Some aspects of the numerical solution of equilibrium problems in finite elasticity

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dc.contributor.advisorReddy, B Dayaen_ZA
dc.contributor.authorDuffett, Gino Alanen_ZA
dc.date.accessioned2016-09-25T16:18:06Z
dc.date.available2016-09-25T16:18:06Z
dc.date.issued1985en_ZA
dc.descriptionBibliography: pages 173-187.en_ZA
dc.description.abstractAnalytical 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.en_ZA
dc.identifier.apacitationDuffett, G. A. (1985). <i>Some aspects of the numerical solution of equilibrium problems in finite elasticity</i>. (Thesis). University of Cape Town ,Faculty of Engineering & the Built Environment ,Department of Civil Engineering. Retrieved from http://hdl.handle.net/11427/21871en_ZA
dc.identifier.chicagocitationDuffett, Gino Alan. <i>"Some aspects of the numerical solution of equilibrium problems in finite elasticity."</i> Thesis., University of Cape Town ,Faculty of Engineering & the Built Environment ,Department of Civil Engineering, 1985. http://hdl.handle.net/11427/21871en_ZA
dc.identifier.citationDuffett, G. 1985. Some aspects of the numerical solution of equilibrium problems in finite elasticity. University of Cape Town.en_ZA
dc.identifier.ris TY - Thesis / Dissertation AU - Duffett, Gino Alan AB - 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. DA - 1985 DB - OpenUCT DP - University of Cape Town LK - https://open.uct.ac.za PB - University of Cape Town PY - 1985 T1 - Some aspects of the numerical solution of equilibrium problems in finite elasticity TI - Some aspects of the numerical solution of equilibrium problems in finite elasticity UR - http://hdl.handle.net/11427/21871 ER - en_ZA
dc.identifier.urihttp://hdl.handle.net/11427/21871
dc.identifier.vancouvercitationDuffett GA. Some aspects of the numerical solution of equilibrium problems in finite elasticity. [Thesis]. University of Cape Town ,Faculty of Engineering & the Built Environment ,Department of Civil Engineering, 1985 [cited yyyy month dd]. Available from: http://hdl.handle.net/11427/21871en_ZA
dc.language.isoengen_ZA
dc.publisher.departmentDepartment of Civil Engineeringen_ZA
dc.publisher.facultyFaculty of Engineering and the Built Environment
dc.publisher.institutionUniversity of Cape Town
dc.subject.otherCivil Engineeringen_ZA
dc.titleSome aspects of the numerical solution of equilibrium problems in finite elasticityen_ZA
dc.typeMaster Thesis
dc.type.qualificationlevelMasters
dc.type.qualificationnameMSc (Eng)en_ZA
uct.type.filetypeText
uct.type.filetypeImage
uct.type.publicationResearchen_ZA
uct.type.resourceThesisen_ZA
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