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Abstract and Applied Analysis
Volume 2013 (2013), Article ID 702132, 8 pages
Research Article

Conservation Laws of Three-Dimensional Perfect Plasticity Equations under von Mises Yield Criterion

1Siberian State Aerospace University, 31 Krasnoyarsky Rabochy Avenue, Krasnoyarsk 660014, Russia
2Departamento de Matemáticas, CUCEI, Universidad de Guadalajara, Boulevard Marcelino García Barragán 1421, 44430 Guadalajara, JAL, Mexico

Received 4 July 2013; Revised 22 September 2013; Accepted 26 September 2013

Academic Editor: A. F. Cheviakov

Copyright © 2013 S. I. Senashov and A. Yakhno. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


For the first time the conservation laws for von Mises plasticity equations in three dimensions as well as for plane stress equations are given. In the plane case conservation laws are used to construct characteristics for the Cauchy problem. For the system of the plane strain, the conservation laws are used to solve the free boundary problem for any convex smooth contour loaded with constant normal and zero tangential stresses.