JOURNAL BROWSE
Search
Advanced SearchSearch Tips
Axisymmetric bending of a circular plate with stiff edge on a soft FGM layer
facebook(new window)  Pirnt(new window) E-mail(new window) Excel Download
 Title & Authors
Axisymmetric bending of a circular plate with stiff edge on a soft FGM layer
Volkov, Sergey S.; Litvinenko, Alexander N.; Aizikovich, Sergey M.; Wang, Yun-Che; Vasiliev, Andrey S.;
 Abstract
A circular plate with constant thickness, finite radius and stiff edge lying on an elastic halfspace is considered. The half-space consists of a soft functionally graded (FGM) layer with arbitrary varying elastic properties and a homogeneous elastic substrate. The plate bends under the action of arbitrary axisymmetric distributed load and response from the elastic half-space. A semi-analytical solution for the problem effective in whole range of geometric (relative layer thickness) and mechanical (elastic properties of coating and substrate, stiffness of the plate) properties is constructed using the bilateral asymptotic method (Aizikovich et al. 2009). Approximated analytical expressions for the contact stresses and deflections of the plate are provided. Numerical results showing the qualitative dependence of the solution from the initial parameters of the problem are obtained with high precision.
 Keywords
plate bending;circular plate;Kirchhoff plate;axisymmetric problem;functionally graded;soft layer;elastic layer;analytic method;
 Language
English
 Cited by
1.
Lubricated point heavily loaded contacts of functionally graded materials. Part 2. Lubricated contacts, Mathematics and Mechanics of Solids, 2017, 108128651770469  crossref(new windwow)
2.
Plane contact problem on indentation of a flat punch into a transversely-isotropic half-plane with functionally graded transversely-isotropic coating, Zeitschrift für angewandte Mathematik und Physik, 2017, 68, 1  crossref(new windwow)
3.
Axisymmetric indentation of an electroelastic piezoelectric half-space with functionally graded piezoelectric coating by a circular punch, Acta Mechanica, 2017  crossref(new windwow)
 References
1.
Aizikovich, S.M, Alexandrov, V.M. and Trubchik, I.S. (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.M. and Aleksandrov, V.M. (1982), "Properties of compliance functions for layered and continuously nonuniform half-space", Soviet Phys. Dokl., 27(9), 765-767.

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., 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.

5.
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. crossref(new window)

6.
Aleksandrov, V.M. (1973), "On the solution of one class of dual equations", Soviet Phys. Dokl., 18.

7.
Aleksandrov, V.M. and Salamatova, V.Yu. (2009), "Axisymmetric contact problem for an elastic half-space and a circular cover plate", Moscow Univ. Mech. Bull., 65(2), 43-46.

8.
Aleksandrov, V.M. and Solodovnik, M.. (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. crossref(new window)

9.
Aleksandrov, V.M, Vorovich, I.I. and Solodovnik, M.D. (1973), "Effective solution of the problem of cylindrical bending of a plate of finite width on an elastic half-space", Izv. AN SSSR. Mekh. Tverd. Tela, (4), 129-138. (in Russian)

10.
Altenbach, H. and Eremeyev, V.A. (2008), "Direct approach-based analysis of plates composed of functionally graded materials", Arch. App. Mech., 78(10), 775-794. crossref(new window)

11.
Altenbach, H. and Eremeyev, V.A. (2009), "Eigen-vibrations of plates made of functionally graded material", Comput. Mater. Continua, 9(2), 153-178.

12.
Arciniega, R. and Reddy, J. (2007), "Large deformation analysis of functionally graded shells", Int. J. Solid. Struct., 44(6), 2036-2052. crossref(new window)

13.
Arefi, M. and Allam, M.N.M. (2015), "Nonlinear responses of an arbitrary FGP circular plate resting on the Winkler-Pasternak foundation", Smart Struct. Syst., 16(1), 81-100. crossref(new window)

14.
Babaei, H., Mostofi, T.M. and Alitavoli, M. (2015), "Study on the response of circular thin plate under low velocity impact", Geomech. Eng., 9(2), 207-218. crossref(new window)

15.
Bosakov, S.V. (2008), "The solution of the contact problem for a circular plate", J. App. Math. Mech., 72(1), 59-61. crossref(new window)

16.
Gorbunov-Posadov, M.I. (1940), "Calculation of beams and plates on elastic half-space", Prikl. Mat. Mekh., 4(3), 61-80. (in Russian)

17.
Guler, M.A. (2008), "Mechanical modeling of thin films and cover plates bonded to graded substrates", J. Appl. Mech., 75(5), 051105. crossref(new window)

18.
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. crossref(new window)

19.
Kudish, I.I., Volkov, S.S., Vasiliev, A.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.

20.
Liu, T.J., Wang, Y.S. and Zhang, C.Z. (2008), "Axisymmetric frictionless contact of functionally graded materials", Arch. App. Mech., 78, 267-282. crossref(new window)

21.
Pak, R.Y.S., Simmons, B.M. and Ashlock, J.C. (2008), "Tensionless contact of a flexible plate and annulus with a smooth half-space under axisymmetric loads by integral equations", Int. J. Mech. Sci., 50, 1004-1011. crossref(new window)

22.
Selvadurai, A.P.S., Dumont, N.A. and de Oliveira, M.F.F. (2010), "Mindlin's problem for a halfspace indented by a flexible circular plate", Proceedings of 11th Pan-American Congress of Applied Mechanics, Foz do Iguacu, Brazil, January.

23.
Shatskih, L.S. (1972), "On calculation of a plate bending on an elastic layer", Izv. AN SSSR. Mekh. Tverd. Tela, (2), 170-176. (in Russian)

24.
Silva, A.R.D., Silveira, R.A.M. and Goncalves, P.B. (2001), "Numerical methods for analysis of plates on tensionless elastic foundations", Int. J. Solid. Struct., 38(10-13), 2083-2100. crossref(new window)

25.
Tseitlin, A.I. (1969), "Bending of a circular plate lying on a linearly deformable foundation", Izv. AN SSSR. Mekh. Tverd. Tela, (1), 99-112. (in Russian)

26.
Vasiliev, A., Sevostianov, I., Aizikovich, S. and Jeng, Y.R. (2012), "Torsion of a punch attached to ransversely-isotropic half-space with functionally gradient coating", Int. J. Eng. Sci., 61, 24-35. crossref(new window)

27.
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. crossref(new window)

28.
Vasiliev, A.S., Swain, M.V., Aizikovich, S.M. and Sadyrin, E.V. (2015), "Torsion of a circular punch attached to an elastic half-space with a coating with periodically depth-varying elastic properties", Arch. Appl. Mech., DOI 10.1007/s00419-015-1089-1. crossref(new window)

29.
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, 263-273. crossref(new window)

30.
Woodward, B. and Kashtalyan, M. (2011), "Three-dimensional elasticity solution for bending of transversely isotropic functionally graded plates", Eur. J. Mech. A/Solid., 30, 705-718. crossref(new window)

31.
Woodward, B. and Kashtalyan, M. (2012), "Performance of functionally graded plates under localised transverse loading", Comp. Struct., 94, 2254-2262. crossref(new window)