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CLASSIFICATION OF CRITICAL STATES OF HETEROGENEOUS PLASTIC LAYER BASED ON THE STUDY OF A FUNCTIONAL EQUATION

Annotation

The boundary value problem for a system of nonlinear partial differential equations modeling the stress state of the heterogeneous plastic layer is studied. The layer is under a tensile load in a plane strain conditions. Assuming the separation of variables for the tangential stress, the problem is reduced to a system of nonlinear ordinary differential equations. The reduction is based on the obtained in the research complete classification of solutions to some purely functional equation.

Keywords

heterogeneous plastic layer; stress state; the hypothesis of separation of variables; the system of nonlinear partial differential equations; functional equation

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UDC

517.958

Pages

1129-1132

References

1. Dil'man V.L., Eroshkina T.V. Matematicheskoe modelirovanie kriticheskikh sostoyaniy myagkikh prosloek v neodnorodnykh soedineniyakh. Chelyabinsk: Izdat. tsentr YuUrGU, 2011. 276 s. 2. Dil'man V.L., Ostsemin A.A. Napryazhennoe sostoyanie i staticheskaya prochnost' plastichnoy prosloyki pri ploskoy deformatsii // Problemy mashinostroeniya i nadezhnosti mashin. 2005. № 4. S. 38-48. 3. Dil'man V.L. O napryazhenno-deformirovannom sostoyanii pri rastyazhenii plasticheskogo sloya s dvumya osyami simmetrii // Izv. RAN. MTT. 2001. № 6. S. 115-124. 4. Dil'man V.L., Nosacheva A.I. Matematicheskoe modelirovanie kriticheskikh sostoyaniy plasticheskogo sloya // Vestnik Tambovskogo universiteta. Seriya Estestvennye i tekhnicheskie nauki. Tambov, 2013. T. 18. Vyp. 5. S. 2502-2504. 5. Dil'man V.L. Napryazhennoe sostoyanie i prochnost' neodnorodnoy plasticheskoy polosy s defektom v bolee prochnoy chasti // Izv. RAN. MTT. 2010. № 2. S. 89-102.

Received

2015-05-25

Section of issue

Scientific articles

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