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

- Journal title : Structural Engineering and Mechanics
- Volume 58, Issue 4, 2016, pp.613-625
- Publisher : Techno-Press
- DOI : 10.12989/sem.2016.58.4.613

Title & Authors

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

Aizikovich, Sergey M.; Mitrin, Boris I.; Seleznev, Nikolai M.; Wang, Yun-Che; Volkov, Sergey S.;

Aizikovich, Sergey M.; Mitrin, Boris I.; Seleznev, Nikolai M.; Wang, Yun-Che; Volkov, Sergey S.;

Abstract

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.

Keywords

bending of a beam;analytic solution;dual integral equation;functionally graded layer;soft layer;elastic half-plane;

Language

English

References

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

21.

Naumenko, K. and Eremeyev, V.A. (2014), "A layer-wise theory for laminated glass and photovoltaic panels", Compos. Struct., 112, 283-291.

22.

Rvachev, V.L. (1958), "On the bending of an infinite beam on an elastic half-space", J. Appl. Math. Mech., 22, 984-988.

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.

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.

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.

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.

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.

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.