AND DEFORMATION OF A THIN ELASTIC SHKI.I, 513 



8 + 2 8/3 

 8v + 2 Sn s 

 810 -|- 2 8n 3 . 



Let A,, BI, C, be the components of the system of forces per unit area applied to 

 the edge of the shell, and holding it in its actual configuration. The systems of 

 forces X,, Y t , Z, acting at all points of a line through P perpendicular to the middle- 

 surface, and the similar (A lt B u C^ system, will each reduce to a resultant force and 

 couple. 



The resultant of the X u Y^ Z, system is a force at P whose components are 



f* f* f* 



X, dz, Y = I Y! dz, Z l dz per unit area, 



and a couple whose components are 



f* f* 



L = J YI 2 dz, M = + I X l z dz, per unit area. 



The resultant of the A t , B,, C, system is a force at the point P in which the 

 middle-surface cuts the edge, whose components are 



A = j A! dz, B = j BI dz, C = \ C^z per unit length of the curve in 



which the middle-surface cuts the edge, and a couple whose components are 



f* /* 



Bj z dz, V = + I A! z dz, per unit length of the same curve. 



The general variational equation of motion is 



= - J|[ [X, (Su + 2 8Z S ) -f Y, (Sv + 2 8m 3 ) + Z l (8w + 2 8n 3 )] dS dz 

 - f f [A! (Su + 2 8/ 8 ) + B, (8v + 2 Sw 8 ) + G! (8; + 2 8n s )] ds dz 

 ~ f f 8W X SS + 2>iA Jf SW Z dS 



MDCCC'LXXXVIII. A. 3 U 



