Buckling of Laminated Glass Beams and Plates using Linear-Elastic Models
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Structural laminated glass elements are composed of two or more glass plies bonded by polymeric interlayers, whose mechanical behaviour is commonly modelled as linear viscoelastic. The buckling analysis of such elements is particularly challenging because the classical superposition principle, widely used in linear viscoelasticity through the Boltzmann integral, cannot be applied due to the geometric nonlinearities inherent to the buckling phenomenon [1]. To overcome these limitations, simplified analytical models based on the quasi-elastic approximation—which neglects memory effects—have been developed to estimate the buckling load of laminated glass beams and plates [1,2]. The versatility of this approach allows its application to a wide range of engineering configurations without resorting to full viscoelastic modelling. These simplified models extend the critical buckling load equations for linear-elastic monolithic elements to laminated structures by introducing an effective stiffness that is dependent on time and temperature. However, their implementation relies on shape- and load-dependent parameters that are only available for specific boundary conditions or require analytical derivations that are not feasible in practical design scenarios [1,2]. In this work, two linear-elastic finite element models—one monolithic and one layered—are employed to estimate the parameters required in the buckling load equations. Validation is carried out by comparing the analytical predictions with results obtained from layered numerical models implemented in ABAQUS, where the eigenvalue problem is solved iteratively.
