Analysis of plastic torsion using physical analogies

Abstract

calculating the torsional deformations of a complex section is a rather complex task even in the elastic stages. Additional difficulties arise when it is necessary to calculate rods of complex cross-section at the stage of plasticity. To at least partially get rid of these difficulties, this work uses a method widely known as the method of analogies. We specifically use a branch of this method that we call physical analogies. In particular, the so-called membrane analogy and hydrodynamic analogy. The problem of torsion of a homogeneous shaft is discussed. The latter is based on the phenomenon that the process of torsion of a solid rod (no matter what cross-section it has) is mathematically expressed  by the same formulas as the flow of an ideal fluid.