398 



Althou^y (xjtO is evidently discontinuous with respect to 

 ^ for Y= oo, both y^ ' i.^t't) ^i^d h^ i^i'^ are anal^i:,ic in ^j/ for finite 

 values of V . Further.-ior.?, it is hoped that these functions are so 

 related to ^ that three-point iriterpolation vath respect to ?/( constant x 

 and ^) among V = 1/2, 3/2, 5/2 i^ives adequate accuracy for functions at 

 intermediate values of ^z* when <_'}^<,k, say. The intenriediate value of 

 }/.U for V is of particular interest here. In Table VII and Figure 1 

 the intei-polated function y^-^'^' (x, '^) is presented numerically and 

 graphically, respectively. This function gives the belaavior of the 



plate profile (if there is no stress relief) when the plate has an initial 



(3/4) o -3/4 



velocity distribution, given by g (x) = (l + x*^) . In Table VIII 



and Figure 2 the interpolated function h^^'^^ (x, "^) is presented. This 



function gives the strain distribution as a function of time (if, again, 



there is no stress relief). In the case of a real plate subject ta stress 



relief, both of the functions y ' ' and Yr'''^ give the correct behavior — 



within the appro :d.:nat ions inherent in the general theory — of the profile 



and strain distributiai up to the tijne of maxinum central strain. 



By three-point interpolation it is found that h^V^) = 0.0932 

 andt ^V4) = o.927. 



The foregoing treatment of the structural behavior of a plastic 

 plate is exact within the limits of the general theory for the special 

 forms of the initial velocity distribution considered, \ihen the initial 

 velocity distribution is due to an underwater explosion, one has to treat 

 a hydro dynamical problem made quite formidable by cavitation and finite 

 amplitude effects. In the next section only a very cinide attempt is made 



81 



