Citation
Messick, Roger Edwin (1962) Applications of an edge andcorner layer technique to elastic plates and shells. Dissertation (Ph.D.), California Institute of Technology. http://resolver.caltech.edu/CaltechTHESIS:08192011135729811
Abstract
This paper contains several problems that can be formulated mathematically as twodimensional boundary value problems for partial differential equations containing a parameter. A method is given which leads directly to asymptotic solutions for large values of the parameter without resorting to the exact solutions. The examples discussed involve linear differential equations and are drawn primarily from various problems in the theory of elasticity. The method involves consideration of what are termed cornerlayers in addition to the well known boundarylayers. The need for considering these cornerlayers arises from the fact that the problems treated lead to boundarylayer differential equations which contain derivatives, not only with respect to the boundarylayer variable, but also with respect to the remaining independent variable. Thus, the solution of such boundarylayer equations requires knowledge of boundary conditions in addition to those needed in standard boundarylayer problems. The applications include: a heat conduction problem, two problems with transverse bending of stretched plates, and two problems from elastic shell theory. The shell problems concern the bending of both the shallow and the nonshallow helicoidal shell. It is found that these shells have boundarylayers whose characteristic length is proportional to the onethird power of the thickness parameter. This may be contrasted with shells of revolution, where this characteristic length is proportional to the onehalf power of the thickness parameter.
Item Type:  Thesis (Dissertation (Ph.D.)) 

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

Thesis Committee: 

Defense Date:  1 January 1962 
Record Number:  CaltechTHESIS:08192011135729811 
Persistent URL:  http://resolver.caltech.edu/CaltechTHESIS:08192011135729811 
Default Usage Policy:  No commercial reproduction, distribution, display or performance rights in this work are provided. 
ID Code:  6609 
Collection:  CaltechTHESIS 
Deposited By:  John Wade 
Deposited On:  19 Aug 2011 21:35 
Last Modified:  26 Dec 2012 04:38 
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