Geodesic
To the calculation of equilibrium parameters and stability of torsion process of circular bars made of weakening material
Journal of Samara State Technical University, Ser. Physical and Mathematical Sciences, no. 2 (2012), pp. 53-64

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The problem of torsion of a bar with circular cross-section is considered. The bar is made of the material with a stress-strain diagram having the falling branch describing the softening state. It is shown that the bar has several possible equilibrium positions during the deformation process. The Newton–Kantorovich method is employed to define the stress-strain state in all equilibriums positions. The definition of stress and strain in both steady and unsteady equilibrium is carried out using the method of simple iterations. It is established that the divergence of simple iterations corresponds to the moment of stability loss.
Mots-clés : torsion
Keywords: hardening, weakening, full diagram of pure shear, nouniqueness of equilibrium positions, Newton–Kantorovich method, method of simple iterations, stability of deformation process. 
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     author = {V. V. Struzhanov and E. A. Bakhareva},
     title = {To the calculation of equilibrium parameters and stability of torsion process of circular bars made of weakening material},
     journal = {Journal of Samara State Technical University, Ser. Physical and Mathematical Sciences},
     pages = {53--64},
     publisher = {mathdoc},
     number = {2},
     year = {2012},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/VSGTU_2012_2_a5/}
}
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V. V. Struzhanov; E. A. Bakhareva. To the calculation of equilibrium parameters and stability of torsion process of circular bars made of weakening material. Journal of Samara State Technical University, Ser. Physical and Mathematical Sciences, no. 2 (2012), pp. 53-64. http://geodesic.mathdoc.fr/item/VSGTU_2012_2_a5/