Structural Engineering and Mechanics

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Axisymmetric analysis of a functionally graded layer resting on elastic substrate

  • Turan, Muhittin (Department of Civil Engineering, Karadeniz Technical University) ;
  • Adiyaman, Gokhan (Department of Civil Engineering, Karadeniz Technical University) ;
  • Kahya, Volkan (Department of Civil Engineering, Karadeniz Technical University) ;
  • Birinci, Ahmet (Department of Civil Engineering, Karadeniz Technical University)
  • Received : 2015.10.12
  • Accepted : 2016.02.05
  • Published : 2016.05.10
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Abstract

This study considers a functionally graded (FG) elastic layer resting on homogeneous elastic substrate under axisymmetric static loading. The shear modulus of the FG layer is assumed to vary in an exponential form through the thickness. In solution, the FG layer is approximated into a multilayered medium consisting of thin homogeneous sublayers. Stiffness matrices for a typical homogeneous isotropic elastic layer and a half-space are first obtained by solving the axisymmetric elasticity equations with the aid of Hankel's transform. Global stiffness matrix is, then, assembled by considering the continuity conditions at the interfaces. Numerical results for the displacements and the stresses are obtained and compared with those of the classical elasticity and the finite element solutions. According to the results of the study, the approach employed here is accurate and efficient for elasto-static problems of FGMs.

Keywords

References

  1. Ai, Z.Y. and Cai, J.B. (2015), "Static analysis of Timoshenko beam on elastic multilayered soils by combination of finite element and analytical layer element", Appl. Math. Model., 39, 1875-1888. https://doi.org/10.1016/j.apm.2014.10.008
  2. Ai, Z.Y., Cheng, Y.C. and Zeng, W.Z. (2011), "Analytical layer-element solution to axisymmetric consolidation of multilayered soils", Comput. Geotech., 38, 227-232. https://doi.org/10.1016/j.compgeo.2010.11.011
  3. Ai, Z.Y. and Wang, L.J. (2015), "Axisymmetric thermal consolidation of multilayered porous thermoelastic media due to a heat source", Int. J. Numer. Anal. Meth. Geomech., 39, 1912-1931. https://doi.org/10.1002/nag.2381
  4. Ai, Z.Y. and Zeng, W.Z. (2012), "Analytical layer-element method for non-axisymmetric consolidation of multilayered soils", Int. J. Numer. Meth. Eng., 36, 533-545. https://doi.org/10.1002/nag.1000
  5. ANSYS 15 (2015), Swanson Analysis Systems.
  6. Bahar, L.Y. (1972), "Transfer matrix approach to layered systems", ASCE J. Eng. Mech. Div., 98, 1159-1172.
  7. Barik, S.P., Kanoria, M. and Chaudhuri, P.K. (2009), "Frictionless contact of a functionally graded halfspace and a rigid base with an axially symmetric recess", J. Mech., 25(1), 9-18. https://doi.org/10.1017/S1727719100003555
  8. Bufler, H. (1971), "Theory of elasticity of a multilayered medium", J. Elast., 1, 125-143. https://doi.org/10.1007/BF00046464
  9. Chen, W.T. (1971), "Computation of stresses and displacements in a layered elastic medium", Int. J. Eng. Sci., 9, 775-800. https://doi.org/10.1016/0020-7225(71)90072-3
  10. Choi, H.J. and Thangjitham, S. (1991), "Stress analysis of multilayered anisotropic elastic media", J. Appl. Mech., 58, 382-387. https://doi.org/10.1115/1.2897197
  11. Iyengar, S.R. and Alwar, R.S. (1964), "Stresses in a layered half-plane", ASCE J. Eng. Mech. Div., 90, 79-96.
  12. Oner, E., Yaylaci, M. and Birinci, A. (2015), "Analytical solution of a contact problem and comparison with the results from FEM", Struct. Eng. Mech., 54(4), 607-622. https://doi.org/10.12989/sem.2015.54.4.607
  13. Pagano, N.J. (1970), "Influence of shear coupling in cylindrical bending of anisotropic laminates", J. Compos. Mater., 4, 330-343. https://doi.org/10.1177/002199837000400305
  14. Pindera, M.J. and Lane, M.S. (1993), "Frictionless contact of layered half-planes, Part I: Analysis", J. Appl. Mech., 60, 633-639. https://doi.org/10.1115/1.2900851
  15. Pindera, M.J. and Lane, M.S. (1993), "Frictionless contact of layered half-planes, Part II: Numerical results", J. Appl. Mech., 60, 640-645. https://doi.org/10.1115/1.2900852
  16. Rhimi, M., El-Borgi, S. and Lajnef, N. (2011), "A double receding contact axisymmetric problem between a functionally graded layer and a homogeneous substrate", Mech. Mater., 43(12), 787-798. https://doi.org/10.1016/j.mechmat.2011.08.013
  17. Small, J.C. and Booker, J.R. (1984), "Finite layer analysis of layered elastic materials using a flexibility approach. Part 1-Strip loadings", Int. J. Numer. Meth. Eng., 20, 1025-1037. https://doi.org/10.1002/nme.1620200606
  18. Small, J.C. and Booker, J.R. (1986), "Finite layer analysis of layered elastic materials using a flexibility approach. Part 2-Circular and rectangular loadings", Int. J. Numer. Meth. Eng., 23, 959-978. https://doi.org/10.1002/nme.1620230515
  19. Senjuntichai, T. and Rajapakse, R.K.N.D. (1995), "Exact stiffness method for quasi-statics of a multilayered poroelastic medium", Int. J. Solid. Struct., 32(11), 1535-1553. https://doi.org/10.1016/0020-7683(94)00190-8
  20. Sun, L. and Luo, F. (2008), "Transient wave propagation in multilayered viscoelastic media: theory, numerical computation and validation", ASME J. Appl. Mech., 75, 1-15.
  21. Sun, L., Gu, W. and Luo, F. (2009), "Steady-State wave propagation in multilayered viscoelastic media excited by a moving dynamic distributed load", ASME J. Appl. Mech., 76, 1-15.
  22. Sun, L., Pan, Y. and Gu, W. (2013), "High-order thin layer method for viscoelastic wave propagation in stratified media", Comput. Meth. Appl. Mech. Eng., 257, 65-76. https://doi.org/10.1016/j.cma.2013.01.004
  23. Liu, T.J., Ke, L.L., Wang, Y.S. and Xing, Y.M (2015), "Stress analysis for an elastic semispace with surface and graded layer coatings under induced torsion", Mech. Bas. Des. Struct. Mach., 43(1), 74-94. https://doi.org/10.1080/15397734.2014.928222
  24. Thangjitham, S. and Choi, H.J. (1991), "Thermal stress analysis of a multilayered anisotropic medium", J. Appl. Mech., 58, 1021-1027. https://doi.org/10.1115/1.2897677
  25. Wang, W. and Ishikawa, H. (2001), "A method for linear elasto-static analysis of multi-layered axisymmetrical bodies using Hankel's transform", Comput. Mech., 27, 474-483. https://doi.org/10.1007/s004660100258

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