Torsion of a Shaft with a Toroidal Cavity

@article{Weiss1954TorsionOA,
  title={Torsion of a Shaft with a Toroidal Cavity},
  author={George Weiss and Lawrence Edward Payne},
  journal={Journal of Applied Physics},
  year={1954},
  volume={25},
  pages={1321-1328}
}
This paper gives the solution to the torsion problem for a near‐cylindrical shaft of circular section having a toroidal cavity. Since the interpretation of the axially symmetric problem as a flow problem in 5 dimensions is well known, the first part of the paper is devoted to developing a method for handling the flow problem about an n dimensional ring‐shaped body of general cross section. In the second part of the paper this method is applied to the case of an n dimensional torus ring. The… 
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References

SHOWING 1-10 OF 10 REFERENCES
Theory of elasticity
This book is designed for use by students and teachers in the field of applied mechanics and mathematics, and for practitioners in civil and mechanical engineering. Since tensor calculus is an
Virtual mass and polarization
In this paper we deal with two classical problems of Potential Theory arising in Hydrodynamics and in the Theory of Electricity, respectively. They are the problems of virtual mass and polarization.
The Theory of Spherical and Ellipsoidal Harmonics
Preface 1. The transformation of Laplaces's equation 2. The solution of Laplace's equation in polar coordinates 3. The Legendres associated functions 4. Spherical harmonics 5. Spherical harmonics of
On axially symmetric flow and the method of generalized electrostatics
Scarborough, 2nd edition, pp. 99-103, the mistake arising from identification of two ^-values in the interval which may be distinct.) Consider the given data / (J) — j for j = 0, 1, • • • , n, for