Trefftz boundary element method applied to fracture mechanics - Sabino Domingues, J.; Portela, A.; de Castro, P.M.S.T. (Engineering fracture mechanics, 1999)
The linear elastic problem is solved by means of Trefftz functions which automatically satisfy the elasticity equations in a 2D domain. Using Kolosov–Muskhelishvili’s complex variable representation, complex potentials are expanded in power series. Trial elementary elastic fields are derived from each expansion term. The Galerkin weighted residuals formulation is used to derive the system of equations in which the unknowns are the retained expansion coefficients. For crack problems, special expansions that satisfy the zero traction condition along crack edges are used to obtain the approximating elastic field, which allow the direct determination of the stress intensity factors. Several numerical results, obtained for typical crack problems using Trefftz Boundary Element Method, are presented and compared with those published by other authors. A simple example of multiple site damage with two offset parallel cracks is also analyzed.