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VI. DAMAQE TO INFINITE PLATr^S BY UNDiiJlWATiiR EXPLOSIONS 



1. Introduction 



The problem of damage to infinite plates — that is, plates having 

 linear surface dimensions many times greater than the charge distance — 

 is treated here as an infinite plastic membrane under impulsive loading. 

 The behavior of an infinite membrane is qualitatively quite different from 

 that of a circularly clamped membrane whose radius is relatively small com- 

 pared with the charge distance. In particular, in the case of the infinite 

 membrane the maximum central strain calculated on the basis of noriual 

 motion is about ten times greater than that calculated on the basis of the 

 similarity of Mohr circles (leading to the equality of principsil strains), 

 whereas in the case of the circularly clamped membrane the calculations on 

 the two bases give -fmrnmbms^^ identical results. Consequently, the case 

 under consideration is one in which it is imperative to use the correct 

 theory of strain (on the basis of the similarity of Mohr circles). 



In Sec. 2, the problem of damage to plates (in the first approx- 

 imation) under an arbitrary loading is considered with particular emphasis 

 on impulsive loading. In Sec. 3, the more special case of impulsive load- 

 ing giving an initial velocity distribution of the form (R^ + r )~ is 

 considered and explicit solutions in terms of elementary functions are 

 given for the profile and strain distribution in the cases of V = 1/2, 

 3/2, and 5/2. The variable r is the radius in cylindrical coordinates in 

 which the z-axis coincides with the center of symmetry of the system. In 

 the case of underwater explosions R is the distance between the middle 



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