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On the existence and uniqueness of the solution to the small-scale nonlinear anti-plane shear crack problem in finite elastostatics

Citation

Wakugawa, Jason Masao (1985) On the existence and uniqueness of the solution to the small-scale nonlinear anti-plane shear crack problem in finite elastostatics. Dissertation (Ph.D.), California Institute of Technology. http://resolver.caltech.edu/CaltechETD:etd-03212008-094413

Abstract

This thesis addresses the issue of existence and uniqueness of the solution to the small-scale nonlinear anti-plane shear crack problem in finite elastostatics. The hodograph transformation, commonly used in the theory of compressible fluid flows, plays an essential role. Existence is established by exhibiting an exact closed form solution, constructed via the hodograph transformation. Uniqueness is established by first proving the uniqueness of the solution to a related boundary-value problem, which is linear by virtue of the hodograph transformation, and then examining the implications of this result on the original problem. The possibility of making some of the conditions imposed on the solution to the small-scale nonlinear crack problem less restrictive is then investigated. This leads to several further results, including estimates of the nonvanishing shear stress component of the stress tensor along the crack faces.

Item Type:Thesis (Dissertation (Ph.D.))
Degree Grantor:California Institute of Technology
Division:Engineering and Applied Science
Major Option:Applied Mechanics
Thesis Availability:Restricted to Caltech community only
Research Advisor(s):
  • Knowles, James K.
Thesis Committee:
  • Unknown, Unknown
Defense Date:16 May 1985
Record Number:CaltechETD:etd-03212008-094413
Persistent URL:http://resolver.caltech.edu/CaltechETD:etd-03212008-094413
Default Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:1050
Collection:CaltechTHESIS
Deposited By: Imported from ETD-db
Deposited On:04 Apr 2008
Last Modified:26 Dec 2012 02:34

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