{"id":{"repo_id":"cape-town","oai_identifier":"oai:open.uct.ac.za:11427/8483"},"canonical_url":"https://search.dev.ndltd.org/etd/cape-town/oai:open.uct.ac.za:11427/8483","repository":{"repo_id":"cape-town","name":"University of Cape Town","base_url":"https://open.uct.ac.za/oai/request"},"display":{"title":"Finite element algorithms for the static and dynamic analysis of time-dependent and time-independent plastic bodies","abstract":"Continuum and finite element formulations of the static and dynamic initial-boundary value evolution (elastoplastic) problems are considered in terms of both the classical and internal variable frameworks. The latter framework is employed to develop algorithms in the form of convex mathematical programming and Newton-Raphson schemes. This latter scheme is shown to be linked to the former in the sense that it expresses the conditions under which the convex non-linear function can be minimised. A Taylor series expansion in time and space is extensively employed to derive integration schemes which include the generalised trapezoidal rule and a generalised Newton-Raphson scheme. This approach provides theoretical foundations for the generalised trapezoidal rule and the generalised Newton-Raphson scheme that have some geometrical insights as well as an interpretation in terms of finite differences and calculus. Conventionally, one way of interpreting the generalised trapezoidal rule is that it uses a weighted average of values (such as velocity or acceleration) at the two ends of the time interval. In this dissertation, the generalised trapezoidal scheme is shown to be a special case of the forward-backward difference scheme for solving first order differential equations.","abstract_html":"Continuum and finite element formulations of the static and dynamic initial-boundary value evolution (elastoplastic) problems are considered in terms of both the classical and internal variable frameworks. The latter framework is employed to develop algorithms in the form of convex mathematical programming and Newton-Raphson schemes. This latter scheme is shown to be linked to the former in the sense that it expresses the conditions under which the convex non-linear function can be minimised. A Taylor series expansion in time and space is extensively employed to derive integration schemes which include the generalised trapezoidal rule and a generalised Newton-Raphson scheme. This approach provides theoretical foundations for the generalised trapezoidal rule and the generalised Newton-Raphson scheme that have some geometrical insights as well as an interpretation in terms of finite differences and calculus. Conventionally, one way of interpreting the generalised trapezoidal rule is that it uses a weighted average of values (such as velocity or acceleration) at the two ends of the time interval. In this dissertation, the generalised trapezoidal scheme is shown to be a special case of the forward-backward difference scheme for solving first order differential equations.","abstract_has_math":false,"creators":["Kaunda, Modify Andrew Elton"],"institution":"Department of Mechanical Engineering","degree_name":null,"degree_level":null,"degree_discipline":null,"degree_department":null,"school":null,"contributors":[],"advisors":["Martin, JB"],"committee_chairs":[],"committee_members":[],"year":1994,"date_issued":"1994","date_published":"1994","updated_at":"2026-07-22T22:23:38Z","subjects":[],"languages":["eng"],"rights":[],"rights_urls":[],"identifier_entries":[]},"links":{"outbound_url":"http://hdl.handle.net/11427/8483","outbound_label":"Handle","outbound_source":"dc:identifier.uri"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor.advisor","label":"Advisor","values":["Martin, JB"]},{"key":"dc:creator","label":"Author","values":["Kaunda, Modify Andrew Elton"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date.accessioned","label":"Dc Date Accessioned","values":["2014-10-17T07:31:07Z"]},{"key":"dc:date.available","label":"Dc Date Available","values":["2014-10-17T07:31:07Z"]},{"key":"dc:date.issued","label":"Date","values":["1994"]},{"key":"dc:publisher.department","label":"Dc Publisher Department","values":["Department of Mechanical Engineering"]},{"key":"dc:publisher.institution","label":"Dc Publisher Institution","values":["University of Cape Town"]},{"key":"dc:type","label":"Dc Type","values":["Doctoral Thesis"]},{"key":"dc:type.qualificationlevel","label":"Dc Type Qualificationlevel","values":["Doctoral"]},{"key":"dc:type.qualificationname","label":"Dc Type Qualificationname","values":["PhD"]}]},{"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/11427/8483"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description","label":"Description","values":["Includes bibliographical references."]},{"key":"dc:description.abstract","label":"Abstract","values":["Continuum and finite element formulations of the static and dynamic initial-boundary value evolution (elastoplastic) problems are considered in terms of both the classical and internal variable frameworks. The latter framework is employed to develop algorithms in the form of convex mathematical programming and Newton-Raphson schemes. This latter scheme is shown to be linked to the former in the sense that it expresses the conditions under which the convex non-linear function can be minimised. A Taylor series expansion in time and space is extensively employed to derive integration schemes which include the generalised trapezoidal rule and a generalised Newton-Raphson scheme. This approach provides theoretical foundations for the generalised trapezoidal rule and the generalised Newton-Raphson scheme that have some geometrical insights as well as an interpretation in terms of finite differences and calculus. Conventionally, one way of interpreting the generalised trapezoidal rule is that it uses a weighted average of values (such as velocity or acceleration) at the two ends of the time interval. In this dissertation, the generalised trapezoidal scheme is shown to be a special case of the forward-backward difference scheme for solving first order differential equations."]},{"key":"dc:title","label":"Title","values":["Finite element algorithms for the static and dynamic analysis of time-dependent and time-independent plastic bodies"]}]}],"canonical_facts":{"dc:contributor.advisor":["Martin, JB"],"dc:creator":["Kaunda, Modify Andrew Elton"],"dc:date.accessioned":["2014-10-17T07:31:07Z"],"dc:date.available":["2014-10-17T07:31:07Z"],"dc:date.issued":["1994"],"dc:description":["Includes bibliographical references."],"dc:description.abstract":["Continuum and finite element formulations of the static and dynamic initial-boundary value evolution (elastoplastic) problems are considered in terms of both the classical and internal variable frameworks. The latter framework is employed to develop algorithms in the form of convex mathematical programming and Newton-Raphson schemes. This latter scheme is shown to be linked to the former in the sense that it expresses the conditions under which the convex non-linear function can be minimised. A Taylor series expansion in time and space is extensively employed to derive integration schemes which include the generalised trapezoidal rule and a generalised Newton-Raphson scheme. This approach provides theoretical foundations for the generalised trapezoidal rule and the generalised Newton-Raphson scheme that have some geometrical insights as well as an interpretation in terms of finite differences and calculus. Conventionally, one way of interpreting the generalised trapezoidal rule is that it uses a weighted average of values (such as velocity or acceleration) at the two ends of the time interval. In this dissertation, the generalised trapezoidal scheme is shown to be a special case of the forward-backward difference scheme for solving first order differential equations."],"dc:identifier.uri":["http://hdl.handle.net/11427/8483"],"dc:language.iso":["eng"],"dc:publisher.department":["Department of Mechanical Engineering"],"dc:publisher.institution":["University of Cape Town"],"dc:title":["Finite element algorithms for the static and dynamic analysis of time-dependent and time-independent plastic bodies"],"dc:type":["Doctoral Thesis"],"dc:type.qualificationlevel":["Doctoral"],"dc:type.qualificationname":["PhD"]},"updated_at":"2026-07-22T22:23:38Z"}