Short Communication
Mechanics of Solids

On the solution of one problem of deformation of rod systems that does not satisfy the Hadamard conditions by the simple iteration method

V. V. Struzhanov, A. V. Korkin

Institute of Engineering Science, Urals Branch, Russian Academy of Sciences, Ekaterinburg, 620049, Russian Federation

Abstract: A rod system under the action of a quasi-statically increasing tensile tension is considered. The load is carried out according to soft and hard schemes. One of the rods of the system has the property of deformation softening, that is, its tension diagram has a branch falling to zero. As a result, the equilibrium equations do not satisfy the Hadamard conditions. The system has several equilibrium positions, including unstable ones. The application of the simple iterations method is shown to determine the parameters of all possible equilibrium positions and their stability when solving these equations that do not satisfy the Hadamard conditions.

Keywords: equilibrium equations, rod system, Hadamard conditions, simple iterations, stability of equilibria, parameters of equilibrium positions.

UDC: 539.3

MSC: 74C10

Received: May 25, 2020
Revised: September 10, 2020
Accepted: September 14, 2020
First online: September 30, 2020

DOI: 10.14498/vsgtu1787

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