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Eigenvalue Problems Associated With Korn's Inequalities in the Theory of Elasticity


Horgan, Cornelius Oliver (1970) Eigenvalue Problems Associated With Korn's Inequalities in the Theory of Elasticity. Dissertation (Ph.D.), California Institute of Technology. doi:10.7907/3VYK-2B81.


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.

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.

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.

Item Type:Thesis (Dissertation (Ph.D.))
Subject Keywords:(Applied Mechanics)
Degree Grantor:California Institute of Technology
Division:Engineering and Applied Science
Major Option:Applied Mechanics
Thesis Availability:Public (worldwide access)
Research Advisor(s):
  • Knowles, James K.
Thesis Committee:
  • Unknown, Unknown
Defense Date:20 May 1970
Funding AgencyGrant Number
Record Number:CaltechTHESIS:08062015-145439790
Persistent URL:
Default Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:9082
Deposited By: Benjamin Perez
Deposited On:06 Aug 2015 22:08
Last Modified:10 May 2024 22:31

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