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Representation and application of spline-based finite elements

dc.contributor.advisorBang, Børre
dc.contributor.authorKravetc, Tatiana
dc.date.accessioned2020-08-14T16:38:50Z
dc.date.available2020-08-14T16:38:50Z
dc.date.issued2020-03-31
dc.description.abstractIsogeometric analysis, as a generalization of the finite element method, employs spline methods to achieve the same representation for both geometric modeling and analysis purpose. Being one of possible tool in application to the isogeometric analysis, blending techniques provide strict locality and smoothness between elements. Motivated by these features, this thesis is devoted to the design and implementation of this alternative type of finite elements. This thesis combines topics in geometry, computer science and engineering. The research is mainly focused on the algorithmic aspects of the usage of the spline-based finite elements in the context of developing generalized methods for solving different model problems. The ability for conversion between different representations is significant for the modeling purpose. Methods for conversion between local and global representations are presented.en_US
dc.description.doctoraltypeph.d.en_US
dc.description.popularabstractThe development of software for modeling and design of geometric shapes is very important for many different areas of product design, for instance, aircraft and automotive engineering, architectural and technical design, and other industries. Additionally, physical analysis of models is required for manufacturing. Use of similar computational tools for both design and analysis is of interest. Because then the shape representation is retained, which is essential for shapes with characteristics sensitive to the geometrical imperfections. Motivated by this challenge, this thesis attempts to link various geometrical representations for the purpose of analysis. The presented concept involves a combination of finite element analysis, spline concept and approximation theory, united by isogeometric analysis. This thesis is directed to examine the behavior of spline-based finite elements applied to various model problems. The presented research provides a base for the implementation of a framework solving the partial differential equations by using spline-based finite elements as a main tool.en_US
dc.identifier.isbn978-82-7823-214-9
dc.identifier.isbn978-82-7823-215-6
dc.identifier.urihttps://hdl.handle.net/10037/18966
dc.language.isoengen_US
dc.publisherUiT Norges arktiske universiteten_US
dc.publisherUiT The Arctic University of Norwayen_US
dc.rights.accessRightsopenAccessen_US
dc.rights.holderCopyright 2020 The Author(s)
dc.subject.courseIDDOKTOR-008
dc.subjectVDP::Mathematics and natural science: 400::Information and communication science: 420::Mathematical modeling and numerical methods: 427en_US
dc.subjectVDP::Matematikk og Naturvitenskap: 400::Informasjons- og kommunikasjonsvitenskap: 420::Matematisk modellering og numeriske metoder: 427en_US
dc.subjectVDP::Mathematics and natural science: 400::Mathematics: 410::Applied mathematics: 413en_US
dc.subjectVDP::Matematikk og Naturvitenskap: 400::Matematikk: 410::Anvendt matematikk: 413en_US
dc.titleRepresentation and application of spline-based finite elementsen_US
dc.typeDoctoral thesisen_US
dc.typeDoktorgradsavhandlingen_US


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