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An enhanced scaled boundary finite element method for linear elastic fracture

Egger, Adrian W.; Chatzi, Eleni N.; Triantafyllou, Savvas P.

Authors

Adrian W. Egger

Eleni N. Chatzi

Savvas P. Triantafyllou



Abstract

A blocked Hamiltonian Schur decomposition is herein proposed for the solution process of the Scaled Boundary Finite Element Method (SBFEM), which is demonstrated to comprise a robust simulation tool for Linear Elastic Fracture Mechanics (LEFM) problems. By maintaining Hamiltonian symmetry increased accuracy is achieved, resulting in higher rates of convergence and reduced computational toll, while the former need for adoption of a stabilizing parameter and, inevitably user-supervision, is alleviated.
The method is further enhanced via adoption of superconvergent patch recovery theory in the formulation of the stress intensity factors. It is shown that in doing so, superconvergence, and in select cases ultraconvergence, is succeeded in the Stress Intensity Factors (SIFs) calculation. Based on these findings, a novel error estimator for the stress intensity factors within the context of SBFEM is proposed.
To investigate and assess the performance of SBFEM in the context of linear elastic fracture mechanics, the method is contrasted against the Finite Element Method (FEM) and the eXtended Finite Element Method (XFEM) variants. The comparison, carried out in terms of computational toll and accuracy for a number of applications, reveals SBFEM as a highly performant method.

Journal Article Type Article
Journal Archive of Applied Mechanics
Print ISSN 0939-1533
Electronic ISSN 1432-0681
Publisher Humana Press
Peer Reviewed Peer Reviewed
Volume 87
Issue 10
APA6 Citation Egger, A. W., Chatzi, E. N., & Triantafyllou, S. P. (in press). An enhanced scaled boundary finite element method for linear elastic fracture. Archive of Applied Mechanics, 87(10), doi:10.1007/s00419-017-1280-7
DOI https://doi.org/10.1007/s00419-017-1280-7
Keywords Scaled Boundary Finite Element Method (SBFEM); Extended Finite Element; Method (XFEM); Linear Elastic Fracture Mechanics (LEFM); Stress Intensity Factors; (SIFs); Block Hamiltonian Schur Decomposition (HSchur); Super Convergent Patch; Recovery Theory (SPR
Publisher URL https://link.springer.com/article/10.1007%2Fs00419-017-1280-7
Copyright Statement Copyright information regarding this work can be found at the following address: http://eprints.nottingh.../end_user_agreement.pdf
Additional Information The final publication is available at Springer via http://dx.doi.org/10.1007/s00419-017-1280-7

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Copyright Statement
Copyright information regarding this work can be found at the following address: http://eprints.nottingham.ac.uk/end_user_agreement.pdf





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