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

Geodesic

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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

Journal of Samara State Technical University, Ser. Physical and Mathematical Sciences, Tome 24 (2020) no. 3, pp. 595-603.

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Résumé

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, simple iterations, stability of equilibria, parameters of equilibrium positions.
Mots-clés : Hadamard conditions

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V. V. Struzhanov; A. V. Korkin. On the solution of one problem of deformation of rod systems that does not satisfy the Hadamard conditions by the simple iteration method. Journal of Samara State Technical University, Ser. Physical and Mathematical Sciences, Tome 24 (2020) no. 3, pp. 595-603. http://geodesic.mathdoc.fr/item/VSGTU_2020_24_3_a9/

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