The Uniform Flexure of an Incomplete Tore

Abstract

In this paper we discuss the flexure of an incomplete tore in the plane of its circular centre-line. We reduce the problem to the determination of two harmonic functions, subject to boundary conditions on the surface of the tore which involve the first two derivatives of the functions. We point out the relation of this solution to the general solution of three-dimensional elasticity problems. The special case of a narrow rectangular cross-section is solved exactly in Appendix II.