Elastoplastic analysis of two-dimensional problems with hole by boundary element method using complex variables

SUMMARYThe complex variables boundary element method (CVBEM) is used to study interaction between a circular opening and fractures originating from its boundary in a piecewise homogeneous plane. A new complex hypersingular equation for piecewise homogeneous media with a circular opening is obtained. The equation is solved using the CVBEM technique with circular and straight boundary elements and polynomial approximations (with square root asymptotics for crack tip elements) for the unknown functions. The algorithm is veri"ed through comparison with known semi-analytical and numerical solutions that involve interaction between a circular opening and speci"c systems of cracks or other openings. New numerical results concerning the interaction of the circular opening with the cracks and circular inclusions are presented. The method is applied to an important problem in the petroleum industry: modelling propagation of hydraulic fractures in the vicinity of a borehole.

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“…The Kolosov}Muskhelishvili potentials for this FS are given in References [6] or [35]. They have the form…”

Section: Chsie For the Homogeneous Part Of A Piecewise Homogeneous Mementioning

confidence: 99%

Interaction between a circular opening and fractures originating from its boundary in a piecewise homogeneous plane

Mogilevskaya

Rothenburg

Dusseault

2000

Int. J. Numer. Anal. Meth. Geomech.

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“…The displacement contribution from the image terms of the point force distribution is obtained by substituting (44)-(47) into (18)…”

Section: Displacement Stress and Tractionmentioning

confidence: 99%

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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Subdomain solutions of complex variable boundary element method

Gadala

Shougao

1998

Engineering with Computers

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Elastoplastic analysis of two-dimensional problems with hole by boundary element method using complex variables

Cited by 4 publications

References 7 publications

Interaction between a circular opening and fractures originating from its boundary in a piecewise homogeneous plane

Interaction between a circular opening and fractures originating from its boundary in a piecewise homogeneous plane

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

Subdomain solutions of complex variable boundary element method

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