Non-uniform and dynamic torsion of elastic beams Part 1: Governing equations and particular solutions
| Autor: | S J K Ritchie, P S Leevers |
|---|---|
| Rok vydání: | 1999 |
| Předmět: |
Partial differential equation
Torsional vibration Differential equation Applied Mathematics Mechanical Engineering Mathematical analysis Torsion (mechanics) Equations of motion Method of undetermined coefficients Classical mechanics Mechanics of Materials Modeling and Simulation Image warping Mathematics Dynamic testing |
| Zdroj: | The Journal of Strain Analysis for Engineering Design. 34:303-311 |
| ISSN: | 2041-3130 0309-3247 |
| DOI: | 10.1243/0309324991513641 |
| Popis: | 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. |
| Databáze: | OpenAIRE |
| Externí odkaz: |
|