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

From the theory of differential equations we know that the
solution to equation (3.63) for a disk of arbitrary shape can be
written in the form
t (r) +Bp (r) +CT3(r), (3.65)
where •l(r) and 9 2 (r) are particular solutions of a homogeneous
I3
equation corresponding to equation (3.63) [i.e., equation (3.63)
without the right side];
q 3 (r) is a particular sulutton to equation (3.63) (i.e., equation
with the right side);
A and B are integration constants determined from the boundary
conditions.
Coefficient C is taken from expression (3.64).
I
A'= const
•
a) (a I) (b)
Fig. 3.33. Shapes of the radial cross section of disks:
a - disk of constant thickness; b - hyperbolic disk;
c - conical disk.
However, equation (3.63) can be integrated in the elementary
functions only for certain particular cases, for example, for a disk
of constant thickness (h = const), for hyperbolic disks, and certain
others.
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