Numerical solutions for polygonal cracks

An effective numerical scheme capable to deal with polygonal and branching cracks in a plane is proposed. It is suggested to decompose the general singular integral equation, SIE, for curvilinear cracks into a set of SIEs for straight cuts coinciding with straight crack segments. Solutions of SIEs are sought as bounded for all internal ends of the cuts and unbounded for the left end of the left cut and the right end of the right cut. The Gauss-Chebyshev quadrature is applied to each SIE that eventually leads to an over-determined system of linear algebraic equations followed by the application of the least squares method to solve this system. Stress intensity factors are calculated for some crack configurations. This scheme provides satisfactory accuracy although no correct asymptotic behaviour of the solution at internal ends is taken into consideration. The results are verified against the known results for branching cracks.