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Aliabadi anisotropic applied traction auxiliary region basic density functions body force boundary conditions boundary element method boundary integral equation calculated collocation components composite laminates Computational crack faces crack front crack front elements crack length crack problems crack tip crack-extension increment cylindrical defined delaminated denotes derived discretized displacement and traction displacement field domain dual boundary element edge crack elastic field elastodynamic Element type energy release rate evaluated Figure finite element finite element method force doublets formulation fracture mechanics fundamental fields fundamental solutions geometry given Green's function infinite body infinite plate intensity factor solutions isotropic J-integral layer linear linear elastic Load type Mech mesh mode Nisitani nodes normalised stress intensity notch obtained penny-shaped crack plane strain point forces present procedure quarter-point elements ratio respectively shear shown in Fig solved special crack front stress concentration stress field stress intensity factor symmetric two-dimensional uniform tensile values variation vector weight functions