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

Movement of the bellows also depends on the ratio of its
diameters. in the first approximation, this dependence can be
assumed equal tc the square of the ratios of the diameters:
)-2 a )I l a 2
To calculate strains and stresses in the walls of the bellows,
it io considered a system of circular plates bound on the external
and the internal contours by cylindrical inserts •Fig. 5.63e).
M
40 (b)
Fig. 5 .641.
Determining the rigidity of a flexible element.
For the internal diameter of the plates we should take the internal
diameter of the bellows 2a and for the external we should take the
external diameter of the bellows 2b. Plate thickness h is assumed
constant. We further assume that all plates operate under identical
conditions.
The angle of turn for the plates on the external and
internal contours is zero. Bends of plates are considered small -
ti-A bend of any plate does not exceed its thickness h. This is
the first
approach to a more accurate solution.
Thus, we seek the stresses and strains of a circular plate with
pinched contours under loading by axial force P (Fig. 5.64a). Using
the steady-state equation for the forces of elasticity of a rigid
plate, we derive a formula for calculating a circular plate [43]:
W a2 [k2-_ k2 ln'k]
4 k2
k2-- (5.117)
where wa is the bend of the plate on radius a; k
b/a.
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