GEOMETRICALLY NONLINEAR FINITE-ELEMENT ANALYSIS OF CIRCULAR AND ARBITRARY ARCHES
AuthorCalhoun, Philip Ray
KeywordsArches -- Mathematical models.
Strains and stresses -- Mathematical models.
Deformations (Mechanics) -- Mathematical models.
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PublisherThe University of Arizona.
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.
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.
Degree ProgramGraduate College
Aerospace and Mechanical Engineering