On the history of the two works of Kolosov and Muskhelishvili

The report presents a comparative analysis of the application of methods of the theory of functions of a complex variable to solve the plane problem of elasticity theory, which was developed by G.V. Kolosov and N.I. Muskhelishvili. In contrast to the widespread view that these approaches are completely equivalent, we shall show that Kolosov's approach is more general. It proved by the use of a closed solution of the problem of the extension of a plane with a periodic system of sections, for which, until recently, a method of complex variable was considered inapplicable. The urgency of a closed solution of the periodic problem of elasticity illustrated by an example of engineering problem of the alignment of a turbo-generator rotor stiffness by cutting it in the periodic system of cross-sections.