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“…This behavior of the method has been theoretically proved in [28]. The results obtained in the 2-D case have encouraged the extension of the method in 3-D problems with a straight-edge singularity [6,13].…”
Section: Introductionmentioning
confidence: 74%
“…This behavior of the method has been theoretically proved in [28]. The results obtained in the 2-D case have encouraged the extension of the method in 3-D problems with a straight-edge singularity [6,13].…”
Section: Introductionmentioning
confidence: 74%
“…The solution Φ of the 3-D Laplace equation, is expressed in cylindrical coordinates and is defined in a domain with a boundary crack singularity along the z-axis or along a line parallel to this axis, as it is the case of the model problems which have been examined in the current study. It is written as follows (Costabel et al 2003, Christodoulou et al 2012b, Elliotis et al 2010, Elliotis 2016:…”
Section: Formulation Of the Methodsmentioning
confidence: 99%
“…Following the standard procedure of the SFBIM for the 3-D case (Christodoulou et al 2012b, Elliotis et al 2010, Elliotis 2016, the governing equation is weighted by the singular functions V k (j) , in the Galerkin sense, to give (N p +1)N a +N λ discretized equations. Then, after applying Gauss divergence theorem and by considering that functions V k (j) satisfy exactly the boundary conditions along S A and S B and also by imposing the Dirichlet boundary condition on S C , by means of Lagrange multiplier μ(θ,z), we finally arrive at the following linear system of (N p +1)N a +N λ discretized equations:…”
Section: Formulation Of the Methodsmentioning
confidence: 99%
See 1 more Smart Citation
“…The QDFM has been successfully applied for the extraction of EFIFs associated with the non‐integer eigenvalues from finite element (FE) solutions, but it does not apply to EFIFs associated with the integer eigenvalues . Other methods for extracting EFIFs are available (e.g., ); however, these methods do not apply to integer eigenvalues either.…”
Section: Introduction and Notationmentioning
confidence: 99%