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A Caltech Library Repository Feedhttp://www.rssboard.org/rss-specificationpython-feedgenenWed, 31 Jan 2024 19:13:31 +0000Eigenvalue problems associated with Korn's inequalities in the theory of elasticity
https://resolver.caltech.edu/CaltechTHESIS:08062015-145439790
Authors: {'items': [{'id': 'Horgan-C-O', 'name': {'family': 'Horgan', 'given': 'Cornelius Oliver'}}]}
Year: 1970
DOI: 10.7907/3VYK-2B81
<p>Interest in the possible applications of a priori inequalities in
linear elasticity theory motivated the present investigation. Korn's
inequality under various side conditions is considered, with emphasis
on the Korn's constant. In the "second case" of Korn's inequality, a
variational approach leads to an eigenvalue problem; it is shown that,
for simply-connected two-dimensional regions, the problem of determining
the spectrum of this eigenvalue problem is equivalent to finding
the values of Poisson's ratio for which the displacement boundary-value
problem of linear homogeneous isotropic elastostatics has a non-unique solution.</p>
<p>Previous work on the uniqueness and non-uniqueness issue for
the latter problem is examined and the results applied to the spectrum
of the Korn eigenvalue problem. In this way, further information on
the Korn constant for general regions is obtained.</p>
<p>A generalization of the "main case" of Korn's inequality is introduced
and the associated eigenvalue problem is a gain related to the
displacement boundary-value problem of linear elastostatics in two
dimensions.</p>
https://thesis.library.caltech.edu/id/eprint/9082