An alternative integral equation approach applied to kinked cracks in finite plane bodies

SUMMARYThe presence of singularities in the integral operators of the boundary element methods requires that the density functions must satisfy certain continuity requirements if the displacements and stresses are to be bounded. Quite often the continuity conditions, particularly on the derivatives of the density functions, are relaxed at the element ends for the sake of simplicity in approximating the unknown density functions. In this paper, a numerical study on the effects of satisfying or violating the continuity requirements and the effect of the boundary condition collocating point on three different BEM formulations is presented. Two are indirect formulations using force singularities and displacement discontinuity singularities, and the third is Rizzo's direct formulation. The two integral operators in the direct BEM appear individually in the two different formulations of the indirect BEM. This makes it possible to study the numerical error and other problems in each integral operator and the interaction of the two integral operators in the direct BEM.

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Continuity and Collocation Effects in the Boundary Element Method

Ammons

Vable

1997

Int. J. Numer. Meth. Engng.

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Dislocation and point-force-based approach to the special Green's Function BEM for elliptic hole and crack problems in two dimensions

Denda

Kosaka

1997

Int. J. Numer. Meth. Engng.

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SUMMARYIn this paper we give the theoretical foundation for a dislocation and point-force-based approach to the special Green's function boundary element method and formulate, as an example, the special Green's function boundary element method for elliptic hole and crack problems. The crack is treated as a particular case of the elliptic hole. We adopt a physical interpretation of Somigliana's identity and formulate the boundary element method in terms of distributions of point forces and dislocation dipoles in the infinite domain with an elliptic hole. There is no need to model the hole by the boundary elements since the traction free boundary condition there for the point force and the dislocation dipole is automatically satisfied. The Green's functions are derived following the Muskhelishvili complex variable formalism and the boundary element method is formulated using complex variables. All the boundary integrals, including the formula for the stress intensity factor for the crack, are evaluated analytically to give a simple yet accurate special Green's function boundary element method. The numerical results obtained for the stress concentration and intensity factors are extremely accurate.1997 by John Wiley & Sons, Ltd.

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An integral equation method applied to mode III crack problems

Liu

Altiero

1992

Engineering Fracture Mechanics

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An alternative integral equation approach applied to kinked cracks in finite plane bodies

Cited by 8 publications

References 6 publications

Continuity and Collocation Effects in the Boundary Element Method

Continuity and Collocation Effects in the Boundary Element Method

Dislocation and point-force-based approach to the special Green's Function BEM for elliptic hole and crack problems in two dimensions

An integral equation method applied to mode III crack problems

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