The dual reciprocity method and the numerical Green’s function for BEM fracture mechanic problems

Abstract

The boundary element method has been applied with success to linear elastic fracture mechanic problems, involving static and dynamic cases. In order to solve body force problems (e.g., gravitational forces and transient problems with velocities and accelerations), Nardini and Brebbia presented, in 1982, the dual reciprocity formulation. Originally with the intention of solving transient problems using fundamental solutions of the static formulation, the procedure was found to be very efficient in the solution of body force problems as well. Also, a Green’s function corresponding to an embedded crack within the infinite medium can be introduced into the boundary element formulation as the fundamental solution. This yields accurate means of calculating only the external boundary unknown displacements and tractions and, in a post-processing scheme, determining the crack opening displacements. This paper introduces an approach that involves the numerical Green’s function procedure, of Telles and coworkers, and the dual reciprocity formulation. It compares beam solutions with the simulated effect of the total weight applied as a concentrated boundary force, the actual self-weight as a body force and a frequency- and time-dependent transient Heaviside load applied to a plate with a central crack.