Multiple crack problems for torsion thin-walled cylinder

Abstract

Multiple crack problems for a torsion thin-walled cylinder are studied in this article. The boundary value problem is reduced to the solution of a Dirichlet problem of the Laplace equation. For the considered doubly connected region, a constant k is involved in the boundary condition which is determined by the single-valuedness condition of the warping function. The finite difference method is suggested to solve the Dirichlet problem. The torsion rigidity coefficient can be evaluated numerically. The inverse of the torsion rigidity coefficient is known as the compliance coefficient. With the knowledge of the compliance coefficient, the stress intensity factor (SIF) can be evaluated. Numerical examples are given to demonstrate the use of the proposed method. Interaction effects between the cracks are also investigated.