d^ 



dn 



Problems in the Theory of Elasticity. 19 



displacement s . Calculating separately the different terms, 

 we have 



grad di v (a r) = ~ [a . grad (~ )J 



= r)H a -[ grad G) r+ ;J} =a £(^)~iU^ r ) 

 - a a6) +a - a ^J)- ft - r r r i(?) + 5] 



= a iG) +a - ngrad C) - 3 i(i)^ rad r © + na - « rad ;- 



Hence 



— 7VJ-, 7- a.n grad : - +na. grad 3-rl -I grad r ( ,-|. (4) 



2(1 + £)L ** ' r dn\rJ B \da) K ; 





In the second term of (2) we have 



div s = a . grad- - ^J+Q V 2 (a • grad r) 



</a\r/ l + *rfaW l + kda\r)' * W 



Lastly, in the third term 



n x curl s = n x curl- 

 r 



— n x (grad - x a) 



= n . a grad 11 . grad - a. . (6) 



r r v ' 



Substituting in (2) the values given by (4), (5), and (6) 

 we find for the value of the surface traction * ^ (sp) due to 

 the displacement s (qp) whose pole is p, 



*« to = ^ify- rh a * (» x **» J) 



* It will lead to no confusion if we speak thus of F= — T as the 

 41 surface traction." The symbol employed Avill always indicate which 

 quantity is referred to. 



C 2 



