Structural Engineering and Mechanics

  • 제58권4호
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  • Pages.613-625
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  • 2016
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  • 1225-4568(pISSN)
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  • 1598-6217(eISSN)
테크노프레스 (Techno-Press)
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DOI QR코드

DOI QR Code

Influence of a soft FGM interlayer on contact stresses under a beam on an elastic foundation

  • Aizikovich, Sergey M. (Research and Education Center "Materials", Don State Technical University) ;
  • Mitrin, Boris I. (Research and Education Center "Materials", Don State Technical University) ;
  • Seleznev, Nikolai M. (Research and Education Center "Materials", Don State Technical University) ;
  • Wang, Yun-Che (Department of Civil Engineering, National Cheng Kung University) ;
  • Volkov, Sergey S. (Research Institute for Mechanics, Lobachevsky State University of Nizhni Novgorod)
  • 투고 : 2015.10.11
  • 심사 : 2016.01.29
  • 발행 : 2016.05.25
⟨ 이전 논문 다음 논문 ⟩

초록

Contact interaction of a beam (flexible element) with an elastic half-plane is considered, when a soft inhomogeneous (functionally graded) interlayer is present between them. The beam is bent under the action of a distributed load applied to the surface and a reaction of the elastic interlayer and the half-space. Solution of the contact problem is obtained for different values of thickness and parameters of inhomogeneity of the layer. The interlayer is assumed to be significantly softer than the underlying half-plane; case of 100 times difference in Young's moduli is considered as an example. The influence of the interlayer thickness and gradient of elastic properties on the distribution of the contact stresses under the beam is studied.

키워드

과제정보

연구 과제 주관 기관 : National Science Council of Taiwan (NSC)

