Quarterly of Applied Mathematics

Quarterly of Applied Mathematics

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Nonlinear analysis of a twisted axially loaded elastic rod


Author: David W. Zachmann
Journal: Quart. Appl. Math. 37 (1979), 67-72
MSC: Primary 73C50; Secondary 34A34
DOI: https://doi.org/10.1090/qam/530669
MathSciNet review: 530669
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Abstract: A slender, inextensible elastic rod is acted upon by a twisting couple and an axial load. The position of the rod's centerline is determined by two fourth-order, coupled, nonlinear boundary value problems, each of which contains two eigenparameters. These equilibrium equations admit the trivial solution for all values of the eigenparameters, i.e., for any axial load and any twisting couple. The linearized equilibrium equations have a countable number of eigencurves. Through using the implicit function theorem for Banach spaces it is shown that from each of the eigencurves of the linear problem there bifurcates a two-parameter sheet of nontrivial solutions of the nonlinear equilibrium equations.


References [Enhancements On Off] (What's this?)

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DOI: https://doi.org/10.1090/qam/530669
Article copyright: © Copyright 1979 American Mathematical Society


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