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A Caltech Library Repository Feedhttp://www.rssboard.org/rss-specificationpython-feedgenenWed, 07 Feb 2024 04:11:31 +0000Some modified bifurcation problems with application to imperfection sensitivity in buckling
https://resolver.caltech.edu/CaltechTHESIS:03292013-095532634
Authors: {'items': [{'id': 'Keener-J-P', 'name': {'family': 'Keener', 'given': 'James Paul'}, 'show_email': 'NO'}]}
Year: 1972
DOI: 10.7907/8P4J-GD34
<p>The branching theory of solutions of certain nonlinear
elliptic partial differential equations is developed, when the nonlinear
term is perturbed from unforced to forced. We find
families of branching points and the associated nonisolated solutions
which emanate from a bifurcation point of the unforced problem.
Nontrivial solution branches are constructed which contain the nonisolated
solutions, and the branching is exhibited. An iteration
procedure is used to establish the existence of these solutions, and
a formal perturbation theory is shown to give asymptotically valid
results. The stability of the solutions is examined and certain
solution branches are shown to consist of minimal positive solutions.
Other solution branches which do not contain branching points are
also found in a neighborhood of the bifurcation point.</p>
<p>The qualitative features of branching points and their
associated nonisolated solutions are used to obtain useful information
about buckling of columns and arches. Global stability characteristics
for the buckled equilibrium states of imperfect columns and
arches are discussed. Asymptotic expansions for the imperfection
sensitive buckling load of a column on a nonlinearly elastic foundation
are found and rigorously justified.</p>https://thesis.library.caltech.edu/id/eprint/7564