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Some aspects of the numerical solution of equilibrium problems in finite elasticity
Bibliography: pages 173-187.
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| Main Author: | |
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| Other Authors: | |
| Format: | Thesis |
| Language: | English |
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Department of Civil Engineering
2016
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| _version_ | 1867613569192820736 |
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| access_status_str | Open Access |
| author | Duffett, Gino Alan |
| author2 | Reddy, B Daya |
| author_browse | Duffett, Gino Alan Reddy, B Daya |
| author_facet | Reddy, B Daya Duffett, Gino Alan |
| author_sort | Duffett, Gino Alan |
| collection | Thesis |
| description | Bibliography: pages 173-187. |
| format | Thesis |
| id | oai:open.uct.ac.za:11427/21871 |
| institution | University of Cape Town (South Africa) |
| language | eng |
| last_indexed | 2026-06-10T12:38:13.911Z |
| license_str | Not specified — see source repository |
| provenance_str_mv | Harvested via OAI-PMH from UCTD — University of Cape Town Open Access Repository |
| publishDate | 2016 |
| publishDateRange | 2016 |
| publishDateSort | 2016 |
| publisher | Department of Civil Engineering |
| publisherStr | Department of Civil Engineering |
| record_format | dspace |
| source_str | UCTD — University of Cape Town Open Access Repository |
| spelling | oai:open.uct.ac.za:11427/21871 Some aspects of the numerical solution of equilibrium problems in finite elasticity Duffett, Gino Alan Reddy, B Daya Civil Engineering Bibliography: pages 173-187. Analytical and computational aspects of solution paths for nonlinear equations are examined, with emphasis on problems in which there are many parameters. The solution to problems of this type is described by an equilibrium hypersurface and methods are presented which allow for the determination of the various features of this surface. These include methods for following numerically any curve on the primary surface, and for determining on such a curve all the singular points (both limit and bifurcation points). Further methods are then presented which allow branching onto secondary paths (subsets of secondary surfaces) from bifurcation points in order to trace out these paths and so determine the bifurcation behaviour of the problem considered. To complete the analysis of the equilibrium surface methods are developed to trace the loci of singular points. The locus of a bifurcation point determines the intersection of the primary and secondary equilibrium surfaces while the loci of limit points allow for the determination of regions of stable and unstable behaviour on the equilibrium surface. These methods are applicable to any system of nonlinear equations but the particular application here is to systems of equations obtained from the finite element approximation of boundary-value problems in elasticity. Attention is restricted to plane boundary-value problems involving incompressible hyperelastic materials. The strain-energy function used to characterise these materials is based on a symmetric function of the principal stretches. All of the above ideas are investigated numerically for the problem of a pressurised rubber cylinder subjected to axial extension. This problem contains two identifiable loading parameters and exhibits complex limit and bifurcation behaviour, which is studied in some detail. 2016-09-25T16:18:06Z 2016-09-25T16:18:06Z 1985 Master Thesis Masters MSc (Eng) http://hdl.handle.net/11427/21871 eng application/pdf Department of Civil Engineering Faculty of Engineering and the Built Environment University of Cape Town |
| spellingShingle | Civil Engineering Duffett, Gino Alan Some aspects of the numerical solution of equilibrium problems in finite elasticity |
| thesis_degree_str | Master's |
| title | Some aspects of the numerical solution of equilibrium problems in finite elasticity |
| title_full | Some aspects of the numerical solution of equilibrium problems in finite elasticity |
| title_fullStr | Some aspects of the numerical solution of equilibrium problems in finite elasticity |
| title_full_unstemmed | Some aspects of the numerical solution of equilibrium problems in finite elasticity |
| title_short | Some aspects of the numerical solution of equilibrium problems in finite elasticity |
| title_sort | some aspects of the numerical solution of equilibrium problems in finite elasticity |
| topic | Civil Engineering |
| url | http://hdl.handle.net/11427/21871 |
| work_keys_str_mv | AT duffettginoalan someaspectsofthenumericalsolutionofequilibriumproblemsinfiniteelasticity |