Abstract
In this paper the stress distribution at a point in a long hollow cylindrically aeolotropic circular cylinder whose plane ends are subjected to systems of forces each of which is statically equivalent to a couple and a longitudinal force, and whose curved surface is subjected to a uniform normal pressure has been studied. The solution of this static mixed Saint-Venant type problem provides results from which the corresponding results of isotropic, transversely isotropic circular cylindrical bodies can be readily deduced. In the end a simple practical application has been made with regard to a similar problem of a long hollow wood pole made up of species walnut.
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Abbreviations
- r, θ, z :
-
cylindrical coordinates
- u x , u y , u z :
-
cartesian components of displacement
- \(\left. {\begin{array}{*{20}c} {e_{rr} ,{\text{ }}e_{\theta \theta } , {\text{ }}e_{zz} } \\ {e_{zr} ,{\text{ }}e_{\theta z} ,{\text{ }}e_{r\theta } } \\ \end{array} } \right\}\) :
-
components of strain
- τ rr , τ θ , τ zz :
-
normal components of stress
- τ rθ , τ θz , τ zr :
-
shear stress components
- a, b (a<b):
-
radii of the hollow cylinder
- S ij , b ij :
-
elastic coefficients
- R :
-
uniform normal pressure
- L, M, N :
-
terminal couples
References
Boley, B. A. and J. H. Weiner, Theory of thermal stress, Wiley, New York, U.S.A. 110, 1960.
Wangaard, F. F., The mechanical properties of wood, Wiley, New York, U.S.A. 74, 1950.
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Ghosh, B. Stresses in a long hollow cylindrically aeolotropic circular cylinder with plane ends subjected to surface forces. Appl. Sci. Res. 25, 113–125 (1972). https://doi.org/10.1007/BF00382288
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DOI: https://doi.org/10.1007/BF00382288