Numerical solution to the problem of a stress wave reflecting in a spherical thick-walled reservoir loaded with a time depending internal pressure

Military Institute of Armament Technology, 05-220 Zielonka, Prymasa Stefana Wyszyńskiego str. 7, Poland

^a e-mail: ZielenkiewiczM@witu.mil.pl

Abstract

In the paper the problem of a stress wave reflecting in the wall of a spherical thick-walled reservoir loaded with a time depending internal pressure was investigated. The material of reservoir wall was assumed to be linearly elastic and isotropic. The stress wave generated on the internal surface of reservoir propagates towards outside and reflects on the external surface, generating the reflected component of wave which superimposes on the incident one due to the linearity of the problem. Consecutive reflections of the wave front generate the successive components of wave. The Laplace transforms determining solution independently for every reflected component of the stress wave were presented. The case of the step pressure, which describes the simplest model of immediate detonation, was considered. Due to the complex form of functions determining in the domain of time the analytical solutions for further reflections, the problem was integrated numerically. It was shown that for the selected finite number of reflections the describing equations can be solved together as one ordinary differential equations system. From the introductory analysis of results it follows that the summed up displacements of particular spherical layers of reservoir wall oscillate around their static values, despite the fact that the amplitude of particular components of wave approaches infinity.