Smart Structures and Systems

Techno-Press (테크노프레스)
권호 표지
DOI QR코드

DOI QR Code

Transfer matrix method for solution of FGMs thick-walled cylinder with arbitrary inhomogeneous elastic response

  • Chen, Y.Z. (Division of Engineering Mechanics, Jiangsu University)
  • Received : 2017.05.08
  • Accepted : 2018.03.19
  • Published : 2018.04.25
⟨ Previous Next ⟩

Abstract

This paper presents a numerical solution for the thick cylinders made of functionally graded materials (FGMs) with a constant Poisson's ratio and an arbitrary Young's modulus. We define two fundamental solutions which are derived from an ordinary differential equation under two particular initial boundary conditions. In addition, for the single layer case, we can define the transfer matrix N. The matrix gives a relation between the values of stress and displacement at the interior and exterior points. By using the assumed boundary condition and the transfer matrix, we can obtain the final solution. The transfer matrix method also provides an effective way for the solution of multiply layered cylinder. Finally, a lot of numerical examples are present.

Keywords

References

  1. Asemi, K., Salehi, M. and Akhlaghi, M. (2011), "Elastic solution of a two-dimensional functionally graded thick truncated cone with finite length under hydrostatic combined loads", Acta Mech., 217(1-2), 119-134. https://doi.org/10.1007/s00707-010-0380-z
  2. Chen, Y.Z. (2015), "A novel solution for thick-walled cylinders made of functionally graded materials", Smart Struct. Syst., 15(6), 1503-1520. https://doi.org/10.12989/sss.2015.15.6.1503
  3. Chen, Y.Z. (2017), "Numerical solution for multiple confocal elliptic dissimilar cylinders", Smart Struct. Syst., 19(2), 203-211. https://doi.org/10.12989/sss.2017.19.2.203
  4. Chen, Y.Z. and Lin, X.Y. (2008), "Elastic analysis for thick cylinders and spherical pressure vessels made of functionally graded materials", Comput. Mater. Sci., 44(2), 581-587. https://doi.org/10.1016/j.commatsci.2008.04.018
  5. Dryden, J. and Jayaraman, K. (2006), "Effect of inhomogeneity on the stress in pipes", J. Elasticity, 83(2), 179-189. https://doi.org/10.1007/s10659-005-9043-z
  6. Eslami, M.R., Babaei, M.H. and Poultangari, R. (2005), "Thermal and mechanical stresses in a functionally graded thick sphere", Int. J. Pres. Ves. Pip., 82(7), 522-527. https://doi.org/10.1016/j.ijpvp.2005.01.002
  7. Hildebrand, F.B. (1974), Introduction to Numerical Analysis (McGraw-Hill, New York)
  8. Horgan, C.O. and Chan, A.M. (1999a), "The pressurized hollow cylinder or disk problem for functionally graded isotropic linearly elastic materials", J. Elasticity, 55(1), 43-59. https://doi.org/10.1023/A:1007625401963
  9. Horgan, C.O. and Chan, A.M. (1999b), "The stress response of functionally graded isotropic linearly elastic rotating disks", J. Elasticity, 55(3), 219-230. https://doi.org/10.1023/A:1007644331856
  10. Kiani, K. (2016), "Stress analysis of thermally affected rotating nanoshafts with varying material properties", Acta Mech. Sinica, 32(5), 813-827.
  11. Li, X.F. and Peng, X.L. (2009), "A pressurized functionally graded hollow cylinder with arbitrarily varying material properties", J. Elasticity, 96(1), 81-95. https://doi.org/10.1007/s10659-009-9199-z
  12. Muskhelishvili, N.I. (1963), Some Basic Problems of the Mathematical Theory of Elasticity, Noordhoff, Groningen.
  13. Nie, G.J. and Batra, R.C. (2010), "Exact solutions and material tailoring for functionally graded hollow circular cylinders", J Elasticity, 99(2), 179-201. https://doi.org/10.1007/s10659-009-9239-8
  14. Nie, G.J. and Batra, R. C. (2013), "Optimum Young's modulus of a homogeneous cylinder energetically equivalent to a functionally graded cylinder", J. Elasticity, 110(1), 95-110. https://doi.org/10.1007/s10659-012-9383-4
  15. Sadeghia, H., Baghani, M. and Naghdabadi, R. (2012), "Strain gradient elasticity solution for functionally graded micro-cylinders", Int. Eng. Sci., 50(1), 22-30. https://doi.org/10.1016/j.ijengsci.2011.09.006
  16. Shi, Z.F., Zhang, T.T. and Xiang, H.J. (2007), "Exact solutions of heterogeneous elastic hollow cylinders", Comput. Struct., 79(1), 140-147. https://doi.org/10.1016/j.compstruct.2005.11.058
  17. Timoshenko, S.P. and Goodier, J.N. (1970), Theory of Elasticity (McGraw-Hill, New York).
  18. Tutuncu, N. (2007), "Stresses in thick-walled FGM cylinders with exponentially-varying properties", Eng. Struct., 29(9), 2032-2035. https://doi.org/10.1016/j.engstruct.2006.12.003
  19. Tutuncu, N. and Temel, B. (2009), "A novel approach to stress analysis of pressurized FGM cylinders, disks and spheres", Comp. Struct., 91(3), 385-390. https://doi.org/10.1016/j.compstruct.2009.06.009
  20. Xin, L.B., Dui, G.S., Yang, S.Y. and Zhang, J.M. (2014), "An elasticity solution for functionally graded thick-walled tube subjected to internal pressure", Int. J. Mech. Sci., 89, 344-349. https://doi.org/10.1016/j.ijmecsci.2014.08.028
  21. You, L.H., Zhang, L.L. and You, X.Y. (2005), "Elastic analysis of internally pressurized thick-walled spherical pressure vessels of functionally graded materials", Int. J. Pres. Ves. Pip., 82(5), 347-354. https://doi.org/10.1016/j.ijpvp.2004.11.001
  22. Zenkour, A.M., Elsibai, K.A. and Mashat, D.S. (2008), "Elastic and viscoelastic solutions to rotating functionally graded hollow and solid cylinders", Appl. Math. Mech., 29(12), 1601-1616. https://doi.org/10.1007/s10483-008-1208-x
  23. Zhang, X. and Hasebe, N. (1999), "Elasticity solution for a radially nonhomogeneous hollow circular cylinder", J. Appl. Mech., 66(3), 598-606. https://doi.org/10.1115/1.2791477