GEOMETRICALLY NONLINEAR FINITE-ELEMENT ANALYSIS OF CIRCULAR AND ARBITRARY ARCHES

Persistent Link:
http://hdl.handle.net/10150/282736
Title:
GEOMETRICALLY NONLINEAR FINITE-ELEMENT ANALYSIS OF CIRCULAR AND ARBITRARY ARCHES
Author:
Calhoun, Philip Ray
Issue Date:
1980
Publisher:
The University of Arizona.
Rights:
Copyright © is held by the author. Digital access to this material is made possible by the University Libraries, University of Arizona. Further transmission, reproduction or presentation (such as public display or performance) of protected items is prohibited except with permission of the author.
Abstract:
A curved nonlinear finite element is developed in this work to observe the behavior of slender arches which undergo large deformations. The derivation of the strain equation is based upon the assumption that cross sections of the undeformed state remain undeformed and plane, but not necessarily normal to the centroidal axis during deformation. It is also assumed that the strain will be small and the rotations will be finite. The in-plane bending and the buckling modes for arches with fixed end and hinged end supports are analyzed. Deep circular arches and deep arches with arbitrary geometry of the centroidal axis are studied. Vertical concentrated loads, uniformly distributed loads, a combination of concentrated and distributed loads, and nonsymmetrical loads are considered. The governing differential equations are differentiated with respect to time to give a system of rate equations. Using these equations, the original nonlinear differential equations are solved using the Runge-Kutta scheme with Simpson's coefficients. If the solution drifts, a Newton-Raphson iteration scheme is used to return the solution to the equilibrium path.
Type:
text; Dissertation-Reproduction (electronic)
Keywords:
Arches -- Mathematical models.; Strains and stresses -- Mathematical models.; Deformations (Mechanics) -- Mathematical models.
Degree Name:
Ph.D.
Degree Level:
doctoral
Degree Program:
Graduate College; Aerospace and Mechanical Engineering
Degree Grantor:
University of Arizona
Advisor:
DaDeppo, Donald

Full metadata record

DC FieldValue Language
dc.language.isoen_USen_US
dc.titleGEOMETRICALLY NONLINEAR FINITE-ELEMENT ANALYSIS OF CIRCULAR AND ARBITRARY ARCHESen_US
dc.creatorCalhoun, Philip Rayen_US
dc.contributor.authorCalhoun, Philip Rayen_US
dc.date.issued1980en_US
dc.publisherThe University of Arizona.en_US
dc.rightsCopyright © is held by the author. Digital access to this material is made possible by the University Libraries, University of Arizona. Further transmission, reproduction or presentation (such as public display or performance) of protected items is prohibited except with permission of the author.en_US
dc.description.abstractA curved nonlinear finite element is developed in this work to observe the behavior of slender arches which undergo large deformations. The derivation of the strain equation is based upon the assumption that cross sections of the undeformed state remain undeformed and plane, but not necessarily normal to the centroidal axis during deformation. It is also assumed that the strain will be small and the rotations will be finite. The in-plane bending and the buckling modes for arches with fixed end and hinged end supports are analyzed. Deep circular arches and deep arches with arbitrary geometry of the centroidal axis are studied. Vertical concentrated loads, uniformly distributed loads, a combination of concentrated and distributed loads, and nonsymmetrical loads are considered. The governing differential equations are differentiated with respect to time to give a system of rate equations. Using these equations, the original nonlinear differential equations are solved using the Runge-Kutta scheme with Simpson's coefficients. If the solution drifts, a Newton-Raphson iteration scheme is used to return the solution to the equilibrium path.en_US
dc.typetexten_US
dc.typeDissertation-Reproduction (electronic)en_US
dc.subjectArches -- Mathematical models.en_US
dc.subjectStrains and stresses -- Mathematical models.en_US
dc.subjectDeformations (Mechanics) -- Mathematical models.en_US
thesis.degree.namePh.D.en_US
thesis.degree.leveldoctoralen_US
thesis.degree.disciplineGraduate Collegeen_US
thesis.degree.disciplineAerospace and Mechanical Engineeringen_US
thesis.degree.grantorUniversity of Arizonaen_US
dc.contributor.advisorDaDeppo, Donalden_US
dc.identifier.proquest8104290en_US
dc.identifier.oclc7712106en_US
dc.identifier.bibrecord.b13499038en_US
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