Three‐Dimensional Stresses in Short Cantilevered Cylinders
Publication: Journal of Engineering Mechanics
Volume 116, Issue 10
Abstract
A three‐dimensional stress analysis for a short cantilevered cylinder subjected to a partial shear load on one end is presented based on the theory of elasticity. A solution to three‐dimensional elasticity problems proposed by the writer is used for the analysis. Boundary conditions on the fixed end are rigorously prescribed by three components of displacement. Basic and additional solutions are determined to satisfy boundary conditions. Numerical results for stresses and displacements in the short cantilevered cylinder, with a length‐to‐radius ratio of 2.0, are illustrated and are compared to those obtained by Saint‐Venant's method. A criterion of applicability of Saint‐Venant's method to this problem is proposed. The values of three components of stress at the loaded end become infinite at the boundary of the loaded area. The values of four components of stress at the fixed end show a tendency for stress concentration at the circumference of the end.
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References
1.
Hirai, H., and Satake, M. (1979). “General forms of Galerkin vector in cylindrical coordinates.” Proc. Japan Soc. Civ. Engrs., 290, 141–144.
2.
Hutchinson, J. R., and El‐Azhari, S. A. (1986). “Vibrations of free hollow circular cylinders.” J. Appl. Mech., 53(3), 641–646.
3.
Kobayashi, M., Ishikawa, H., and Hata, K. (1976). “The three‐dimensional stress analysis of the short rectangular prism.” Bull. Japan Soc. Mech. Engrs., 19(130), 351–359.
4.
Levine, H. S., and Klosner, J. M. (1967). “Transversally isotropic cylinders under band loads.” J. Engrg. Mech., ASCE, 93(3), 157–174.
5.
Matsuoka, K. G., and Nomachi, S. G. (1974). “On a 3‐dimensional stress analysis of an annular cylindrical body by means of Fourier‐Hankel transforms.” Theor. Appl. Mech., 22, 199–209.
6.
Noda, N. (1983). “Transient thermal stress problem in a transversely isotropic finite circular cylinder under three‐dimensional temperature field.” J. Therm. Stresses, 6(1), 57–71.
7.
Okumura, I. (1976). “On the three‐dimensional stress analysis for a short cylinder under a semi‐circularly distributed uniform load.” Theor. Appl. Mech., 24, 249–262.
8.
Okumura, I. (1977). “On the three‐dimensional stress analysis for a rectangular block under a partially distributed tangential load.” Theor. Appl. Mech., 25, 521–538.
9.
Okumura, I. A., and Miyake, K. (1981). “Stresses in a short hollow cylinder and a long hollow cylinder subjected to partial pressure on the side surface.” Theor. Appl. Mech., 30, 81–93.
10.
Okumura, I. A., and Onaka, T. (1986). “An expression for solutions to three‐dimensional elasticity problems in cylindrical and spherical coordinates.” Proc. Japan Soc. Civ. Engrs., 374(I‐6), Struct. Engrg./Earthquake Engrg., 3, 185–194.
11.
Timoshenko, S. P., and Goodier, J. N. (1970). Theory of elasticity. McGraw‐Hill, Kogakusha, Tokyo, Japan.
12.
Zureick, A. H., and Eubanks, R. A. (1988). “Spheroidal cavity with prescribed asymmetric tractions in three‐dimensional transverse isotropy.” J. Engrg. Mech., ASCE, 114(1), 24–48.
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Copyright © 1990 ASCE.
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Published online: Oct 1, 1990
Published in print: Oct 1990
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