An Asymptotic Approach for the Elastodynamic Problem of a Plate under Impact Loading

Abstract

An approach is presented for analyzing the transient elastodynamic problem of a plate under an impact loading. The plate is considered to be in the form of a long strip under plane strain conditions. The loading is taken as a concentrated line force applied normal to the plate surface. It is assumed that this line force is suddenly applied and maintained thereafter (i.e., it is a Heaviside step function of time). Inertia effects are taken into consideration and the problem is treated exactly within the framework of elastodynamic theory. The approach is based on multiple Laplace transforms and on certain asymptotic arguments. In particular, the one-sided Laplace transform is applied to suppress time dependence and the two-sided Laplace transform to suppress the dependence upon a spatial variable (along the extent of the infinite strip). Exact inversions are then followed by invoking the asymptotic Tauber theorem and the Cagniard-deHoop technique. Various extensions of this basic analysis are also discussed.