Nonlinear Finite-Element Analysis of Laminated Glass Using the Four-Node Reissner-Mindlin Formulation and Assumed Transverse Shear Strain Fields

Abstract

Laminated glass consists of at least two monolithic glass lites bonded together by an elastomeric interlayer. Existing mathematical models using the finite-difference method or the nine-node quadrilateral finite-element method were developed to numerically characterize the nonlinear behavior of laminated glass lites under bending and were benchmarked against available test data. The finite-difference solution was predicated on the well-known von Kármán equations, which are generally limited to the case of thin plates, while the nine-node quadrilateral finite element was predicated on the nonlinear Reissner-Mindlin plate formulation applicable to thick and thin plates but could result in a system of nonlinear equations that are computationally inefficient to solve. Therefore, a nonlinear four-node quadrilateral finite-element model for laminated glass based on the Reissner-Mindlin formulation is advanced. The assumed transverse shear strain fields method is employed to prevent shear locking and all the required stiffness terms are fully integrated. Hourglassing effects due to the reduced integration technique commonly used to prevent shear locking are mitigated and the stability of the numerical solution is preserved. The numerical solution obtained from the four-node element is in good agreement with available test data as well as the finite-difference solution.