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

Stresses in a circular diret.ion or
05; (ro) = E u3 +
-80. 10. 3.5.10-6.1411,5 + 12,) = 4,b2 daN/mm 2 ;
2,(rj)= 1,77 6aIl.m.0.; c•(r)=--3,44 daN/mm 2
Fi; .ire 5. ?i shows the tends and stresses of an anode.
Integral method of solving the equation
of a conical shell
As 13 apparent from the example of shell analysis, the asymptotic
method is rather cumbersome. In many cases, calculations should be
r-erformed according to the integral method.
Let us examine a case when the anode parameters h,
constant and the only variable is At.
E, D are
The initial equation will have the form
(r' )"--r WO + DrtgOe =Dtg" ( 5 .54)
The procedure for solving the problem remains the same. We shall
seek a general solution to equation (5.54) as the sum of its
particular solution and a general solution without the right side:
Wp = W0 + Wr.
Let us find the particular solution. We assume that the temperature
& 2
gradient is given by formula At = B 0 + Blr + B 2 r
We also assume wr = A 0 + Air + A 2 r 2 + A 3 r 3 . Let us substitute
this expression into (5.54), equate the terms with identical
functions relative to r, and obtain the values for AO; A 1 ; A 2 ; A 3
and, consequently, w :
572
mmm _ m ~ lm m •.
ip • • _ • : -- :. . ,e .- m