On the Energy Conserved in a Buckling Fung Hyperelastic Cylindrical Shell Subjected to Torsion, Internal Pressure and Axial Tension

dc.contributor.advisorGui, Changfeng
dc.contributor.authorShadfan, Ramsey Harbi
dc.contributor.committeeMemberChen, Fengxin
dc.contributor.committeeMemberFazly, Mostafa
dc.creator.orcidhttps://orcid.org/0000-0001-9488-4377
dc.date.accessioned2024-01-26T23:08:57Z
dc.date.available2024-01-26T23:08:57Z
dc.date.issued2018
dc.descriptionThe author has granted permission for their work to be available to the general public.
dc.description.abstractA theoretical model is proposed for the buckling of a three-dimensional vein subjected to torsion, internal pressure, and axial tension using energy conservation methods. The vein is assumed to be an anisotropic hyperelastic cylindrical shell which obeys the Fung constitutive model. Finite deformation theory for thick-walled blood vessels is used to characterize the vessel dilation in the pre-buckling state. The pre-buckling state is identified by its midpoint and then perturbed by a displacement vector field dependent on the circumferential and axial directions to define the buckled state. The total potential energy functional of the system is extremized by minimizing the first variation with respect to the elements of the set of all continuous bounded functions on $\mathbb{R}^3$. The Euler-Lagrange equations form three coupled linear partial differential equations with Dirichlet boundary conditions characterizing the buckling displacement field under equilibrium. A second solution method approximates the first variation of the total potential energy functional using a variational Taylor series expansion. The approximation is minimized and combined with equations of equilibrium derived from elasticity theory to yield a polynomial relating buckling eigenmodes, material parameters, geometric parameters, and the critical angle of twist which induces buckling. Various properties of the total potential energy functional specific to the problem are proved. Another solution method is outlined using the first variation approximation and the basis of the kernel of the linear transformation which maps buckling displacement amplitudes during static equilibrium.
dc.description.departmentMathematics
dc.format.extent125 pages
dc.format.mimetypeapplication/pdf
dc.identifier.isbn9780438300576
dc.identifier.urihttps://hdl.handle.net/20.500.12588/2719
dc.languageen
dc.subjectbuckling
dc.subjectenergy functional
dc.subjectFung
dc.subjectshell
dc.subjecttorsion
dc.subjectvariation
dc.subject.classificationApplied mathematics
dc.subject.classificationBiomechanics
dc.subject.classificationMechanics
dc.titleOn the Energy Conserved in a Buckling Fung Hyperelastic Cylindrical Shell Subjected to Torsion, Internal Pressure and Axial Tension
dc.typeThesis
dc.type.dcmiText
dcterms.accessRightspq_OA
thesis.degree.departmentMathematics
thesis.degree.grantorUniversity of Texas at San Antonio
thesis.degree.levelMasters
thesis.degree.nameMaster of Science

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