Abstract
We state upper and lower bound formulas for the torsional stiffness of shafts of varying circular cross section, in accordance with the classical Michell formulation of this problem, through use of the principles of minimum potential and complementary energy. The general results are used to obtain explicit first-approximation bounds which, for the limiting case of the cylindrical shaft, reproduce the known elementary exact results. It is conjectured that the first-approximation lower bound is significantly closer to the exact result than the first-approximation upper bound.
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References
E.Reissner, Upper and Lower bounds for Deflections of Laminated Cantilever Beams Including the Effect of Transverse Shear Deformation, J. Appl. Mech. 40 (1973) 988–991.
S. P. Timoshenko and J. N. Goodier, Theory of Elasticity, 3rd Ed., 341–349, 1970.
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A report on work supported by the Office of Naval Research, Washington, D.C.
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Reissner, E. On bounds for the torsional stiffness of shafts of varying circular cross section. J Elasticity 8, 221–225 (1978). https://doi.org/10.1007/BF00052485
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DOI: https://doi.org/10.1007/BF00052485