Citation
Levinson, Mark (1964) Variational principles and applications in finite elastic theory. Dissertation (Ph.D.), California Institute of Technology. http://resolver.caltech.edu/CaltechETD:etd09272002145537
Abstract
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 neoHookean 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 semiinverse 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.)) 

Degree Grantor:  California Institute of Technology 
Division:  Engineering and Applied Science 
Major Option:  Aeronautics 
Thesis Availability:  Public (worldwide access) 
Research Advisor(s): 

Group:  GALCIT 
Thesis Committee: 

Defense Date:  11 May 1964 
Record Number:  CaltechETD:etd09272002145537 
Persistent URL:  http://resolver.caltech.edu/CaltechETD:etd09272002145537 
Default Usage Policy:  No commercial reproduction, distribution, display or performance rights in this work are provided. 
ID Code:  3795 
Collection:  CaltechTHESIS 
Deposited By:  Imported from ETDdb 
Deposited On:  27 Sep 2002 
Last Modified:  22 Oct 2018 16:44 
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