Numerical treatment of finite part integrals in 2-D boundary element analysis with application infracture mechanics

✍ Scribed by J. Hildenbrand; G. Kuhn

• Book ID: 104734855
• Publisher: Springer
• Year: 1993
• Tongue: English
• Weight: 697 KB
• Volume: 13
• Category: Article
• ISSN: 0178-7675
• DOI: 10.1007/bf00350702

✦ Synopsis

For the solutlon of problems in fracture mechanics by the boundary element method usually the subregion technique is employed to decouple the crack surfaces. In this paper a different procedure is presented. By using the displacement boundary integral equation on one side of the crack surface and the hypersingular traction bonndary integral equation on the opposite side, one can renounce the subregion technique.

An essential point when applying the traction boundary integral equation is the treatment of the thus arising hypersingular integrals. Two methods for their numerical computation are presented, both based on the finite part concept. One may either scale the integrals properly and use a specific quadrature rule, or one may apply the definition formula for finite part integrals and transform the resulting regular integrals into the usual element coordinate system afterwards. While the former method is restricted to linear or circular approximations of the boundary geometry, the latter one all¦ for arbitrary curved (e.g. isoparametric) elements. Two numerical examples are enclosed to demonstrate the accuracy of the two boundary integral equations technique compared with the subregion technique.