HYPERSINGULAR BEM FOR TRANSIENT ELASTODYNAMICS

The topic of hypersingular boundary integral equations is a rapidly de veloping one due to the advantages which this kind of formulation offe rs compared to the standard boundary integral one. In this paper the h ypersingular formulation is developed for time-domain antiplane elasto dynamic problems. Firstly, the gradient representation is found from t he displacement one, removing the strong singularities (Dirac's delta functions) which arise due to the differentiation process. The gradien t 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 in tegral equation and its application to crack problems are presented. F or the boundary discretization, conforming quadratic elements are test ed, which are introduced in this paper for the first time, and it is s hown that the results are very good in spite of the lesser number of u nknowns of this approach in comparison to the non-conforming element a lternative. A procedure is devised to numerically perform the hypersin gular integrals that is both accurate and versatile. Several crack pro blems 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.