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

Hyperbolic disks. If the, thickness of. such a'disk h = a/(D/2)m
is. substituted int6 equation (3.63), the solution for u is obtained
in the form (3.65), whereupon, in tjhis case, particular solutions
* q 1 q.•' and (3 are elementary functions..,
The equations for strcssbs or and a 9 can be obtained from
formulas (3.62) after' sibstituting ih them the solutions for u:
* I .
- -- p 4 A 'n + /Yc7 :. q.. (3.66)
where p and q are coefficients depending on the geometric dimensions
of the disk cross sectioh (including exponent m), on the characteristics
of the disk materidl (E; p; p), on th6 angular velocity of disk
i otation and the presentifunctions of the diameter (or radius), on
which stresses are bding defined;
A and B are the integration constants;
* 2
LDuring practical dnalyses of disks ccusisting 'of several sections,
the stresses ar and ,ao on the current diameter D are expressed in
terms of the khown strepses arl and a91 on the initial
Such formulas can be obtained from formulas (3.66) if
diameter DI.
we determine
the constailts A and B from the follow~ng conditions: when D = D
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t r = al'; 09 I o91, and then again substitute thert into formulas
) I (3.66). The results are written In the following form:
wherg a; a; a; 0 r
disks represent lengthy
(3.67)
9; OC are the coefficients which for hyperbolic
algebraic expressions.
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4•
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29.