Soft-core sandwich plate dynamics: Theory and blast analysis

This work presents an analytical and computational platform that aims to face the modeling, analytical, and computational challenges associated with highly transient dynamics of soft-core sandwich plates and shed light on the dynamic behavior of this unique structural form. This platform comprises a dynamic tri-layered plate analytical model and a corresponding specially tailored triangular finite element formulation. The model is based on extended high-order kinematics for the soft core layer, and it accounts for geometrical nonlinearity, high-order inertia terms, material orthotropy in the three physical layers, the presence of interfaces linking those layers, the interfacial tractions that develop across them, and the bi-directional dynamic response of the plate structure. The governing equations of the finite element formulation are solved in the time domain using a nonlinear Newmark-type time-stepping algorithm. The methodology is validated with regard to free vibration analysis and forced motion analysis against experimental results, 2D-, and 3D-elasticity-based closed form solutions, and multilayered plate finite elements reported in the literature. Following the validation, a numerical example considers the transient response of a soft-core sandwich plate subjected to highly transient air blast loading and compares the response with experimental results taken from the literature. The study examines the ability of present formulations to capture the experimentally observed response and to shed light on some aspects of the response, including the inherently 2D nature of the response, the propagation of stress fronts through the structural medium, and the interfacial interactions.