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Elements with penalized equilibrium and rotational degrees of freedom in fracture mechanics problems
Dissertation (MEng(Mechanical))--University of Pretoria, 2007.
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University of Pretoria
2013
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| _version_ | 1867613719907794944 |
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| access_status_str | Open Access |
| author2 | Groenwold, Albert A. |
| author_browse | Groenwold, Albert A. |
| author_facet | Groenwold, Albert A. |
| collection | Thesis |
| dc_rights_str_mv | © 2006, University of Pretoria. All rights reserved. The copyright in this work vests in the University of Pretoria. No part of this work may be reproduced or transmitted in any form or by any means, without the prior written permission of the University of Pretoria. |
| description | Dissertation (MEng(Mechanical))--University of Pretoria, 2007. |
| format | Thesis |
| id | oai:repository.up.ac.za:2263/23983 |
| institution | University of Pretoria (South Africa) |
| last_indexed | 2026-06-10T12:40:37.576Z |
| license_str | Other — see source repository |
| provenance_str_mv | Harvested via OAI-PMH from UPSpace — University of Pretoria Institutional Repository |
| publishDate | 2013 |
| publishDateRange | 2013 |
| publishDateSort | 2013 |
| publisher | University of Pretoria |
| publisherStr | University of Pretoria |
| record_format | dspace |
| source_str | UPSpace — University of Pretoria Institutional Repository |
| spelling | oai:repository.up.ac.za:2263/23983 Elements with penalized equilibrium and rotational degrees of freedom in fracture mechanics problems Groenwold, Albert A. Visser, A.G. Su, K.L. antoinette.deklerk@sasol.com De Klerk, Antoinette Fracture mechanics UCTD Dissertation (MEng(Mechanical))--University of Pretoria, 2007. This thesis deals with the solution of linear elastic fracture mechanics problems. To solve the linear elastic fracture mechanics problems, the finite element method and path independent integrals are employed, namely Rice's J integral and an alternative path independent integral I *, which is the energy complement to J. Stress intensity factors for typical mode I and mode II fracture mechanics problems in isotropic and orthotropic elastic plates are calculated. The problems considered are a center cracked panel subjected to uniform tension, a single edge cracked panel subjected to uniform tension, a double edge cracked panel subjected to uniform tension, and a center cracked panel subjected to uniform shear. Firstly, classical displacement based finite elements, elements with penalized equilibrium and elements with drilling degrees of freedom are presented and implemented in a MATLAB environment. Secondly, two different ways to evaluate the stress intensity factor are considered, namely the displacement extrapolation approach, and the path independent integrals J and I *. The numerical implementation and path independence of the J and I * integral is demonstrated. It is shown that the J integral can estimate the lower bound of the stress intensity factor when used with displacement based finite elements, while the I * integral can estimate the upper bound of the stress intensity factor, when used with stress equilibrium elements. Thirdly, the path independent integrals J and I * are applied to isotropic fracture mechanics problems to determine the stress intensity factor at the tip of a crack. Convergence studies are presented to investigate the influence of mesh refinement on the stress intensity factor predicted using the J and I * integral. The path independence of J and I * are investigated. Numerical results for typical fracture specimens are presented and discussed. Finally, the path independent integrals J and I * are applied to orthotropic fracture mechanics problems to determine the stress intensity factor at the crack tip. Again, convergence studies are done, and the path independence of J and I * are investigated for orthotropic problems. Numerical results for typical fracture specimens are presented and discussed. The effect of the degree of anisotropy and fiber orientation on the stress intensity factor is also demonstrated. A novel contribution in this thesis are the results for elements with drilling degrees of freedom in fracture mechanics problems. In addition, the results presented here may serve to clarify published stress intensity factor results for orthotropic materials presented in the literature, since many of the results previously presented are contradictory. Mechanical and Aeronautical Engineering unrestricted 2013-09-06T16:19:31Z 2007-04-17 2013-09-06T16:19:31Z 2006-04-26 2007-04-17 2007-04-17 Dissertation De Klerk, A 2006, Elements with penalized equilibrium and rotational degrees of freedom in fracture mechanics problems, MEng(Mechanical) dissertation, University of Pretoria, Pretoria, viewed yymmdd < http://hdl.handle.net/2263/23983 > http://hdl.handle.net/2263/23983 http://upetd.up.ac.za/thesis/available/etd-04172007-115809/ © 2006, University of Pretoria. All rights reserved. The copyright in this work vests in the University of Pretoria. No part of this work may be reproduced or transmitted in any form or by any means, without the prior written permission of the University of Pretoria. application/pdf University of Pretoria |
| spellingShingle | Fracture mechanics UCTD Elements with penalized equilibrium and rotational degrees of freedom in fracture mechanics problems |
| title | Elements with penalized equilibrium and rotational degrees of freedom in fracture mechanics problems |
| title_full | Elements with penalized equilibrium and rotational degrees of freedom in fracture mechanics problems |
| title_fullStr | Elements with penalized equilibrium and rotational degrees of freedom in fracture mechanics problems |
| title_full_unstemmed | Elements with penalized equilibrium and rotational degrees of freedom in fracture mechanics problems |
| title_short | Elements with penalized equilibrium and rotational degrees of freedom in fracture mechanics problems |
| title_sort | elements with penalized equilibrium and rotational degrees of freedom in fracture mechanics problems |
| topic | Fracture mechanics UCTD |
| url | http://hdl.handle.net/2263/23983 http://upetd.up.ac.za/thesis/available/etd-04172007-115809/ |