Complex variable approach to the BEM for multiple crack problems Original Research Article

A boundary element method for straight multiple center and edge crack problems is developed in this paper. The method is constructed upon the systematic use of the elastic singularity solutions in complex variables. The crack opening is represented by the continuous distribution of dislocation dipoles and the effect of the non-crack boundary by the continuous distributions of point forces and dislocation dipoles. The crack-tip singularity is embedded into the interpolation using orthogonal polynomials (i.e. Chebyshev and Jacobi) and their associated singular weight functions. The proposed analytical integration procedure of the Cauchy-type integrals defined over the crack eliminates the need for the quadrature formulae for numerical integration, streamlines, and enhances the accuracy of the traditional singular integral equation method for crack problems. The stress intensity factors for the fifteen problems analyzed in this paper have been accurate enough to substitute those given in stress intensity factor handbooks. Since non-crack boundary of arbitrary shape can be introduced at will the method is expected to give accurate stress intensity factors for complex real life problems.