On the problems of tension, twisting and bending of ropes. (English) Zbl 1411.74014

Summary: The paper gives a brief description of the construction of a new theory of the rope, based on the spectral theory operators. The ropes are modeled as a cylinder with a helical anisotropy, in which the filler is eliminated by means of the limiting transition in the material characteristics obtained on the basis of the averaging theory. Based on the solutions of the Saint-Venant problems of tension-torsion and bending of ropes, new formulas for calculating the elements of the stiffness matrix are obtained. The calculation results are presented graphically.


74B05 Classical linear elasticity
74F05 Thermal effects in solid mechanics