322 



It is instructive to compare the meridional strain g, , given 

 by Eq. (30), vd.th that obtained on the basis of normal motion to the same 

 degree of approximation. If x. Cr^ t ) is ejiqjressible in the form 

 TCi)^,Cr) , and if R(r) is of the parabolic form A-* r*- , the two 

 assvunptions give identical values for the meridional strain, 2/ However, 

 if R,(r) is not of the above parabolic form, the quantity 'iLS - — ^fi 

 gives a measure of the deviations to be expected to occur between the two 

 calculations of the meridional strain. 



The plastic defonnation of an infinite thin plate under varioits 

 types of loading otp (r,t) ■»- OCat') > of which the ajiticipated special 

 applications can be considered special cases, reduces to the solution of 





and subsequently to the evaluation of 





(32) 



to give the distribution of strains. The conditions for rupture are obtained 

 by setting the time maximum of the central strain, £, ^ (o, t^) , equal to 

 the critical rupture strain £. . 



^7 If z^" =• ~m ? 1? Cr ) , the assumption of normal motion gives for 



the meridional strain £,, (in the first appiX)ximation) 



and the assamption of similarity of Mohr circles /see Eq, (30 }_/ gives 



If the two results are to agree for r arbitrary, then 



13 



