BEM analysis for curved cracks

The boundary integral equations (BIE) and displacement discontinuity methods (DDM) are formulated for solution of smooth curved crack problems within 2D elasticity and Reissner?s plate bending theory. The equivalence between the direct boundary element method and the indirect boundary element method is shown here. The Chebyshev polynomials of the second kind are employed to solve the integral equations numerically. This enables determination of the stress intensity factors at the crack tips directly5 by the coefficients of Chebyshev polynomials. In the DDM, the coefficients of stress influence for the constant displacement discontinuity element are derived in closed form for the Reissner?s plate bending problem. The degree of convergence of BIE is demonstrated with increasing numbers of the collocation points. Comparison is made with the analytical solutions from the stress intensity factor handbook for an embedded circular crack in a flat plate under tensile force. High accuracy of the presented numerical solutions makes possible to use them as benchmarks to evaluate the degree of accuracy for any numerical algorithms.

Automated summary

The study utilizes boundary integral equations and displacement discontinuity methods to solve smooth curved crack problems, numerically determining stress intensity factors and showing equivalence between direct and indirect boundary element methods. Convergence is demonstrated by increasing collocation points, and comparison is made with analytical solutions. High accuracy of numerical solutions allows for benchmarking and evaluating accuracy of numerical algorithms.