Torsion problem of rectangular cross section bar with inner crack

Abstract

The torsion problem of a rectangular cross section bar with inner crack is studied in this paper. The boundary value problem is reduced to the solution of a modified Dirichlet problem. The modified Dirichlet problem is converted into the solution of two Dirichlet problems of Laplace equation. The finite difference method is suggested to solve the problem. Finally, the torsion rigidity coefficient can be evaluated numerically. The inverse of the torsion rigidity coefficient is called the compliance coefficient. With the knowledge of the compliance coefficient, the stress intensity factor can be evaluated. Numerical examples are given to demonstrate the use of the proposed method.