An enhanced scaled boundary finite element method for linear elastic fracture
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...
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| Format: | Article |
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Springer
2017
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| Online Access: | https://eprints.nottingham.ac.uk/44105/ |
| _version_ | 1848796839162150912 |
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| author | Egger, Adrian W. Chatzi, Eleni N. Triantafyllou, Savvas P. |
| author_facet | Egger, Adrian W. Chatzi, Eleni N. Triantafyllou, Savvas P. |
| author_sort | Egger, Adrian W. |
| building | Nottingham Research Data Repository |
| collection | Online Access |
| description | 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. |
| first_indexed | 2025-11-14T19:54:21Z |
| format | Article |
| id | nottingham-44105 |
| institution | University of Nottingham Malaysia Campus |
| institution_category | Local University |
| last_indexed | 2025-11-14T19:54:21Z |
| publishDate | 2017 |
| publisher | Springer |
| recordtype | eprints |
| repository_type | Digital Repository |
| spelling | nottingham-441052020-05-04T18:57:31Z https://eprints.nottingham.ac.uk/44105/ An enhanced scaled boundary finite element method for linear elastic fracture Egger, Adrian W. Chatzi, Eleni N. Triantafyllou, Savvas P. 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. Springer 2017-07-28 Article PeerReviewed Egger, Adrian W., Chatzi, Eleni N. and Triantafyllou, Savvas P. (2017) An enhanced scaled boundary finite element method for linear elastic fracture. Archive of Applied Mechanics, 87 (10). pp. 1667-1706. ISSN 1432-0681 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) https://link.springer.com/article/10.1007%2Fs00419-017-1280-7 doi:10.1007/s00419-017-1280-7 doi:10.1007/s00419-017-1280-7 |
| spellingShingle | 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) Egger, Adrian W. Chatzi, Eleni N. Triantafyllou, Savvas P. An enhanced scaled boundary finite element method for linear elastic fracture |
| title | An enhanced scaled boundary finite element method for linear elastic fracture |
| title_full | An enhanced scaled boundary finite element method for linear elastic fracture |
| title_fullStr | An enhanced scaled boundary finite element method for linear elastic fracture |
| title_full_unstemmed | An enhanced scaled boundary finite element method for linear elastic fracture |
| title_short | An enhanced scaled boundary finite element method for linear elastic fracture |
| title_sort | enhanced scaled boundary finite element method for linear elastic fracture |
| topic | 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) |
| url | https://eprints.nottingham.ac.uk/44105/ https://eprints.nottingham.ac.uk/44105/ https://eprints.nottingham.ac.uk/44105/ |