Waves From Suddenly Punched Hole in Plate Subjected to Uniaxial Tension Field

Abstract

The plane-stress unloading waves emanating from a suddenly punched circular hole in a thin plate subjected to a uniform uniaxial tension field are considered. It is assumed that the plate is linearly elastic and that the plugging of the hole takes place over a finite time with the stress components at the circumference of the hole decreasing, linearly with time, to zero. A modification of the method of near characteristics, introduced by Sauer [1], for problems of gas dynamics with two or three spatial variables is used to obtain a numerical solution to the governing equations, which have three independent variables, time and two plane polar coordinates. The numerical results obtained approach those for the well-known statical solution, for a hole in a plate subjected to a tension field [2], as the time after the arrival of the wave front becomes large.