163 



TABLE OF GONTHJTS 



Page 



Historical Background 1 



Observations of Deformation of Diaphragms 1 



Surmises Concerning the Motion. .,, 3 



Basic Suppositions 4 



Mathematical Formulation of the Theory 8 



Part 1. Conditions in the Neighborhood of the Bending 



VJave »...8 



Part 2, Equations of Motion in the Flat Central Region. , .12 



Part 3. The Application of Plasticity Theory ll^ 



Part 4. The Specification of the Initial State 16 



Sumnary of the Equations of Motion 19 



An Elementary Approximation to the Solution 20 



The Exact Solution for a Material with no Work-hardening 22 



2 2 

 Special Cases A, X ^ /^ = ^1 23 



B. S »1, ■^^=— «1 24 



^2 



Considerations of Work-hardening 26 



Conclusions , , 28 



Acknowledgment 30 



