Non-uniform and dynamic torsion of elastic beams Part 1: governing equations and particular solutions

The double torsion fracture test has been widely used in the past for measu ring resistance to crack growth under static loading and more recently, und er high-loading-rate conditions. Specimen deformation in this test is conve ntionally analysed on the basis of a one-dimensional torsion equation. Unde r dynamic conditions, it is imperative to establish an accurate torsion equ ation which can be used to model the double torsion test. The present paper describes the development, in this context, of a dynamic fourth-order part ial differential equation for one-dimensional torsion, based on Barr's equa tion. The equation obtained in this paper accounts for the axial inertia as sociated with cross-sectional warping and the axial stresses which arise wh en warping is constrained. The equation can also accommodate non-linear ela sticity. The equation is validated, using Barr's own data, for the torsiona l resonance problem which he studied and, using finite-element analysis, fo r a problem of constrained static torsion analysed by Timoshenko.