Formulation and implementation of conforming finite element approximations to static and eigenvalue problems for thin elastic shells

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dc.contributor.advisorReddy, B Dayaen_ZA
dc.contributor.authorEve, Robin Andrewen_ZA
dc.date.accessioned2016-11-14T06:52:00Z
dc.date.available2016-11-14T06:52:00Z
dc.date.issued1987en_ZA
dc.descriptionBibliography: pages 132-135.en_ZA
dc.description.abstractIn deriving asymptotic error estimates for a conforming finite element analyses of static thin elastic shell problems, the French mathematician Ciarlet (1976) proposed an approach to the formulation of such problems. The formulation he uses is based on classical shell theory making use of Kirchhoff-Koiter assumptions. The shell problem is posed in two-dimensional space to which the real problem, in three-dimensional space, is related by a mapping of the domain of the problem to the shell mid-surface. The finite element approximation is formulated in terms of the covariant components of the shell mid-surface displacement field. In this study, Ciarlet's formulation is extended to include the eigenvalue problem for the shell. In addition to this, the aim of the study is to obtain some indication of how well this approach might be expected to work in practice. The conforming finite element approximation of both the static and eigenvalue problems are implemented. Particular attention is paid to allowing generality of the shell surface geometry through the use of an approximate mapping. The use of different integration rules, in-plane displacement component interpolation schemes and approximate geometry schemes are investigated. Results are presented for shells of different geometries for both static and eigenvalue analyses; these are compared with independently obtained results.en_ZA
dc.identifier.apacitationEve, R. A. (1987). <i>Formulation and implementation of conforming finite element approximations to static and eigenvalue problems for thin elastic shells</i>. (Thesis). University of Cape Town ,Faculty of Engineering & the Built Environment ,Department of Civil Engineering. Retrieved from http://hdl.handle.net/11427/22509en_ZA
dc.identifier.chicagocitationEve, Robin Andrew. <i>"Formulation and implementation of conforming finite element approximations to static and eigenvalue problems for thin elastic shells."</i> Thesis., University of Cape Town ,Faculty of Engineering & the Built Environment ,Department of Civil Engineering, 1987. http://hdl.handle.net/11427/22509en_ZA
dc.identifier.citationEve, R. 1987. Formulation and implementation of conforming finite element approximations to static and eigenvalue problems for thin elastic shells. University of Cape Town.en_ZA
dc.identifier.ris TY - Thesis / Dissertation AU - Eve, Robin Andrew AB - In deriving asymptotic error estimates for a conforming finite element analyses of static thin elastic shell problems, the French mathematician Ciarlet (1976) proposed an approach to the formulation of such problems. The formulation he uses is based on classical shell theory making use of Kirchhoff-Koiter assumptions. The shell problem is posed in two-dimensional space to which the real problem, in three-dimensional space, is related by a mapping of the domain of the problem to the shell mid-surface. The finite element approximation is formulated in terms of the covariant components of the shell mid-surface displacement field. In this study, Ciarlet's formulation is extended to include the eigenvalue problem for the shell. In addition to this, the aim of the study is to obtain some indication of how well this approach might be expected to work in practice. The conforming finite element approximation of both the static and eigenvalue problems are implemented. Particular attention is paid to allowing generality of the shell surface geometry through the use of an approximate mapping. The use of different integration rules, in-plane displacement component interpolation schemes and approximate geometry schemes are investigated. Results are presented for shells of different geometries for both static and eigenvalue analyses; these are compared with independently obtained results. DA - 1987 DB - OpenUCT DP - University of Cape Town LK - https://open.uct.ac.za PB - University of Cape Town PY - 1987 T1 - Formulation and implementation of conforming finite element approximations to static and eigenvalue problems for thin elastic shells TI - Formulation and implementation of conforming finite element approximations to static and eigenvalue problems for thin elastic shells UR - http://hdl.handle.net/11427/22509 ER - en_ZA
dc.identifier.urihttp://hdl.handle.net/11427/22509
dc.identifier.vancouvercitationEve RA. Formulation and implementation of conforming finite element approximations to static and eigenvalue problems for thin elastic shells. [Thesis]. University of Cape Town ,Faculty of Engineering & the Built Environment ,Department of Civil Engineering, 1987 [cited yyyy month dd]. Available from: http://hdl.handle.net/11427/22509en_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.otherApplied Mechanicsen_ZA
dc.titleFormulation and implementation of conforming finite element approximations to static and eigenvalue problems for thin elastic shellsen_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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