CIRCULAR CYLINDERS UNDER CERTAIN PRACTICAL SYSTEMS OF LOAD. 189 
■w.^ = fyE, u.2= — -/j(l -y)E, 
+ 'T®’ 
F--|(l+y)E, E'=-|yE 
and these satisfy the equations and the condition (86). 
It is noticeable that a solution can be obtained, in the form 
» = v + f+ 5f^+r, 
w = vv + ?^ + W, 
which can be made to satisfy all the conditions except (86). If, however, one 
works out this solution, it is found, as we should expect, to give infinite values for 
the stresses, all round the perimeter of the plane ends. Thus, though simpler in 
form, this solution is not really simpler to work with. I have given on pp. 217-219 
the expressions for the stresses and displacements ol^tained from such a solution. 
— 
8^2 
o 
O 
§ 14. Determination of the Coefficients so as to Satisfy the Conditions at the 
Curved Surface. 
If we write down the expressions for the stresses, we find 
—) = (D + D') + Eah + (F/ + F) _p ^ dW 
\ U jr^a 
dz ^ d r ' 
We have therefore to make 
- (D + D') az - Ea^^ _ (E' + F) 
Now we find easily 
20 
— S (A^ + Ag) Ij (a) fi- — af (a) sin 
niTZ 
c 
Hence if we expand — (D fi- D') 
sin 
1 c 
CO 
(- 1)"- 
, 2c . 
HTTZ 
s 
^ - sm 
) 
1 
'HIT 
c 
CO 
, I2d 
12c-^\ . nir: 
S 
(~ i)“ 
1 (- 
■ - sm - 
1 
\niT 
"/rTT'*/ c 
1 
"T 
D') az 
- Eah 
- (F/ + F) ( 
a,, = [— (D + D') ac — Ea^c — (E' + F) ac^~] (— 1)" ^ X 
nir 
