We show that for a confocally elliptical hollow section under Saint-Venant’s torsion, there always exists a confocally elliptical closed contour inside the section that exhibits no warping. This property is generally true without any regard to the thickness or the aspect ratio of the hollow section, as long as the inner and the outer ellipses are confocal. This property allows us to apply Packham and Shail’s (Packham, B. A, and Shail, R., 1978, “St. Venant Torsion of Composite Cylinders,” J. Elast., 8, pp. 393–407) superposition method for the torsion solutions of a two-phase elliptical hollow section. Previously, this superposition method is only applicable to symmetric compound sections with respect to a straight line or a circular arc.
Issue Section:Brief Notes
Keywords:torsion, mechanical stability, dynamic response, rotation
Sokolnikoff, I. S., 1956, Mathematical Theory of Elasticity, McGraw-Hill, New York.
On Torsion of Closed Thin-Wall Members With Arbitrary Stress-Strain Laws: A General Criterion for Cross Sections Exhibiting No Warping,”
ASME J. Appl. Mech.,
B. A., and
St. Venant Torsion of Composite Cylinders,”
Ahlfors, L. V., 1966, Complex Analysis: An Introduction to the Theory of Analytic Functions of One Complex Variable, McGraw-Hill, Tokyo.
Caratheodory, C., 1969, Conformal Representation, Cambridge University Press, Cambridge, UK.
Exact Solutions in Torsion of Composite Bars: Thickly Coated Neutral Inhomogeneities and Composite Cylinder Assemblages,”
Proc. R. Soc. London, Ser. A,
Wang, C. T., 1953, Applied Elasticity. McGraw-Hill, New York.
Muskhelishvili, N. I., 1953, Some Basic Problems of the Mathematical Theory of Elasticity, Noordhoff, Groningen.
Lurie, A. I., 1970, Theory of Elasticity, Nauka, Moscow (in Russian).
R. C. F.,
Torsion of Hollow Cylinders,”
Trans. Am. Math. Soc.,
Fluid Motion Between Confocal Elliptic Cylinders and Confocal Ellipsoids,”
Q. J. Math.,
Love, A. E. H., 1944, A Treatise on the Mathematical Theory of Elasticity, Dover, New York.
Timishenko, S. P., and Goodier, J. N., 1970, Theory of Elasticity, 3rd Ed., McGraw-Hill, New York.
B. A., and
Stratified Laminar Flow of Two Immiscible Fluids,”
Proc. Cambridge Philos. Soc.,
Saint-Venant Torsion of a Two-Phase Circumferentially Symmetric Compound Bar,”
Kellogg, O. D., 1953 Foundations of Potential Theory, Dover, New York.
Torsion of a Rectangular Checkerboard and the Analogy Between Rectangular and Curvilinear Cross-Sections,”
Q. J. Mech. Appl. Math.,
Copyright © 2002