Finite element algorithms for the static and dynamic analysis of time-dependent and time-independent plastic bodies

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dc.contributor.advisorMartin, JBen_ZA
dc.contributor.authorKaunda, Modify Andrew Eltonen_ZA
dc.date.accessioned2014-10-17T07:31:07Z
dc.date.available2014-10-17T07:31:07Z
dc.date.issued1994en_ZA
dc.descriptionIncludes bibliographical references.en_ZA
dc.description.abstractContinuum 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.en_ZA
dc.identifier.apacitationKaunda, M. A. E. (1994). <i>Finite element algorithms for the static and dynamic analysis of time-dependent and time-independent plastic bodies</i>. (Thesis). University of Cape Town ,Faculty of Engineering & the Built Environment ,Department of Mechanical Engineering. Retrieved from http://hdl.handle.net/11427/8483en_ZA
dc.identifier.chicagocitationKaunda, Modify Andrew Elton. <i>"Finite element algorithms for the static and dynamic analysis of time-dependent and time-independent plastic bodies."</i> Thesis., University of Cape Town ,Faculty of Engineering & the Built Environment ,Department of Mechanical Engineering, 1994. http://hdl.handle.net/11427/8483en_ZA
dc.identifier.citationKaunda, M. 1994. Finite element algorithms for the static and dynamic analysis of time-dependent and time-independent plastic bodies. University of Cape Town.en_ZA
dc.identifier.ris TY - Thesis / Dissertation AU - Kaunda, Modify Andrew Elton AB - 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. DA - 1994 DB - OpenUCT DP - University of Cape Town LK - https://open.uct.ac.za PB - University of Cape Town PY - 1994 T1 - Finite element algorithms for the static and dynamic analysis of time-dependent and time-independent plastic bodies TI - Finite element algorithms for the static and dynamic analysis of time-dependent and time-independent plastic bodies UR - http://hdl.handle.net/11427/8483 ER - en_ZA
dc.identifier.urihttp://hdl.handle.net/11427/8483
dc.identifier.vancouvercitationKaunda MAE. Finite element algorithms for the static and dynamic analysis of time-dependent and time-independent plastic bodies. [Thesis]. University of Cape Town ,Faculty of Engineering & the Built Environment ,Department of Mechanical Engineering, 1994 [cited yyyy month dd]. Available from: http://hdl.handle.net/11427/8483en_ZA
dc.language.isoeng
dc.publisher.departmentDepartment of Mechanical Engineeringen_ZA
dc.publisher.facultyFaculty of Engineering and the Built Environment
dc.publisher.institutionUniversity of Cape Town
dc.subject.otherMechanical Engineeringen_ZA
dc.titleFinite element algorithms for the static and dynamic analysis of time-dependent and time-independent plastic bodiesen_ZA
dc.typeDoctoral Thesis
dc.type.qualificationlevelDoctoral
dc.type.qualificationnamePhDen_ZA
uct.type.filetypeText
uct.type.filetypeImage
uct.type.publicationResearchen_ZA
uct.type.resourceThesisen_ZA
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