460 IX. DYNAMICS OF DEFORMABLE BODIES. 



175. Stresses in Isotropic Bodies. We may now calculate 

 the stresses by means of equations 126), inserting the values of 

 Sx, s y , s s , g x , g y , g z . 



. 



v ' 1 d$ ftw dv\ 



J-2 = AV = IT o = V* o -- h -o 



2 C 9 X \dy o*J 



1 fo du . dw 



The first equation of equilibrium 90) becomes 



i^o\ 

 143) 



or, considering the value of tf, we may write the equation with its 

 two companions, 



144) 



The equations at the surface of the body are by 86), using the 

 above values of the stresses, 



X n = (it + 2{*|| - P) cos (na?) 



f ^ (du . dw\ f N 



cos ( w ^) ^. ffJiw-t W cos (w ^' 



c s ( nx ^ + ( ie + ^ ll - p ) cos ^ 



146 ) 



. dw , 



* = ~-t l - + cos v + cos 



-r P cos (ne). 



