficient and accurate nonlinear model for the analysis of laminated glass structures, which describes well the through-thickness variation of displacement fields and the transverse shear strains and enables large displacement analysis. An efficient lamination model is proposed for the analysis of laminated composites with an alternating stiff/soft lay-up, where the zigzag variation of planar displacements is taken into account by adding to the Reissner-Mindlin formulation a specific set of zigzag functions. Furthermore, a piecewise linear through-thickness distribution of the material transverse shear strain is assumed, which agrees well with the real distribution, yet it avoids layer coupling by not imposing continuity constraints on transverse shear stresses. Local formulations of curved multi-layer shell elements are established employing the proposed lamination model, which are framed within local co-rotational systems to allow large displacement analysis for small-strain problems. In order to eliminate the locking phenomenon for the shell elements, an assumed strain method is employed and improved, which readily addresses shear locking, membrane locking, and distortion locking for each constitutive layer. Furthermore, a local shell system is proposed for the direct definition of the additional zigzag displacement fields and associated parameters, which allows the additional displacement variables to be coupled directly between adjacent elements without being subject to the large displacement co-rotational transformations. The developed multi-layer shell elements are employed in this work for typical laminated glass problems, including double glazing systems for which a novel volume-pressure control algorithm is proposed. Several case studies are finally presented to illustrate the effectiveness and efficiency of the proposed modelling approach for the nonlinear analysis of glass structures.