The non-linear Saint-Venant problem of the torsion, stretching and bending of a naturally twisted rod

✍ Scribed by L.M. Zubov

• Publisher: Elsevier Science
• Year: 2006
• Tongue: English
• Weight: 309 KB
• Volume: 70
• Category: Article
• ISSN: 0021-8928
• DOI: 10.1016/j.jappmathmech.2006.06.016

✦ Synopsis

Problems on large stretching, torsional and bending deformations of a naturally twisted rod, loaded with end forces and moments, are considered from the point of view of the non-linear three-dimensional theory of elasticity. Particular solutions of the equations of elastostatics are found, which are two-parameter families of finite deformations and which possess the property that, for these deformations, the initial system of three-dimensional non-linear equations reduces to a system of equations with two independent variables. The use of these equations enables one to reduce certain Saint-Venant problems for a naturally twisted rod to twodimensional non-linear boundary-value problems for a planar domain in the form of the cross-section of a rod. Different formulations of the two-dimensional boundary-value problem for the cross-section are proposed, which differ in the choice of the unknown functions. A non-linear problem of the torsion and stretching of a circular cylinder with helical anisotropy, which is reduced to ordinary differential equations, is considered as a special case.