Stress analysis of transversely isotropic sectors weakened by multiple defects

In this article, the anti-plane deformation of a transversely isotropic sector with multiple defects is studied analytically. The solution of a Volterra-type screw dislocation problem in a sector is first obtained by means of a finite Fourier cosine transform. The closed form solution is then derived for displacement and stress fields over the sector domain. Next, the distributed dislocation method is employed to obtain integral equations of the sector with cracks and cavities under an anti-plane traction. The ensuing integral equations are of the Cauchy type singular and have been solved numerically. A set of examples are presented to demonstrate the applicability of the proposed solution procedure. The geometric and force singularities of stress fields in the sector are also studied and compared to the earlier reports in the literature.