Plane-Stress Unloading Waves Emanating From a Suddenly Punched Hole in a Stretched Elastic Plate

Abstract

The present paper points out that Kromm’s [1] plane-stress solution, for compressional waves in an infinite elastic plate subjected to radial pressure in a circular hole at its center, has application to still another problem of interest. This is the problem of a stretched elastic plate in which a circular hole is suddenly punched. The plane-stress solution for the tensile circumferential stresses, generated by the unloading mechanism in punching, is given here. This solution is derived independently of Kromm’s work in which a rather special Laplace-transform technique was used. The derivation given here also makes use of the Laplace transform but in a more direct manner, employing the inversion integral and a contour integration. It is also shown that the present inversion technique offers important simplifying features over that used by Selberg [3] in the closely related plane-strain problem. The numerical results presented are of interest in fragmentation studies. It is shown that the dynamic circumferential stress field in the vicinity of the punched hole is quite severe; which would be important to the creation and propagation of radial cracks.

Soil-structure interaction and wave propagation problems in 2D by a Duhamel integral based approach and the convolution quadrature method

“…The problem can be solved analytically in the Laplace domain, but no closed-form inverse transform can be found. Selberg [24] and Miklowitz [16] suggest a numerical evaluation of the inverse Laplace transform by contour integrals. Kromm [12], also starting from the Laplace domain solution, uses the convolution theorem to derive a Volterra type integral equation which he then solves numerically.…”

Dynamic fracture of simulated solid propellant

“…The hoop stress at the inner bore is plotted as a function of time for both plane stress and plane strain calculations. For the plane strain case the wave front speed is 63,000 in/sec, the dilatation wave speed; for the plane stress case the speed is 25,000 in/sec, the in-plane plate speed [5]. Because of this difference the plane-strain case shows a more rapid rise of hoop stress than does the plane stress case.…”

Isochromatic lines and dynamic punching of a stressed elastic plate

“…At t = 0 a flat-nosed projectile, travelling along the z-axis, begins to punch out a hole of radius a » h in the where H(-) denotes the Heaviside step function and t* is the punching time, which according to [2] is t* = 2 h/w, (2.3) where w is the punch velocity. The situation is illustrated in Fig.…”