Theory of Thin-Walled Rods Page: 4 of 54
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NACA UK 1322
described by a linear combination of the particular integral of a non-
homogeneous system of equations of the rod and very slowly damping
solutions of the homogeneous equations. The boundary conditions at the
transverse ends of the rod-shell can not in this case be set up at each
point but must be replaced by integral conditions. The method resulting
from such approach of the computation of short rods leads to practical
formulas. Rods of medium length, occupying in the character of their
behavior an intermediate position between short and long rods (the lat-
ter do not require investigation since they may be considered as solid)
were not capable of being investigated to the end.
The method thus obtained of the computation of short thin-walled
rods was found to be more complicated than that arrived at by V. Z. Vlasov
(reference 1). These two methods approach each other considerably if
the equations here presented are simplified by rejecting the components
which take into account the effect of shear. Even with this simplifica-
tion, however, agreement in the computational relations is not complete.
Specifically, the equation determining in the theory of V. Z. Vlasov
the torsion of a thin-walled rod is not confirmed.
As regards the fundamental assumption made in the theory of Vlasov
that the cross-section of the rod maintains its shape, it is not in
itself true, nor is there a need for such an assumption. The use of
the assumption does not, however, lead to errors in the computations of
stresses because the principal stress state is affected only by those
deformations for which the cross-section does not vary.
We may remark in conclusion that in the Soviet Union (A. I. Adadurov)
and later abroad (Korman) a theory was worked out of the computation of
cylindrical shells, the cross-sectional contour of which can not deform
due to the presence of a large number of diaphragms. This structure
must be distinguished from a thin-walled rod. For this reason it is
not possible from our point of view to agree with G. Y. Dzhanelidze and
Y. G. Panovko (reference 2) who consider the theory of A. R. Adadurov
as a generalization of the theory of V. Z. Vlasov based on the fact that
Adadurov rejected the assumption on the absence of shear. The theory
of thin-walled rods is in principle different from the theory of shells
with transverse forces because for the former there is sought only the
principal stress state while for the latter it is necessary to investi-
gate also the local stress states. It is due to this fact and not to
the fact that the assumption on the absence of shear is rejected in the
theory of shells with diaphragms that the conditions on the transverse
ends are set up at each point. In the present paper, formulas are given
for the computation of thin-walled rods with account taken of shear
deformations. In view.. of what was said above, however, they do not
agree with the results of A. R. Adadurov.
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Goldenveizer, A. L. Theory of Thin-Walled Rods, report, October 1951; (digital.library.unt.edu/ark:/67531/metadc62968/m1/4/: accessed January 17, 2019), University of North Texas Libraries, Digital Library, digital.library.unt.edu; crediting UNT Libraries Government Documents Department.