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

Functions S, T, U and V during differentiation have the property
of circular replacement, i.e.,
S" ( a)=2U (a-); S"'(a7)== 'T (a-);
T (aZ);
T' (a)=aS (C);
T" (a )=•-•V ( 7s); T" (a)= L (Z);
U(c); U' ( a)=raT (jz);
U" (a) =a-s (aii); U", (Ci,•) =a 3 " (a-);
v (Q); V' (a.) =au ()
V"/(a1).=u-T(a); V"(Z')=a3S(UZ). )
(3.33)
The use of these functions makes it possible to immediately
obtain a solution to equation (3.28) which satisfies the boundary
conditions. We have the following boundary conditions for our
problem:
1) " = 0; u(0) = 0 (deflection in-the seal is zero);
2) z = 0; u'(0) = 0 (the angle of pitch of the section in the
framing is equal to zero);
3) • = 1; u"(M) = 0 (bending moment at the free blade tip is
equal to zero);
4) -z = 1; u"0(a) = 0 (shearing force at the free blade tip is
equal to zero).
If we use the first two boundary conditions, we obtain A = 0;
B = 0. Then the solution to (3.31') will be
u() =CU(,;):+Dv (a). (3.31")
We shall use the third and fourth botu•dary condition.s (when = 1).
From formulas (3.33) we obtain:
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