311 



position (r , z) at time -^ ; ^ is the density of the plate material and ^ 

 is the actual thickness of the plate at the point ( r , x) and at time "t ; 

 p is the pressxore acting on the lower side of the plate at the radius r 

 and at time t ; <r, and tf~ are the principal stresses in the meridional 

 and c irciomf erential directions, respectively. Equations (1) and (2), ex- 

 pressed with a briefer but less explicit notation, have been derived in 

 OSRD-4200, 



(2) The modified von Mises plasticity condition . The biaxial 

 reduced engineering stresses. 



5. = 



affT 



3oCi 



and (6) 



5.= 





are assumed to satisfy the von Mises condition in the plane-stress approxi- 

 mation, which in these terms may be written, 



5, - 5^ - S, 5^ =^ I. 



Here <3^is the initial thickness of the plate and j^ is the yield stress. 

 Equation (?) is assumed to hold in the limit of vanishing strains implying 

 ignoration of the elastic domain of strain, 



(3) Incompressibility of material. The material is incompressi- 

 ble, or, in other words, Poisson's ratio equals 1/2. Incompressibility im- 

 poses the following relation on the ratio of the actual thickness 3- to the 

 initial thickness a^ : 



r^^' 



