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

• Published in: Journal of strain analysis for engineering design 1999-07, Vol.34 (5), p.303-311
• Main Authors: Ritchie, S J K, Leevers, P S
• Format: Article
• Language: English
• Subjects: Axial stress; Crack propagation; Deformation; Elastic beams; Elasticity; Exact sciences and technology; Finite element method; Fracture mechanics (crack, fatigue, damage...); Fracture mechanics, fatigue and cracks; Fundamental areas of phenomenology (including applications); Measurement and testing methods; Measurement methods and techniques in continuum mechanics of solids; Partial differential equations; Physics; Solid mechanics; Static torsion; Structural and continuum mechanics; Warping
• ISSN: 0309-3247; 2041-3130
• DOI: 10.1243/0309324991513641

Abstract The double torsion fracture test has been widely used in the past for measuring resistance to crack growth under static loading and, more recently, under high-loading-rate conditions. Specimen deformation in this test is conventionally analysed on the basis of a one-dimensional torsion equation. Under dynamic conditions, it is imperative to establish an accurate torsion equation which can be used to model the double torsion test. The present paper describes the development, in this context, of a dynamic fourth-order partial differential equation for one-dimensional torsion, based on Barr's equation. The equation obtained in this paper accounts for the axial inertia associated with cross-sectional warping and the axial stresses which arise when warping is constrained. The equation can also accommodate non-linear elasticity. The equation is validated, using Barr's own data, for the torsional resonance problem which he studied and, using finite-element analysis, for a problem of constrained static torsion analysed by Timoshenko.