{"id":{"repo_id":"cape-town","oai_identifier":"oai:open.uct.ac.za:11427/17269"},"canonical_url":"https://search.dev.ndltd.org/etd/cape-town/oai:open.uct.ac.za:11427/17269","repository":{"repo_id":"cape-town","name":"University of Cape Town","base_url":"https://open.uct.ac.za/oai/request"},"display":{"title":"Mixed finite element analysis for arbitrarily curved beams","abstract":"A convergence of a mixed finite element method for three-dimensional curved beams with arbitary geometry is investigated. First, the governing equations are derived for linear elastic curved beams with uniformly loaded based on the Timoshenko-Reissner-Mindlin hypotheses. Then, standard and mixed variational problems are formulated. A new norm, equivalent to H¹- type norm, is introduced. By making use of this norm, sufficient conditions for existence and uniqueness of the solutions of the above problems are established for both continuous and discrete cases. The estimates of the optimal order and minimal regularity are then derived for errors in the generalised displacement vector and the internal force vector. These analytical findings are compared with numerical results, verifying the role of reduced integration and the accuracy of the methods.","abstract_html":"A convergence of a mixed finite element method for three-dimensional curved beams with arbitary geometry is investigated. First, the governing equations are derived for linear elastic curved beams with uniformly loaded based on the Timoshenko-Reissner-Mindlin hypotheses. Then, standard and mixed variational problems are formulated. A new norm, equivalent to H¹- type norm, is introduced. By making use of this norm, sufficient conditions for existence and uniqueness of the solutions of the above problems are established for both continuous and discrete cases. The estimates of the optimal order and minimal regularity are then derived for errors in the generalised displacement vector and the internal force vector. These analytical findings are compared with numerical results, verifying the role of reduced integration and the accuracy of the methods.","abstract_has_math":false,"creators":["Arunakirinathar, Kanagaratnam"],"institution":"Department of Mathematics and Applied Mathematics","degree_name":null,"degree_level":null,"degree_discipline":null,"degree_department":null,"school":null,"contributors":[],"advisors":["Reddy, B Daya"],"committee_chairs":[],"committee_members":[],"year":1991,"date_issued":"1991","date_published":"1991","updated_at":"2026-07-22T22:23:09Z","subjects":[],"languages":["eng"],"rights":[],"rights_urls":[],"identifier_entries":[]},"links":{"outbound_url":"http://hdl.handle.net/11427/17269","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":["Arunakirinathar, Kanagaratnam"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date.accessioned","label":"Dc Date Accessioned","values":["2016-02-26T07:16:33Z"]},{"key":"dc:date.available","label":"Dc Date Available","values":["2016-02-26T07:16:33Z"]},{"key":"dc:date.issued","label":"Date","values":["1991"]},{"key":"dc:publisher.department","label":"Dc Publisher Department","values":["Department of Mathematics and Applied Mathematics"]},{"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"]}]},{"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/11427/17269"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description","label":"Description","values":["Bibliography: pages 90-94."]},{"key":"dc:description.abstract","label":"Abstract","values":["A convergence of a mixed finite element method for three-dimensional curved beams with arbitary geometry is investigated. First, the governing equations are derived for linear elastic curved beams with uniformly loaded based on the Timoshenko-Reissner-Mindlin hypotheses. Then, standard and mixed variational problems are formulated. A new norm, equivalent to H¹- type norm, is introduced. By making use of this norm, sufficient conditions for existence and uniqueness of the solutions of the above problems are established for both continuous and discrete cases. The estimates of the optimal order and minimal regularity are then derived for errors in the generalised displacement vector and the internal force vector. These analytical findings are compared with numerical results, verifying the role of reduced integration and the accuracy of the methods."]},{"key":"dc:title","label":"Title","values":["Mixed finite element analysis for arbitrarily curved beams"]}]}],"canonical_facts":{"dc:contributor.advisor":["Reddy, B Daya"],"dc:creator":["Arunakirinathar, Kanagaratnam"],"dc:date.accessioned":["2016-02-26T07:16:33Z"],"dc:date.available":["2016-02-26T07:16:33Z"],"dc:date.issued":["1991"],"dc:description":["Bibliography: pages 90-94."],"dc:description.abstract":["A convergence of a mixed finite element method for three-dimensional curved beams with arbitary geometry is investigated. First, the governing equations are derived for linear elastic curved beams with uniformly loaded based on the Timoshenko-Reissner-Mindlin hypotheses. Then, standard and mixed variational problems are formulated. A new norm, equivalent to H¹- type norm, is introduced. By making use of this norm, sufficient conditions for existence and uniqueness of the solutions of the above problems are established for both continuous and discrete cases. The estimates of the optimal order and minimal regularity are then derived for errors in the generalised displacement vector and the internal force vector. These analytical findings are compared with numerical results, verifying the role of reduced integration and the accuracy of the methods."],"dc:identifier.uri":["http://hdl.handle.net/11427/17269"],"dc:language.iso":["eng"],"dc:publisher.department":["Department of Mathematics and Applied Mathematics"],"dc:publisher.institution":["University of Cape Town"],"dc:title":["Mixed finite element analysis for arbitrarily curved beams"],"dc:type":["Master Thesis"],"dc:type.qualificationlevel":["Masters"],"dc:type.qualificationname":["MSc"]},"updated_at":"2026-07-22T22:23:09Z"}