Hypersingular BEM for transient elastodynamic

The topic of hypersingular boundary integral equations is a rapidly developing one due to the advantages which this kind of formulation offers compared to the standard boundary integral one. In this paper the hypersingular formulation is developed for time-domain antiplane elastodynamic problems. Firstly, the gradient representation is found from the displacement one, removing the strong singularities (Dirac's delta functions)which arise due to the differentiation process. The gradient representation is carried to the boundary through a limiting process and the resulting equation is shown to be consistent with the static formulation. Next, the numerical treatment of the traction boundary integral equation and its application to crack problems are presented. For the boundary discretization, conforming quadratic elements are tested, which are introduced in this paper for the first time, and it is shown that the results are very good in spite of the lesser number of unknowns of this approach in comparison to the non-conforming element alternative. A procedure is devised to numerically perform the hypersingular integrals that is both accurate and versatile. Several crack problems are solved to show the possibilities of the method. To this end both straight and curved elements are employed as well as regular and distorted quarter point elements.