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

where B is a coefficient;
n is the exponent equal to 0, 1, 2, with uniform heating,
linear and quadratic variation in the temperature gradient, respectively.
We further assume that the temperature of the shell isiconstant
throughout its thickness.
SS
is
As indicated, the relative strain of an eiement during heating
determined by formula
88t+8 • y,
S~y
where stis
Sis
of its deformation.
tt
the thermal strain of a free element;
the elastic strain of an element due to the constriction
For a cylindrical shell relative strains in the circular
direction e = e + C are substantial and are easily converted
to radial strain w with formula w - re., ginally
W=Wt+Wy.
Free thermal strain wt is
known (Fig.:5.14d):
w=rv= raAt.
It is also known that the stress in the shell creates the7 elastic
component of total thermal strain in the element w-. Finding it
involves considerable difficulties.
t|
Elastic component of shell strain is
for a temperature problem.
fdund by common procedures
a) We impose on a cold shell rigid bonds in the form of a
rigid housing and then heat it to temperature t. Thermal expansion
of the shell does not occur, compressive stress arises in it, and
on the surface a reaction from the rigid walis in the form of pressure
•Rt" The same eff'z;6 tn be obtained if we compress a shell expanding
to wt =rcAt by external pressure up to the initial parameter.
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