Design and Stress Analysis of Extraterrestrial ... - The Black Vault

-II
Constant azial relative strain e in each particular case must
* * be chosen' so that the eguaily acting forces, distributed along the
cross section of the, cylinder, vanish, i.e.,
b
'a -rdr==0.
*6 (2.18)
' A jpint solution of equations (;2.17) and (2.18) gives
I
I
whereAt 0 t t is the maximum; value of the temperature gradient
along the cross sdction of the fuel element.
hif ta is the temperature on the internal surface of the cylinder and
the temperature on the external surface is
, at any distance r from center: is
zero, the temperature
A t= / 1
U / In --. b
Substit~utiig this value intd formulas (2.17), we find the following
exoressions fbr thermal stresses: ,
a2 a
• (-'•./ i-n ---- - -- i In-i;
2(1p) In ba [ r bV.a2 2 ) a4
Et2( ,-,:2lb/ ir b: 2a2 In
"r . . . l:
6
2(1-r b2V- a2 a (2.19)
bj
IIf ta is positive, radial stress for all points is compressive
and vanishjs on the internal and external surfaces of the cylinder.
The stress components a q, and Ox reach their highest absolute values
on the inner and outer surýfaces of the cylinder. Assuming r = a,
we:find
120
LI
'9.