Citation
Brockway, George Samuel (1972) On the uniqueness of singular solutions to boundaryinitial value problems in linear elastodynamics. Dissertation (Ph.D.), California Institute of Technology. http://resolver.caltech.edu/CaltechTHESIS:04012016123848510
Abstract
This investigation deals with certain generalizations of the classical uniqueness theorem for the second boundaryinitial value problem in the linearized dynamical theory of not necessarily homogeneous nor isotropic elastic solids. First, the regularity assumptions underlying the foregoing theorem are relaxed by admitting stress fields with suitably restricted finite jump discontinuities. Such singularities are familiar from known solutions to dynamical elasticity problems involving discontinuous surface tractions or nonmatching boundary and initial conditions. The proof of the appropriate uniqueness theorem given here rests on a generalization of the usual energy identity to the class of singular elastodynamic fields under consideration.
Following this extension of the conventional uniqueness theorem, we turn to a further relaxation of the customary smoothness hypotheses and allow the displacement field to be differentiable merely in a generalized sense, thereby admitting stress fields with squareintegrable unbounded local singularities, such as those encountered in the presence of focusing of elastic waves. A statement of the traction problem applicable in these pathological circumstances necessitates the introduction of "weak solutions'' to the field equations that are accompanied by correspondingly weakened boundary and initial conditions. A uniqueness theorem pertaining to this weak formulation is then proved through an adaptation of an argument used by O. Ladyzhenskaya in connection with the first boundaryinitial value problem for a secondorder hyperbolic equation in a single dependent variable. Moreover, the second uniqueness theorem thus obtained contains, as a special case, a slight modification of the previously established uniqueness theorem covering solutions that exhibit only finite stressdiscontinuities.
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): 
 
Thesis Committee: 
 
Defense Date:  19 May 1972  
Funders: 
 
Record Number:  CaltechTHESIS:04012016123848510  
Persistent URL:  http://resolver.caltech.edu/CaltechTHESIS:04012016123848510  
Default Usage Policy:  No commercial reproduction, distribution, display or performance rights in this work are provided.  
ID Code:  9640  
Collection:  CaltechTHESIS  
Deposited By:  Leslie Granillo  
Deposited On:  01 Apr 2016 20:17  
Last Modified:  01 Apr 2016 20:17 
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