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Variational Principles and Applications in Finite Elastic Strain Theory


Levinson, Mark (1964) Variational Principles and Applications in Finite Elastic Strain Theory. Dissertation (Ph.D.), California Institute of Technology. doi:10.7907/PK58-HQ71.


The variational principles of finite elastostatic strain theory are presented in a unified manner for both compressible and incompressible bodies. Whereas the principle of stationary potential energy, a restricted case of the general principle of Hu and Washizu, is valid for any elastic deformation, it is found that the principle of stationary complementary energy is valid only for infinitesimal elastic strains. Consequently, Reissner's Theorem is the appropriate stationary principle to use in finite elastic strain theory when the complementary strain energy density is to be the argument function. The potential energy principle is applied to several problems dealing with the finite straining of a neo-Hookean material. All but one of these problems are concerned with plane strain deformations; the one other problem, in a spherical geometry, involves an unusual stability question. Approximate solutions are obtained for some mixed boundary value problems which are not amenable to the semi-inverse methods of solution frequently used in finite elastic strain theory. Another plane strain problem, requiring more detailed stress information than can be obtained from the potential energy principle, is studied approximately by means of Reissner's Theorem.

Item Type:Thesis (Dissertation (Ph.D.))
Subject Keywords:(Aeronautics)
Degree Grantor:California Institute of Technology
Division:Engineering and Applied Science
Major Option:Aeronautics
Thesis Availability:Public (worldwide access)
Research Advisor(s):
  • Blatz, Paul J. (advisor)
  • Knowles, James K. (advisor)
Thesis Committee:
  • Unknown, Unknown
Defense Date:11 May 1964
Record Number:CaltechETD:etd-09272002-145537
Persistent URL:
Default Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:3795
Deposited By: Imported from ETD-db
Deposited On:27 Sep 2002
Last Modified:19 Jan 2024 22:42

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