Axisymmetric torsion problem by a rigid disc of an elastic half-space weakened by an annular crack

This investigation is devoted to an axisymmetric torsion of a circular disc subjected to a half-space, containing an annular crack. The stress-strain state and the stress intensity factors pertaining to the inner and outer crack edges are investigated. The proposed problem is solved by applying the Hankel integral transformation method. The mixed boundary-value problem is reduced to a system of coupled dual and triple integral equations. We developed a new method to solve this system. By using the Gegenbauer formulas, we obtain a system of infinite algebraic equations for getting the unknown functions. The solution is analysed and discussed. Numerical computations are carried out and the results are presented in the form of tables and graphs. Some special cases are considered.