Stress intensity factors for a rectangular plate with a point-loaded edge crack by a boundary collocation procedure, and an investigation into the convergence of the solutions

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The stress intensity factors K 1 for a rectangular plates with edge crack loaded on the crack surface has not been obtained so far. In this article, this calculation is done by a least square boundary collocation procedure. A criterion for the validity of the solution is given from the consideration of uniform approximation, which makes it possible to judge the validity of the solution by the method itself, independent to the analytical solution. The convergence of two different approximations usually used, i.e., interpolation approximation and average approximation, are discussed. It is found that the divergence of the former is caused by fluctuation of the approximating functions, known as “Runge phenomenon” in algebraic interpolation. For the latter, there will be no fluctuation in general, and the solutions are always convergent, but it may not converge to the exact solution of the problem. This shows the incompleteness of the Williams function.