Abstract

The anti-plane deformation of an uncracked transversely isotropic sector is studied for two different types of boundary conditions. The solution of the problem is accomplished by means of two methods for each boundary condition, namely using the finite Fourier cosine transform and the method of separation of variables. The closed-form solutions are obtained for displacement and stress fields in the whole domain for each kind of boundary conditions. In the special cases, i.e. finite wedges, the results for the stress field show an exact agreement with those in the literature. In the following, the stress analysis of a transversely isotropic sectors weakened by a circular crack as well as radial crack is accomplished. The resultant singular integral equation of the Cauchy type are solved numerically and, finally, the stress intensity factors of the crack tips versus the ratios of the material properties are plotted and discussed.