TRANSIENT-RESPONSE OF AN ORTHOTROPIC ELASTIC MEDIUM WITH A CAVITY

A class of traction boundary-value problems related to an orthotropic elastic half plane with an arbitrary shaped cavity is considered. The problems under consideration are formulated in the Laplace transform space by using a boundary integral equation method based on Green's functions for unit impulsive loads applied in the interior of an orthotropic half plane. Time domain solutions are obtained by solving the boundary integral equation numerically and applying a numerical scheme for Laplace inversion. It is found that the accurate numerical evaluation of half plane Green's functions is critical for both the accuracy and the numerical stability of boundary integral equation solutions. The accuracy of present results is confirmed by comparing with the existing solutions for transient pressurization of a circular cavity in an isotropic elastic full plane. Selected time histories of displacements and hoop stresses of an orthotropic half plane due to a pressurised circular cavity located at a finite depth below the free surface are presented. Surface displacement profiles of isotropic, and of orthotropic graphite-epoxy and cobalt half planes with circular cavities excited by a surface loading (transducer) pulse are also presented. Features of the response profiles are discussed for potential applications in nondestructive evaluation of composites, geomechanics and other disciplines. The boundary integral equation scheme presented in this study can also be extended to analyse displacement and mixed boundary-value problems realted to an orthotropic elastic half plane.