Dynamic Stresses and Deformations in a Thick Cylinder under Nonaxially Symmetrical Impulsive Loads : 1st Report, Analysis Based on the Two Dimensional Dynamic Theory of Elasticity

Abstract

In this paper, the response of a hollow infinite circular cylinder (as a plane strain field) of a circular disk (as a plane stress field) is studied, which is subjected to a pair of impulsive line loads along its outer generators facing each other. First, the line loads are expanded in a Fourier series and represented as a sum of a uniformly distributed pressure and pressures in the form of trigonometric functions. By the use of this method of superposition, the dynamic stresses in the cylinder or the disk are analized based on the two dimensional dynamic theory of elasticity by using the stress functions and the Laplace transformation. As the result, it is shown that the maximum tensile stress is produced along the inner generators corresponding to the loaded ones and the value is about twice as large as the corresponding static result.