Stressed state of two-layer strip when interacting with rigid base

Cover Page

Abstract


Relevance. In the calculation of multilayer bases, when the material of one or several layers has a pronounced anisotropy, the nature of the distribution of displacements and stresses depends on the direction of the anisotropy axes in each layer. Therefore, it is necessary to have an evaluation of the influence of this factor in the design and analysis of the operation of multilayer media. The aim of the work - to research the stress state in a strip composed of two anisotropic plane-parallel layers with different physical characteristics, lying without friction on a rigid base. Methods. The integration of the equations of the plane problem of the theory of elasticity of an anisotropic body is carried out by the symbolic method in combination with the method of initial functions. The initial functions on the contact line of the strip and the base are determined from the conditions of tight adhesion between the layers, the conditions of tight contact and the absence of friction between the strip and the base, the nature of the load applied to the upper plane of the strip. After transformations, the functions of displacements and stresses in each layer are written through the normal surface load in the form of improper integrals. Results. Plots of changes in stresses in the strip from the values of the characteristics of anisotropic materials, layer thicknesses are given. The maximum stresses on the interface line of the layers and on the line of contact with the base, depending on the direction of the anisotropy axes in each layer, are presented in the tables and shown in graphs. The effect of the elastic modules of materials on the nature of the stress distribution in a strip composed of two isotropic materials is estimated.


About the authors

Julia M. Buldakova

Volga State University of Technology

Author for correspondence.
Email: KudryavcevSG@volgatech.net
SPIN-code: 5677-6126
3 Lenina Sq, Yoshkar-Ola, 424000, Mari El Republic, Russian Federation

senior lecturer of the Department of Resistance of Materials and Applied Mechanics

Sergey G. Kudryavtsev

Volga State University of Technology

Email: KudryavcevSG@volgatech.net
SPIN-code: 9756-6211
3 Lenina Sq, Yoshkar-Ola, 424000, Mari El Republic, Russian Federation

Associate Professor of the Department of Resistance of Materials and Applied Mechanics, Candidate of Technical Sciences

References

  1. Shehter O.Y. Raschet beskonechnoi fundamentalnoi pliti, lejaschei na uprugom osnovanii konechnoi i beskonechnoi moschnosti i nagrujennoi sosredotochennoi siloi [Calculation of an infinite fundamental plate lying on an elastic base of finite and infinite power and loaded with a concentrated force]. Sbornik trudov Nauchno-issledovatelskogo sektora Tresta glubinnih rabot [Collected Works of the Research Sector of the Trust of Deep Works]. Moscow, Leningrad: Stroiizdat Narkomstroya Publ.; 1939. p. 133–139. (In Russ.)
  2. Rappoport R.M. Zadacha Bussineska dlya sloistogo uprugogo poluprostranstva [The Boussinesq problem for a layered elastic half-space]. Trudi Leningradskogo politehnicheskogo instituta [Proceedings of the Leningrad Polytechnic Institute]. 1948;(5):3–18. (In Russ.)
  3. Kogan B.I. Napryajeniya i deformacii mnogosloinih pokritii [Stresses and deformations of multilayer coatings]. Trudi HADI [Proceedings of HADI]. 1953;(14):33–46. (In Russ.)
  4. Vlasov V.Z., Leontev N.N. Balki, pliti i obolochki na uprugom osnovanii [Beams, plates and shells on an elastic base]. Moscow: Gos. izd. fiz.-mat. lit-ry. Publ.; 1960. (In Russ.)
  5. Uflyand Ya.S. Integralnie preobrazovaniya v zadachah teorii uprugosti [Integrated transformations in tasks of the theory of elasticity]. Moscow, Leningrad: AN SSSR Publ.; 1963. (In Russ.)
  6. Garg N.R., Singh S.J. Residual response of a multilayered half- space to two-dimensional surface loads. Bull. Ind. Soc. Earthq. Tech. 1985;(22):39–52.
  7. Pan E. Static Green’s functions in multilayered half-spaces. Applied Mathematical Modelling. 1997;21(8):509–521.
  8. Torskaya E.V., Lushnikov N.A., Lushnikov P.A. Analysis of stress-strain state of multi-layer pavements. Journal of Friction and Wear. 2008;29(2):204–210. (In Russ.)
  9. Shirunov G.N. Method of initial functions in model of compression linearly deformable layered foundation under normal local load. Magazine of civil engineering. 2015;1(53): 91–96. (In Russ).
  10. Tarntira K., Senjuntichai T., Keawsawasvong S. Multilayered Elastic Medium under Axisymmetric Loading and Surface Energy. Advanced Materials and Engineering Materials VIII. 2019;814:320–326.
  11. Lehnickii S.G. Uprugoe ravnovesie transversalno-izotropnogo sloya i tolstoi pliti [The elastic equilibrium of a transversely isotropic layer and a thick plate]. Prikladnaya mehanika i matematika [Journal of Applied Mathematics and Mechanics]. 1962;26(4):687–696. (In Russ.)
  12. Pan E. Static response of transversely isotropic and layered half-space to general surface loads. Phys. Earth Planet Inter. 1989;(54):353–363.
  13. Garg N.R., Sharma R.K. Displacements and stresses at any point of a transversely isotropic multilayered half-space due to strip loading. Indian. J. Pure Appl. Math. 1991; 22(10):859–877.
  14. Garg N.R., Singh S.J., Manchanda S. Static deformation of an orthotropic multilayered elastic half-space by two-dimensional surface loads. Proceedings of the Indian Academy of Sciences – Earth and Planetary Sciences. 1991;100(2):205–218.
  15. Krupoderov A.V. Fundamental solutions for transversely isotropic multilayered. News of the Tula State University. Sciences of Earth. 2011;(1):137–146. (In Russ.)
  16. Kudryavtsev S.G., Buldakova J.M. Interaction of anisotropic band and rigid base. Structural Mechanics of Engineering Constructions and Buildings. 2012;(4):29–35. (In Russ.)
  17. Ai Z.Y., Cang N.R., Han J. Analytical layer-element solutions for a multi-layered transversely isotropic elastic medium subjected to axisymmetric loading. Journal of Zhejiang University Science A. 2012;13(1):9–17.
  18. Lin C. Green’s function for a transversely isotropic multilayered half-space: an application of the precise integration method. Acta Mechanica. 2015;226(11):3881–3904.
  19. Kudryavtsev S.G., Buldakova J.M. Stress-strain state of two-layered anisotropic foundation. Structural Mechanics of Engineering Constructions and Buildings. 2015;(5):9–20. (In Russ.)
  20. Liu J., Zhang P., Lin G., Li C., Lu S. Elastostatic solutions of a multilayered transversely isotropic piezoelectric system under axisymmetric loading. Acta Mechanica. 2017;228(1):107–128.
  21. Lehnickii S.G. Teoriya uprugosti anizotropnogo tela [Theory of elasticity of an anisotropic body]. Moscow: Nauka Publ.; 1977. (In Russ.)

Statistics

Views

Abstract - 77

PDF (Russian) - 33

Cited-By


PlumX

Dimensions


Copyright (c) 2020 Buldakova J.M., Kudryavtsev S.G.

Creative Commons License
This work is licensed under a Creative Commons Attribution 4.0 International License.

This website uses cookies

You consent to our cookies if you continue to use our website.

About Cookies