Fracture analysis of mode iii problems by the Trefftz boundary element approach

"Trefftz approach can be referred to the boundary-type solution procedure employing the regular T-complete function satisfying the governing equation. Since Trefftz [1] in 1926 applied his approach that was forced to satisfy the boundary condition to achieve the outcomes, numerous papers, concerning fundamentals, applications and analysis, have emerged in the literature. For the Trefftz boundary element method, Cheung et al [2] developed a direct formulation for solving two-dimensional potential problem. Kita et al [3] studied the same problem by the direct formulation and domain decomposition approach. Portela and Charafi [4] applied Trefftz Boundary element formulation to potential problems with thin internal or edge cavities. Sladek et al [5] presented a global and local Trefftz bpundary integral approach to solve Helmholtz equation. Domingues et al [6] extended the Trefftz boundary element approach to the analysis of linear elastic fracture mechanics. Most of the developments in the field can also be found in [7]."--p. 321.