The singular function boundary integral method for biharmonic problems with crack singularities
Date
2007Source
Engineering Analysis with Boundary ElementsVolume
31Issue
3Pages
209-215Google Scholar check
Keyword(s):
Metadata
Show full item recordAbstract
We use the singular function boundary integral method (SFBIM) to solve two model fracture problems on the plane. In the SFBIM, the solution is approximated by the leading terms of the local asymptotic solution expansion, which are also used to weight the governing biharmonic equation in the Galerkin sense. The discretized equations are reduced to boundary integrals by means of the divergence theorem and the Dirichlet boundary conditions are weakly enforced by means of Lagrange multipliers. The main advantage of the method is that the leading stress intensity factors (SIFs) are calculated directly together with the Lagrange multipliers, i.e. no post-processing of the numerical solution is necessary. The numerical results for the two model problems show the fast convergence of the method and compare well with those of the collocation Trefftz method. © 2006 Elsevier Ltd. All rights reserved.
Collections
Cite as
Related items
Showing items related by title, author, creator and subject.
-
Article
The Singular Function Boundary Integral Method for singular Laplacian problems over circular sections
Christodoulou, Evgenia; Xenophontos, Christos A.; Georgiou, Georgios C. (2010)The Singular Function Boundary Integral Method (SFBIM) for solving two-dimensional elliptic problems with boundary singularities is revisited. In this method the solution is approximated by the leading terms of the asymptotic ...
-
Article
Analysis of the singular function boundary integral method for a biharmonic problem with one boundary singularity
Christodoulou, Evgenia; Elliotis, Miltiades C.; Georgiou, Georgios C.; Xenophontos, Christos A. (2012)In this article, we analyze the singular function boundary integral method (SFBIM) for a two-dimensional biharmonic problem with one boundary singularity, as a model for the Newtonian stick-slip flow problem. In the SFBIM, ...
-
Article
The singular function boundary integral method for 3-D Laplacian problems with a boundary straight edge singularity
Christodoulou, Evgenia; Elliotis, Miltiades C.; Xenophontos, Christos A.; Georgiou, Georgios C. (2012)Three-dimensional Laplace problems with a boundary straight-edge singularity caused by two intersecting flat planes are considered. The solution in the neighbourhood of the straight edge can be expressed as an asymptotic ...