THE DTN FINITE-ELEMENT METHOD FOR ELASTIC DOMAINS WITH CRACKS AND REENTRANT CORNERS

A combined analytic-finite element method is proposed for the efficien t solution of problems in elasticity involving geometrical singulariti es. The Dirichlet-to-Neumann (DtN) map is used in the procedure, to en able the replacement of the original singular problem by an equivalent regular problem. which is then solved by a finite element scheme. Pro blems involving the Saint Venant torsion of long rods with cross-secti ons containing cracks or re-entrant corners are considered in detail. Mode I and II fracture problems are also discussed. The method yields the stress field in the entire domain, as well as the stress intensity factor. Numerical examples are presented for the torsion problem, whi ch demonstrate the performance of the method.