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Solving transient dynamic crack problems by the hypersingular boundary element method
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DOI：10.1111/j.1460-2695.1997.tb00309.x.png)
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Abstract
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The subject of hypersingular boundary integral equations is a rapidly developing topic due to the advantages which this kind of formulation offers compared to the standard boundary integral method. The hypersingular formulation is particularly well suited for fracture mechanics problems, where there are important gradients of the stress field and singularities. This formulation for time domain antiplane problems has been recently addressed by the authors and in the present paper, the formulation for time domain plane problems is presented and applied for the first time. A mixed Boundary Element approach based on the standard integral equation and the hypersingular integral equation is developed. The mixed formulation allows for a very simple discretization of the problem, where no subregion is needed. Conforming quadratic elements are used for the crack and the external boundaries. The hypersingular integral equation is used for collocation points within the crack elements, while the standard integral representation is used for the external boundaries. Several examples with different crack geometries are studied to illustrate the possibilities of the method. The Stress Intensity Factor (S.I.F.) is very accurately computed from the crack tip opening displacements along the crack tip element. The results show that the proposed approach for S.I.F. evaluation is simple and produces accurate solutions.
Keywords:
hypersingular boundary integral equations
boundary element method
fracture mechanics
dynamic stress intensity factor
wave propagation
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