This article is cited in 4 papers

Mathematical modeling of the stress state of a transverse plastic layer in a round rod

T. V. Eroshkina, V. L. Dil'man

Chair of Higher Mathematics, Southern Ural State University, Chelyabinsk, Russia

Abstract: We construct mathematical models of the plastic deformation of a continuous round rod containing a transverse (less strong) inhomogeneous layer under an axial load. We study the obtained models by analytical and numerical methods. We thoroughly study the local strengthening of such layers by involving the base material of the rod in the plastic deformation process. We obtain explicit formulas for the critical stress states in the layer and the critical axial load on the rod.

Keywords: less strong layer, plastic deformation, local strengthening, system of hyperbolic partial differential equations.

UDC: 517.958+539.4

Received: 08.09.2010

 English version: Russian Mathematics (Izvestiya VUZ. Matematika), 2011, 55:11, 9–17

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