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.
Highlights
This work introduces an asymptotic approach based on oneand two-sided Laplace transforms to deal with the transient problem of a plate under impact
An approach was presented for analyzing the transient elastodynamic problem of a plate in the form of a long strip under impact
Plane strain conditions were assumed and the loading was taken as a concentrated line force applied normal to the plate surface
Summary
This work introduces an asymptotic approach based on oneand two-sided Laplace transforms to deal with the transient problem of a plate under impact. The plate is taken in the form of a long strip under plane strain conditions. A Green’s function type of loading is taken here, that is, a concentrated line force (applied normal to the plate surface) with a Heaviside step function time-dependence. In this way, the present solution can be used as a fundamental solution for more general loadings. Inertia effects are taken into consideration and the problem is treated exactly within the framework of elastodynamic theory. Our main concern is on the stress and displacement field beneath the point of application of the impact load
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