A weakly singular SGBEM for analysis of two-dimensional crack problems in multi-field media

A weakly singular symmetric Galerkin boundary element method (SGBEM) is developed for analysis of fractures in two-dimensional multi-field media. Specialization for the cases of anisotropic linear elasticity, piezoelectricity and magnetoelectroelasticity is considered. The basis for the method is a...

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Bibliographic Details
Published in:Engineering analysis with boundary elements 2014-04, Vol.41, p.60-73
Main Authors: Tran, Han D., Mear, Mark E.
Format: Article
Language:English
Subjects:
Anisotropic
Asymptotic properties
Boundary element method
Crack
Cracks
Displacement
Integral equation
Magnetoelectroelastic
Mathematical analysis
Mathematical models
Media
Piezoelectric
Two dimensional
Weakly singular SGBEM
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Summary:A weakly singular symmetric Galerkin boundary element method (SGBEM) is developed for analysis of fractures in two-dimensional multi-field media. Specialization for the cases of anisotropic linear elasticity, piezoelectricity and magnetoelectroelasticity is considered. The basis for the method is a pair of weak-form integral equations for ‘generalized’ displacement and traction that involve only (at most) weakly singular kernels of order lnr. Standard Co elements are employed everywhere except at the crack tips. A special crack-tip element is developed to properly model the asymptotic behavior of the relative crack-face displacements. Extra degrees of freedom at the tip node are incorporated in the crack-tip element so that the ‘generalized’ stress intensity factors are directly obtained from the solution to the system of discretized equations. Various examples for cracks in both infinite and finite domains are examined. Highly accurate results are obtained with relatively coarse meshes.
ISSN:0955-7997
1873-197X
DOI:10.1016/j.enganabound.2014.01.003