Structural Engineering and Mechanics

Techno-Press (테크노프레스)
권호 표지
DOI QR코드

DOI QR Code

A unified method for stresses in FGM sphere with exponentially-varying properties

  • Celebi, Kerimcan (Department of Mechanical Engineering, Adana Science and Technology University) ;
  • Yarimpabuc, Durmus (Department of Mathematics, Osmaniye Korkut Ata University) ;
  • Keles, Ibrahim (Department of Mechanical Engineering, Ondokuz Mayis University)
  • Received : 2015.06.29
  • Accepted : 2016.01.11
  • Published : 2016.03.10
⟨ Previous Next ⟩

Abstract

Using the Complementary Functions Method (CFM), a general solution for the one-dimensional steady-state thermal and mechanical stresses in a hollow thick sphere made of functionally graded material (FGM) is presented. The mechanical properties are assumed to obey the exponential variations in the radial direction, and the Poisson's ratio is assumed to be constant, with general thermal and mechanical boundary conditions on the inside and outside surfaces of the sphere. In the present paper, a semi-analytical iterative technique, one of the most efficient unified method, is employed to solve the heat conduction equation and the Navier equation. For different values of inhomogeneity constant, distributions of radial displacement, radial stress, circumferential stress, and effective stress, as a function of radial direction, are obtained. Various material models from the literature are used and corresponding temperature distributions and stress distributions are computed. Verification of the proposed method is done using benchmark solutions available in the literature for some special cases and virtually exact results are obtained.

Keywords

References

  1. Agarwal, R.P. (1982), "On the method of complementary functions for nonlinear boundary-value problems", J. Optim. Theory Appl., 36(1), 139-144. https://doi.org/10.1007/BF00934344
  2. Aktas, Z. (1972), Numerical Solutions of Two-Point Boundary Value Problems, METU, Dept of Computer Eng, Ankara, Turkey.
  3. Alavi, F., Karimi, D. and Bagri, A. (2008), "An investigation on thermoelastic behavior of functionally graded thick spherical vessels under combined thermal and mechanical loads", J. Ach. Mater. Manuf. Eng., 31, 422-428.
  4. Atefi, G. and Moghimi, M.(2006), "A temperature fourier series solution for a hollow sphere", J. Heat Trans., 128, 963-968. https://doi.org/10.1115/1.2241914
  5. Bagri, A. and Eslami, M.R. (2007), "A unified generalized thermoelasticity; solution for cylinders and spheres", Int. J. Mech. Sci., 49, 1325-1335. https://doi.org/10.1016/j.ijmecsci.2007.04.004
  6. Bayat, Y., Ghannad, M. andTorabi, H. (2012), "Analytical and numerical analysis for the FGM thick sphere under combined pressure and temperature loading", Arch. Appl. Mech., 82, 229-242. https://doi.org/10.1007/s00419-011-0552-x
  7. Boroujerdy, S. and Eslami, M.R. (2013), "Thermal buckling of piezo-FGM shallow shells", Meccanica, 48, 887-899. https://doi.org/10.1007/s11012-012-9642-2
  8. Calim, F.F. (2009), "Free and forced vibrations of non-uniform composite beams", Compos. Struct., 88, 413-423. https://doi.org/10.1016/j.compstruct.2008.05.001
  9. Calim, F.F. and Akkurt, F.G. (2011), "Static and free vibration analysis of straight and circular beams on elastic foundation", Mech. Res. Commun., 38(2), 89-94. https://doi.org/10.1016/j.mechrescom.2011.01.003
  10. Dai, H.L. and Rao, Y.N. (2011), "Investigation on electromagnetothermoelastic interaction of functionally graded piezoelectric hollow spheres", Struc. Eng. Mech., 40(1), 49-64. https://doi.org/10.12989/sem.2011.40.1.049
  11. Ding, H.J., Wang, H.M. and Chen, W.Q. (2002), "Analytical thermo-elastodynamic solutions for a nonhomogeneous transversely isotropic hollow sphere", Arch. Appl. Mech., 72, 545-553. https://doi.org/10.1007/s00419-002-0225-x
  12. Eslami, M.R., Babaei, M.H. and Poultangari, R. (2005), "Thermal and mechanical stresses in a functionally graded thick sphere", Int. J. Press. Ves. Pip., 82, 522-527. https://doi.org/10.1016/j.ijpvp.2005.01.002
  13. Guven, U. and Baykara, C. (2001), "On stress distributions in functionally graded isotropic spheres subjected to internal pressure", Mech. Res. Commun., 28, 277-281. https://doi.org/10.1016/S0093-6413(01)00174-4
  14. Jabbari, M., Dehbani, H. and Eslami, M.R. (2010), "An exact solution for classic coupled thermoelasticity in spherical coordinates", J. Pres. Ves. Tech., 132, 1-11.
  15. Lutz, M.P. and Zimmerman, R.W. (1996), "Thermal stresses and effective thermal expansion coefficient of a functionally graded sphere", J. Therm. Stress., 19, 39-54. https://doi.org/10.1080/01495739608946159
  16. Nejad, M.Z., Abedi, M., Lotfian, M.H. and Ghannad, M. (2012), "An exact solution for stresses and displacements of pressurized FGM thick-walled spherical shells with exponential-varying properties", J. Mech. Sci. Technol., 26, 4081-4087. https://doi.org/10.1007/s12206-012-0908-3
  17. Obata, Y. and Noda, N. (1994), "Steady thermal stress in a hollow circular cylinder and a hollow sphere of a functionally gradient materials", J. Therm. Stress., 14, 471-487.
  18. Poultangari, R., Jabbari, M. and Eslami, M.R. (2008), "Functionally graded hollow spheres under nonaxisymmetric thermo-mechanical loads", Int. J. Press. Ves. Pip., 85, 295-305. https://doi.org/10.1016/j.ijpvp.2008.01.002
  19. Roberts, S.M. and Shipman, J.S. (1979), "Fundamental matrix and two-point boundary-value problems", J. Optim. Theory Appl., 28(1), 77-78. https://doi.org/10.1007/BF00933601
  20. Tanigawa, Y. and Takeuti, Y. (1982), "Coupled thermal stress problem in a hollow sphere under partial heating", Int. J. Eng. Sci., 20, 41-48. https://doi.org/10.1016/0020-7225(82)90070-2
  21. Temel, B., Yildirim, S. and Tutuncu, N. (2014), "Elastic and viscoelastic response of heterogeneous annular structures under arbitrary transient pressure", Int. J. Mech. Sci., 89, 78-83. https://doi.org/10.1016/j.ijmecsci.2014.08.021
  22. Tutuncu, N. and Temel, B. (2009), "A novel approach to stress analysis of pressurized FGM cylinders, disks and spheres", Compos. Struct., 91(3), 385-390. https://doi.org/10.1016/j.compstruct.2009.06.009
  23. Tutuncu, N. and Temel, B. (2013), "An efficient unified method for thermoelastic analysis of functionally graded rotating disks of variable thickness", Mech. Adv. Mater. Struct., 30(1), 38-46.
  24. Wang, H.M., Ding, H.J. and Chen, W.Q. (2003), "Theoretical solution of a spherically isotropic hollow sphere for dynamic thermoelastic problems", J. Zhejiang Univ. Sci., 4, 8-12. https://doi.org/10.1631/jzus.2003.0008
  25. Yildirim, V. (1997), "Free vibration analysis of non-cylindrical coil springs by combined use of the transfer matrix and the complementary functions methods", Commun. Numer. Meth. Eng., 13, 487-494. https://doi.org/10.1002/(SICI)1099-0887(199706)13:6<487::AID-CNM77>3.0.CO;2-X
  26. You, L.H., Zhang, J.J. and You, X.Y. (2004), "Elastic analysis of internally pressurized thick-walled spherical pressure vessels of functionally graded materials", Int. J. Press. Ves. Pip., 82, 347-354.