참고문헌

  1. Aizikovich, S., Alexandrov, V. and Trubchik, I. (2009), "Bilateral asymptotic solution of one class of dual integral equations of the static contact problems for the foundations inhomogeneous in depth", Operator Theory: Adv. Appl., 191, 3-17.
  2. Aizikovich, S., Vasiliev, A., Sevostianov, I., Trubchik, I., Evich, L. and Ambalova, E. (2011), "Analytical solution for the bending of a plate on a functionally graded layer of complex structure", Eds. H. Altenbach, V.A. Eremeyev, Shell-like Structures: Non-classical Theories and Applications, Springer-Verlag, Heidelberg, Germany.
  3. Aizikovich, S.M. and Aleksandrov, V.M. (1984) "Axisymmetric problem of indentation of a circular die into an elastic half-space that is nonuniform with respect to depth", Mech. Solid., 19(2), 73-82.
  4. Aizikovich, S.M. and Vasiliev, A.S. (2013), "A bilateral asymptotic method of solving the integral equation of the contact problem of the torsion of an elastic half-space inhomogeneous in depth", J. Appl. Math. Mech., 77(1), 91-97. https://doi.org/10.1016/j.jappmathmech.2013.04.011
  5. Aleksandrov, V.M. (1973), "On the solution of one class of dual equations", Soviet Phys. Dokl., 18, 351.
  6. Aleksandrov, V.M. and Salamatova, V.Y. (2009), "Axisymmetric contact problem for an elastic half-space and a circular cover plate", Moscow University Mechanics Bulletin, 65(2), 43-46.
  7. Aleksandrov, V.M. and Solodovnik, M.D. (1974), "Asymptotic problem of the cylindrical bending of a plate of finite breadth in an elastic half-space", Soviet Appl. Mech., 10(7), 749-754. https://doi.org/10.1007/BF00886304
  8. Altenbach, H., Eremeyev, V.A. and Naumenko, K. (2015), "On the use of the first order shear deformation plate theory for the analysis of three-layer plates with thin soft core layer", ZAMM Z. Ang. Math. Mech., 95(10), 1004-1011. https://doi.org/10.1002/zamm.201500069
  9. Biot, M. (1937), "Bending of an infinite beam on an elastic foundation", J. Appl. Mech., ASME, 4, A1-A7.
  10. Bosakov, S.V. (2008), "The solution of the contact problem for a circular plate", J. Appl. Math. Mech., 72(1), 59-61. https://doi.org/10.1016/j.jappmathmech.2008.03.014
  11. Galin, L.A. (1961), Contact Problems in the Theory of Elasticity, North Carolina State College, Raleigh, N.C., USA.
  12. Guler, M.A., Gulver, Y.F. and Nart, E. (2012), "Contact analysis of thin films bonded to graded coatings", Int. J. Mech. Sci., 55(1), 50-64. https://doi.org/10.1016/j.ijmecsci.2011.12.003
  13. Ke, L.L., Yang, J., Kitipornchai, S. and Wang, Y.S. (2008), "Frictionless contact analysis of a functionally graded piezoelectric layered half-plane", Smart Mater. Struct., 17(2), 025003. https://doi.org/10.1088/0964-1726/17/2/025003
  14. Kim, N.I. (2009), "Series solutions for spatially coupled buckling anlaysis of thin-walled Timoshenko curved beam on elastic foundation", Struct. Eng. Mech., 33(4), 447-484. https://doi.org/10.12989/sem.2009.33.4.447
  15. Krenev, L., Aizikovich, S., Tokovyy, Y.V. and Wang, Y.C. (2015), "Axisymmetric problem on the indentation of a hot circular punch into an arbitrarily nonhomogeneous half-space", Int. J. Solid. Struct., 59, 18-28. https://doi.org/10.1016/j.ijsolstr.2014.12.017
  16. Kudish, I.I., Vasiliev, A.S., Volkov, S.S. and Aizikovich, S.M. (2016), "Some criteria for coating effectiveness in heavily loaded line EHL contacts. Part 1. dry contacts", J. Trib., ASME, 138(2), 021504.
  17. Liu, T.J., Wang, Y.S. and Xing, Y.M. (2012), "The axisymmetric partial slip contact problem of a graded coating", Meccanica, 47(7), 1673-1693. https://doi.org/10.1007/s11012-012-9547-0
  18. Ma, J., Ke, L.L. and Wang, Y.S. (2015), "Sliding frictional contact of functionally graded magneto- electroelastic materials under a conducting flat punch", J. Appl. Mech., 82, 011009. https://doi.org/10.1115/1.4029090
  19. Mao, J.J., Ke, L.L. and Wang, Y.S. (2014), "Thermoelastic contact instability of a functionally graded layer and a homogeneous half-plane", Int. J. Solid. Struct., 51, 3962-3972. https://doi.org/10.1016/j.ijsolstr.2014.07.019
  20. Mao, J.J., Ke, L.L. and Wang, Y.S. (2015), "Thermoelastic instability of a functionally graded layer and a homogeneous layer", Int. J. Mech. Sci., 99, 218-227. https://doi.org/10.1016/j.ijmecsci.2015.05.018
  21. Naumenko, K. and Eremeyev, V.A. (2014), "A layer-wise theory for laminated glass and photovoltaic panels", Compos. Struct., 112, 283-291. https://doi.org/10.1016/j.compstruct.2014.02.009
  22. Rvachev, V.L. (1958), "On the bending of an infinite beam on an elastic half-space", J. Appl. Math. Mech., 22, 984-988. https://doi.org/10.1016/0021-8928(58)90136-9
  23. Selvadurai, A.P.S. (1979), Elastic Analysis of Soil-Foundation Interaction, Elsevier, Amsterdam, The Netherlands.
  24. Selvadurai, A.P.S. (1984), "The flexure of an infinite strip of finite width embedded in an isotropic elastic medium of infinite extent", Int. J. Numer. Anal. Meth. Geomech., 8, 157-166. https://doi.org/10.1002/nag.1610080205
  25. Sneddon, I.N. (1951), Fourier Transforms, McGraw-Hill, New York, NY, USA.
  26. Tokovyy, Y. and Ma, C.C. (2015), "Analytical solutions to the axisymmetric elasticity and thermoelasticity problems for an arbitrarily inhomogeneous layer", Int. J. Eng. Sci., 92, 1-17. https://doi.org/10.1016/j.ijengsci.2015.03.003
  27. Tullini, N., Tralli, A. and Baraldi D. (2013), "Stability of slender beams and frames resting on 2D elastic half-space", Arch. Appl. Mech., 83, 467-482. https://doi.org/10.1007/s00419-012-0694-5
  28. Vasiliev, A.S., Volkov, S.S. and Aizikovich, S.M. (2016), "Normal point force and point electric charge in a piezoelectric transversely isotropic functionally graded half-space", Acta Mech., 227(1), 263-273. https://doi.org/10.1007/s00707-015-1414-3
  29. Vasiliev, A.S., Volkov, S.S., Aizikovich, S.M. and Jeng, Y.R. (2014), "Axisymmetric contact problems of the theory of elasticity for inhomogeneous layers", ZAMM Z. Ang. Math. Mech., 94(9), 705-712. https://doi.org/10.1002/zamm.201300067
  30. Vesic, A. (1961), "Bending of beams resting on isotropic elastic solid", J. Eng. Mech. Div., ASCE, 87(2), 35-54.
  31. Volkov, S.S., Aizikovich, S.M., Wang, Y.S. and Fedotov, I. (2013), "Analytical solution of axisymmetric contact problem about indentation of a circular indenter with flat base into the soft functional-gradient layer", Acta Mech. Sin., 29(2), 196-201. https://doi.org/10.1007/s10409-013-0022-5
  32. Vorovich, I.I. and Ustinov, I.A. (1959), "Pressure of a die on an elastic layer of finite thickness", J. Appl. Math. Mech., 23, 637-650. https://doi.org/10.1016/0021-8928(59)90158-3
  33. Wang, Y., Tham, L. and Cheung, Y. (2005), "Beams and plates on elastic foundations: a review", Prog. Struct. Eng. Mater., 7, 174-182. https://doi.org/10.1002/pse.202

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