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.

Automated summary

This investigation focuses on the axisymmetric torsion of a circular disc with an annular crack subjected to a half-space. The stress-strain state and stress intensity factors at the inner and outer crack edges are studied. The problem is solved using the Hankel integral transformation method, and a new method is developed to solve the resulting system of coupled dual and triple integral equations. The solution is analyzed and discussed, and numerical computations are performed with results presented in tables and graphs. Several special cases are also considered.