Cited by

  1. Transient analysis of axially functionally graded Timoshenko beams with variable cross-section vol.98, 2016, https://doi.org/10.1016/j.compositesb.2016.05.040
  2. Dynamic response of curved Timoshenko beams resting on viscoelastic foundation vol.59, pp.4, 2016, https://doi.org/10.12989/sem.2016.59.4.761
  3. A four variable refined nth-order shear deformation theory for mechanical and thermal buckling analysis of functionally graded plates vol.13, pp.3, 2016, https://doi.org/10.12989/gae.2017.13.3.385
  4. A new and simple HSDT for thermal stability analysis of FG sandwich plates vol.25, pp.2, 2016, https://doi.org/10.12989/scs.2017.25.2.157
  5. A novel simple two-unknown hyperbolic shear deformation theory for functionally graded beams vol.64, pp.2, 2016, https://doi.org/10.12989/sem.2017.64.2.145
  6. Free vibration of functionally graded plates resting on elastic foundations based on quasi-3D hybrid-type higher order shear deformation theory vol.20, pp.4, 2017, https://doi.org/10.12989/sss.2017.20.4.509
  7. An efficient and simple four variable refined plate theory for buckling analysis of functionally graded plates vol.25, pp.3, 2016, https://doi.org/10.12989/scs.2017.25.3.257
  8. A novel and simple higher order shear deformation theory for stability and vibration of functionally graded sandwich plate vol.25, pp.4, 2017, https://doi.org/10.12989/scs.2017.25.4.389
  9. A new quasi-3D HSDT for buckling and vibration of FG plate vol.64, pp.6, 2016, https://doi.org/10.12989/sem.2017.64.6.737
  10. An efficient hyperbolic shear deformation theory for bending, buckling and free vibration of FGM sandwich plates with various boundary conditions vol.25, pp.6, 2016, https://doi.org/10.12989/scs.2017.25.6.693
  11. A novel four-unknown quasi-3D shear deformation theory for functionally graded plates vol.27, pp.5, 2016, https://doi.org/10.12989/scs.2018.27.5.599
  12. Exact Thermomechanical Analysis of Functionally Graded (FG) Thick-Walled Spheres vol.22, pp.4, 2018, https://doi.org/10.2478/mme-2018-0093
  13. A Practical Jointed Approach to Thermal Stress Analysis of FGM Disc vol.12, pp.3, 2016, https://doi.org/10.24107/ijeas.809300
  14. Thermal stress analysis of functionally graded solid and hollow thick-walled structures with heat generation vol.38, pp.1, 2016, https://doi.org/10.1108/ec-02-2020-0120