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

V. L. Dilman, D. A. Trunova

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.

Keywords


soft layer, stress state, hypothesis of variables separation, systems of nonlinear differential equations, functional equations.

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References


Dilman V.L., Eroshkina T.V. Mathematical Modelling of Critical States of the Soft Layers in Heterogeneous Joints. Chelyabinsk, Publishing Center of South Ural State University, 2011. (in Russian)

DilmanV.L. Mathematical Models of the Stress State of Heterogeneous Thin-walled Cylindrical Shells. Chelyabinsk, Publishing Center of South Ural State University, 2007. (in Russian)

Dilman V.L., Ostsemin A.A. Stress State and Static Strength of the Plastic Interlayer in Plane Deformation. Journal of Machinery Manufacture and Reliability, 2005, no. 4, pp. 38-48. (in Russian)

Dilman V.L., Ostsemin A.A. On the Stress-deformed State at the Tension of the Plastic Layer with Two Axes of Symmetry. Mechanics of Solids, 2001, no. 6, pp. 115-124 (in Russian)

Dilman V.L., Nosachova A.A. Mathematical Simulation of Critical States of the Plastic Layer. Tambov University Reports. Series: Natural and Technical Sciences, 2013, vol. 18, issue 5-2, pp. 2502-2504. (in Russian)

DilmanV.L. The Stress State of the Plastic Layer with Variable Strength Broadwise. Mechanics of Solids, 2000, no. 1, pp. 141-148. (in Russian)

Dilman V.L. Research of the Mathematical Models of the Stress Condition of the Thin-walled Heterogeneous Cylindrical shells Based on Analytical Methods. Bulletin of the South Ural State University. Series "Mathematical Modelling, Programming & Computer Software", 2009, issue 3, no. 17(150), pp. 36-58. (in Russian)

Dilman V.L., Trunova D.A. Mathematical Modeling of the Critical Sates of a Heterogeneous Plastic Rectangle at Plane Deformation. Bulletin of the Magnitogorsk State University. Mathematics, 2012, issue 14, pp. 46-55. (in Russian)

Dilman V.L., Trunova D.A. Mathematical Modelling of the Critical States of the Heterogeneous Layer Under Different Conditions of Heterogeneity. Molodoy Issledovatel' - Materialy 66-y Studencheskoy Nauchnoy Konferentsii. Young Researcher - Proceedings of 66-th Student Scientific Conference. Chelyabinsk, Publishing center of SUSU, 2013, vol. 2, pp. 166-171. (in Russian)

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)


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