﻿172 - Mr. C. Chree on the Local Alteration of 



Referring to equations (19) to (24) and (25) to (30) we 

 see this implies that the influence of the altered layer on the 

 strains and stresses of the remainder depends only on the 

 volume and not at all on the position of the layer. 



In the coefficient of (ki — k)/k in both (34) and (35) p' 

 occurs multiplied by a 3 and p occurs multiplied by e d . Thus 

 a layer differing slightly from the rest only in compressibility 

 has a greater effect on the strains and stresses arising from a 

 pressure over the outer surface than on those arising from a 

 pressure over the inner surface of the compound shell. 



If in (34) and (35) 



tC± ^ = /C, 



we have 



Referring to equations (19) to (24) and (25) to (30) we 

 see that the effect of the layer of altered rigidity, when its 

 volume is given, is greater the nearer it is to the centre. 



The layer in this case, however, is as effective in modifying 

 the strains and stresses arising from internal pressure as those 

 arising from external pressure. 



Displacements in general case of 3 Layers. 



§ 9. When fa—nj/n and fa—ty/h are not small it will be 

 sometimes more convenient, especially when the volume of 

 the altered layer is considerable, to deal with the complete 

 values of the displacements, strains, and stresses than with 

 the increments to the values in the simple shell (e . a . a) . 

 The strains and stresses may easily be written down from the 

 displacements, so it will suffice to give the complete values of 

 the latter. These are as follows, II being given as before 

 by (18) :- 



In (e . a, . c) 



1 rl 



pe d —p'a d 



(3^4 4?2)(3^ 1 + 4ti 1 ) 



~nL3 r { {aef 



-3p^^K--w)(^ 1 (3^ + 47i)a 3 --47i(^ 1 -^)(a 3 -6 3 ))| 



+ gi{(p-p f )*(a*+4n)(Mk + 4%) 



