Torsion of a Shaft with a Toroidal Cavity
- 1 October 1954
- journal article
- conference paper
- Published by AIP Publishing in Journal of Applied Physics
- Vol. 25 (10) , 1321-1328
- https://doi.org/10.1063/1.1721553
Abstract
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 case n=3 then yields the solution to the classical flow problem, and n=5 gives the solution to the torsion problem under consideration.This publication has 7 references indexed in Scilit:
- Axisymmetric Flow of an Ideal Incompressible Fluid About a Solid TorusJournal of Applied Mechanics, 1953
- Generalized axially symmetric potential theoryBulletin of the American Mathematical Society, 1953
- Capacity, virtual mass, and generalized symmetrizationPacific Journal of Mathematics, 1952
- On cracks and dislocations in shafts under torsionQuarterly of Applied Mathematics, 1952
- On axially symmetric flow and the method of generalized electrostaticsQuarterly of Applied Mathematics, 1952
- Virtual mass and polarizationTransactions of the American Mathematical Society, 1949
- Discontinuous integrals and generalized potential theoryTransactions of the American Mathematical Society, 1948