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Determination of singularity exponents in 3D elasticity problems using enriched base functions in the Scaled Boundary Finite Element Method
Author(s) -
Hell Sascha,
Becker Wilfried
Publication year - 2016
Publication title -
pamm
Language(s) - English
Resource type - Journals
ISSN - 1617-7061
DOI - 10.1002/pamm.201610057
Subject(s) - singularity , finite element method , discretization , mathematical analysis , elasticity (physics) , mathematics , boundary value problem , boundary element method , displacement field , displacement (psychology) , boundary (topology) , convergence (economics) , physics , structural engineering , engineering , psychology , economics , psychotherapist , thermodynamics , economic growth
The SBFEM is employed for the extraction of 3D stress singularity exponents and their associated deformation modes. It makes use of a separation of variables approach, which is substituted into the virtual work equation so that only parts of the boundary need to be discretized while the 3D boundary value problem is considered analytically in a scaling variable. The enrichment of the standard separation of variables representation for the displacements with a decomposition of the analytical crack displacement field yields a substantial improvement of the method's accuracy and convergence properties. (© 2016 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)