# Dislocation and point-force-based approach to the special green's function bem for elliptic hole and crack problems in two dimensions

M. Denda, I. Kosaka

Research output: Contribution to journalArticlepeer-review

22 Scopus citations

## Abstract

In 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.

Original language English (US) 2857-2889 33 International Journal for Numerical Methods in Engineering 40 15 https://doi.org/10.1002/(SICI)1097-0207(19970815)40:15<2857::AID-NME195>3.0.CO;2-3 Published - 1997

## All Science Journal Classification (ASJC) codes

• Numerical Analysis
• Engineering(all)
• Applied Mathematics

## Keywords

• Boundary element method
• Complex variable
• Dislocation dipole and point force
• Elliptic hole and crack
• Green's functions
• Physical interpretation of Somigliana's identity

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