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IssuesArchive of Issues2005-5pp.102-106

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B. G. Mironov, "On the statically determinate relations in the general 2D perfect plasticity problem," Mech. Solids. 40 (5), 102-106 (2005)
Year 2005 Volume 40 Number 5 Pages 102-106
Title On the statically determinate relations in the general 2D perfect plasticity problem
Author(s) B. G. Mironov (Cheboksary)
Abstract The relations of the general 2D problem, including the plane and antiplane deformation relations as special cases, are considered in [1] under the full plasticity condition. The limiting states of a perfectly plastic half-space under indentation by a punch were studied in [2, 3] in the framework of the general 2D problem with shear stresses taken into account. The relations of the general 2D problem under the full plasticity condition for nonhomogeneous media were analyzed in [4, 5].

The present paper studies statically determinate relations in the general 2D perfect plasticity problem for the cases in which the limit-state condition does not coincide with the full plasticity condition. For the cases in question, it is shown that the statically determinate relations of the general 2D problem belong to the hyperbolic type. The characteristics of these hyperbolic systems are found.
References
1.  D. D. Ivlev and L. A. Maksimova, "On the properties of the relations of the general 2D perfect plasticity problem," Doklady AN, Vol. 373, No. 1, pp. 39-41, 2000.
2.  D. D. Ivlev, L. A. Maksimova and R. I. Nepershin, "On the indentation of a punch into a perfectly plastic half-space with shear stresses taken into account," Doklady AN, Vol. 379, No. 2, pp. 169-199, 2001.
3.  D. D. Ivlev, L. A. Maksimova and R. I. Nepershin, "On the definition of the velocity field of a perfectly plastic flow for the general plane problem," Doklady AN, Vol. 379, No. 6, pp. 758-763, 2001.
4.  A. V. Gorskii and P. V. Gorskii, "On the stress analysis in a nonhomogeneous perfectly plastic solid," Izv. TulGU. Matematika. Mekhanika. Informatika, Vol. 10, No. 2, pp. 52-69, 2004.
5.  P. V. Gorskii, "On the indentation of a circular punch into a nonhomogeneous rigidly plastic solid," Izv. TulGU. Matematika. Mekhanika. Informatika, Vol. 10, No. 3, pp. 62-75, 2004.
Received 01 June 2005
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