RESEARCH INTO FUNCTIONAL EQUATIONS ARISING FROM MATHEMATICAL MODELING OF CRITICAL STATES OF HETEROGENEOUS SOFT LAYERS

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Published: Jul 6, 2015
Keywords:
soft layer stress state hypothesis of variables separation systems of nonlinear differential equations functional equations.

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V. L. Dilman
South Ural State University
D. A. Trunova
South Ural State University

Abstract

We obtained the classification of solutions to a functional equation arising from the research into mathematical models of critical states of the plastic layer. The layer is exposed to a tensile stress under conditions of plane deformation. The function of the layer heterogeneity depends presumably on two variables. We demonstrated how the research into the mentioned mathematical models can be reduced to the solution of some nonlinear systems of ordinary differential equations under the conditions of separating the variables for tangent stress and for the heterogeneity function.

Article Details

Issue
Vol. 2 No. 2 (2015): JOURNAL OF COMPUTATIONAL AND ENGINEERING MATHEMATICS
Section
Survey Articles

References

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Dilman V.L., Trunova D.A. The Stress State of a Rectangular Plastic Layer with the Function of Heterogeneity Depending on Two Variables. Yuzhno-Uralskaya Molodezhnaya Shkola po Matematicheskomu Modelirovaniyu, Chelyabinsk, 29-30 Maya 2014. South Ural Youth School on Mathematical Modeling, Chelyabinsk, 29-30 May 2014. Chelyabinsk, Publishing center of SUSU, 2014, pp. 144-151. (in Russian)