{"id":{"repo_id":"cape-town","oai_identifier":"oai:open.uct.ac.za:11427/22509"},"canonical_url":"https://search.dev.ndltd.org/etd/cape-town/oai:open.uct.ac.za:11427/22509","repository":{"repo_id":"cape-town","name":"University of Cape Town","base_url":"https://open.uct.ac.za/oai/request"},"display":{"title":"Formulation and implementation of conforming finite element approximations to static and eigenvalue problems for thin elastic shells","abstract":"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.","abstract_html":"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.","abstract_has_math":false,"creators":["Eve, Robin Andrew"],"institution":"Department of Civil Engineering","degree_name":null,"degree_level":null,"degree_discipline":null,"degree_department":null,"school":null,"contributors":[],"advisors":["Reddy, B Daya"],"committee_chairs":[],"committee_members":[],"year":1987,"date_issued":"1987","date_published":"1987","updated_at":"2026-07-22T22:23:13Z","subjects":[],"languages":["eng"],"rights":[],"rights_urls":[],"identifier_entries":[]},"links":{"outbound_url":"http://hdl.handle.net/11427/22509","outbound_label":"Handle","outbound_source":"dc:identifier.uri"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor.advisor","label":"Advisor","values":["Reddy, B Daya"]},{"key":"dc:creator","label":"Author","values":["Eve, Robin Andrew"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date.accessioned","label":"Dc Date Accessioned","values":["2016-11-14T06:52:00Z"]},{"key":"dc:date.available","label":"Dc Date Available","values":["2016-11-14T06:52:00Z"]},{"key":"dc:date.issued","label":"Date","values":["1987"]},{"key":"dc:publisher.department","label":"Dc Publisher Department","values":["Department of Civil Engineering"]},{"key":"dc:publisher.institution","label":"Dc Publisher Institution","values":["University of Cape Town"]},{"key":"dc:type","label":"Dc Type","values":["Master Thesis"]},{"key":"dc:type.qualificationlevel","label":"Dc Type Qualificationlevel","values":["Masters"]},{"key":"dc:type.qualificationname","label":"Dc Type Qualificationname","values":["MSc (Eng)"]}]},{"id":"language_rights","label":"Language and Rights","entries":[{"key":"dc:language.iso","label":"Language (ISO)","values":["eng"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier.uri","label":"Identifier URI","values":["http://hdl.handle.net/11427/22509"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description","label":"Description","values":["Bibliography: pages 132-135."]},{"key":"dc:description.abstract","label":"Abstract","values":["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."]},{"key":"dc:title","label":"Title","values":["Formulation and implementation of conforming finite element approximations to static and eigenvalue problems for thin elastic shells"]}]}],"canonical_facts":{"dc:contributor.advisor":["Reddy, B Daya"],"dc:creator":["Eve, Robin Andrew"],"dc:date.accessioned":["2016-11-14T06:52:00Z"],"dc:date.available":["2016-11-14T06:52:00Z"],"dc:date.issued":["1987"],"dc:description":["Bibliography: pages 132-135."],"dc:description.abstract":["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."],"dc:identifier.uri":["http://hdl.handle.net/11427/22509"],"dc:language.iso":["eng"],"dc:publisher.department":["Department of Civil Engineering"],"dc:publisher.institution":["University of Cape Town"],"dc:title":["Formulation and implementation of conforming finite element approximations to static and eigenvalue problems for thin elastic shells"],"dc:type":["Master Thesis"],"dc:type.qualificationlevel":["Masters"],"dc:type.qualificationname":["MSc (Eng)"]},"updated_at":"2026-07-22T22:23:13Z"}