An Analysis of Transient Stresses Produced around Cavities of Arbitrary Shape during the Passage of Traveling Waves

Abstract

The present paper is concerned with an application of the integral equation method to the analysis of the transient stresses produced around cavities of arbitrary shape, which are excavated in an infinite elastic medium and subject to longitudinal and transverse waves of arbitrary pressure-time history. The method used in the present paper consists of such a technique as devising a solution for the transient problem from the superposition of appropriate steady-state solutions, which are obtained by use of the integral equation. The validity of the present method is demonstrated by several examples such as : (1) steady-state stresses around a circular cavity due to longitudinal and transverse waves, (2) transient stresses around a circular cavity due to stepform longitudinal and transverse waves, and a triangular-form longitudinal wave, (3) transient stresses around a horseshoe-shaped cavity due to a step-formed longitudinal wave. It may be concluded that the present method is advantageously applied to transient problems, specifically with boundaries of arbitrary shape and accompanied also with traveling waves of arbitrary pressue-time history.