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On the search for functionals of variational principles with applications in elasticity

dc.contributor.authorLie, Wong Siong
dc.date.accessioned2011-06-21T01:56:15Z
dc.date.accessioned2022-10-26T21:11:18Z
dc.date.available2011-06-21T01:56:15Z
dc.date.available2022-10-26T21:11:18Z
dc.date.copyright1987
dc.date.issued1987
dc.description.abstractThis thesis involves the calculus of variations and explores a method of construction for functionals of variational principles, particularly in the area of static elasticity. The background material in small displacement theory of static elasticity is briefly presented. The general idea and historical development of the calculus of variations are then briefly reviewed. A new precise definition of variations is proposed in connection with the ∂-operator which is introduced. The consequences of this definition and the properties of variations are discussed in detail. These matters are often not carefully examined by other authors. A more powerful basic lemma is developed so that the choice of the test functions becomes more flexible. The calculus of variations is applied to problems in static elasticity, which are classified according to different variational constraints. The variational process with zero complement is recommended for some particular cases. A method for finding functional of variational principles is developed. Fifty one functionals for distinct principles are then derived. These include the functionals of the Hellinger-Reissner principle, the Hu-Washizu principle, and all other important functionals of variational principles in static elasticity.en_NZ
dc.formatpdfen_NZ
dc.identifier.urihttps://ir.wgtn.ac.nz/handle/123456789/24929
dc.languageen_NZ
dc.language.isoen_NZ
dc.publisherTe Herenga Waka—Victoria University of Wellingtonen_NZ
dc.rights.holderAll rights, except those explicitly waived, are held by the Authoren_NZ
dc.rights.licenseAuthor Retains Copyrighten_NZ
dc.rights.urihttps://www.wgtn.ac.nz/library/about-us/policies-and-strategies/copyright-for-the-researcharchive
dc.subjectCalculus of variationsen_NZ
dc.subjectElasticityen_NZ
dc.subjectMathematicsen_NZ
dc.titleOn the search for functionals of variational principles with applications in elasticityen_NZ
dc.typeTexten_NZ
thesis.degree.disciplineMathematicsen_NZ
thesis.degree.grantorTe Herenga Waka—Victoria University of Wellingtonen_NZ
thesis.degree.levelMastersen_NZ
thesis.degree.nameMaster of Scienceen_NZ
vuwschema.type.vuwAwarded Research Masters Thesisen_NZ

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