Methods of analysing ropes. The extension–torsion method

Two new approaches are used for calculating the stress–strain state of a rope and its stiffnesses. The first approach relies on the theory of fibrous composites and Saint-Venant's solution for a cylinder with helical anisotropy. The second approach is based on the solution by the finite element method of the three-dimensional problem of elasticity theory for a solid inhomogeneous cylinder formed by a finite number of elastic fibres arranged in helical lines and connected by a weak filler (in the sense that its Young's modulus is several orders of magnitude less than the Young's modulus of the fibre). The behaviour of the stiffness when the modulus of elasticity of the filler tends to zero is analysed, and the results of the limiting transition are discussed. The numerical results obtained are compared with calculations by other well-known applied theories.