Problem of an equivalent rod in nonlinear theory of springs
A spring with a large number of coils can approximately be considered as a one-dimensional continuum (an equivalent rod), whose particles are the coils of the spring. The problem of an equivalent rod is to construct the equations describing this continuum and to calculate the characteristics of the equivalent rod by means of the coil geometry and the elastic properties of the spring material. The problem of an equivalent rod has been investigated thoroughly in linear theory. In the geometrically nonlinear theory it remains substantially open (only certain exact solutions of problems on the tension, torsion, and bending of springs were known). The problem of an equivalent rod is solved by a variational- asymptotic method.
scientific article; zbMATH DE number 3940809