Saint-Venant problem for solids with helical anisotropy
| Autor: | Natalia V. Kurbatova, Yury A. Ustinov |
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| Rok vydání: | 2015 |
| Předmět: |
Quantitative Biology::Biomolecules
Mathematical analysis Coordinate system General Physics and Astronomy Torsion (mechanics) Tangent Stiffness Geometry 02 engineering and technology 021001 nanoscience & nanotechnology 020303 mechanical engineering & transports 0203 mechanical engineering Mechanics of Materials Ordinary differential equation Pure bending medicine General Materials Science medicine.symptom 0210 nano-technology Anisotropy Stiffness matrix Mathematics |
| Zdroj: | Continuum Mechanics and Thermodynamics. 28:465-476 |
| ISSN: | 1432-0959 0935-1175 |
| DOI: | 10.1007/s00161-015-0445-2 |
| Popis: | We discuss the solution of Saint-Venant’s problem for solids with helical anisotropy. Here the governing relations of the theory of elasticity in terms of displacements were presented using the helical coordinate system. We proposed an approach to construct elementary Saint-Venant solutions using integration of ordinary differential equations with variable coefficients in the case of a circular cylinder with helical anisotropy. Elementary solutions correspond to problems of extension, of torsion, of pure bending and of bending of shear force. The solution of the problem is obtained using small parameter method for small values of twist angle and numerically for arbitrary values. Numeric results correspond to problems of extension–torsion. Dependencies of the stiffness matrix (in dimensionless form) on angle between the tangent to the helical coil and the axis of the cylinder corresponding to stiffness on stretching and torsion are illustrated graphically for different values of material and geometrical parameters. |
| Databáze: | OpenAIRE |
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