Thermo-mechanical behavior of a functionally graded hollow cylinder with an elliptic hole

  • Javad Jafari FesharakiEmail author
  • Mehran Roghani
Technical Paper


In this paper, the behavior of functionally graded material hollow cylinders with an elliptic hole under thermal and mechanical loads is investigated. The problem is considered as plane strain condition, and to obtain the governing equations and boundary condition for this complex geometry, an elliptic cylindrical coordinate is used. The material properties are considered to vary along the elliptic cylindrical direction with power-law function except for the Poisson’s ratio. To solve the two coupled differential equations, differential quadrature method is used. For solving the governing equations, two different boundary conditions are considered for thermal and mechanical loads. The results show that unconventional shape for a hole in the cylinder can affect the results expected such as stresses or displacements, and this information about thermo-mechanical loads can be used for designing the advanced sensors. Also with considering special material index, the stress and displacement along the cylinder can be controlled. The presented results in this paper are verified with those reported in the previous publication.


Thermo-mechanic Functionally graded material DQM Cylinder with elliptic hole 



  1. 1.
    Hosseini-Hashemi S, Derakhshani M, Fadaee M (2013) An accurate mathematical study on the free vibration of stepped thickness circular/annular Mindlin functionally graded plates. Appl Math Model 37(6):4147–4164. MathSciNetCrossRefzbMATHGoogle Scholar
  2. 2.
    Alashti RA, Khorsand M, Tarahhomi MH (2012) Asymmetric thermo-elastic analysis of long cylindrical shells of functionally graded materials by differential quadrature method. Proc Inst Mech Eng Part C J Mech Eng Sci 226(5):1133–1147. CrossRefGoogle Scholar
  3. 3.
    Heydarpour Y, Malekzadeh P, Golbahar Haghighi MR, Vaghefi M (2012) Thermoelastic analysis of rotating laminated functionally graded cylindrical shells using layerwise differential quadrature method. Acta Mech 223(1):81–93. CrossRefzbMATHGoogle Scholar
  4. 4.
    Malekzadeh P, Ghaedsharaf M (2014) Three-dimensional thermoelastic analysis of finite length laminated cylindrical panels with functionally graded layers. Meccanica 49(4):887–906. MathSciNetCrossRefzbMATHGoogle Scholar
  5. 5.
    Rajasekaran S (2013) Differential transformation and differential quadrature methods for centrifugally stiffened axially functionally graded tapered beams. Int J Mech Sci 74:15–31. CrossRefzbMATHGoogle Scholar
  6. 6.
    Zhang J-H, Li G-Z, Li S-R, Ma Y-B (2015) DQM-based thermal stresses analysis of a functionally graded cylindrical shell under thermal shock. J Therm Stress 38(9):959–982. CrossRefGoogle Scholar
  7. 7.
    Ghorbanpour Arani A, Jafari Fesharaki J, Mohammadimehr M, Golabi S (2010) Electro-magneto-thermo-mechanical behaviors of a radially polarized FGPM thick hollow sphere. J Solid Mech 2(4):305–315Google Scholar
  8. 8.
    Zamani Nejad M, Jabbari M, Ghannad M (2017) A general disk form formulation for thermo-elastic analysis of functionally graded thick shells of revolution with arbitrary curvature and variable thickness. Acta Mech 228(1):215–231. MathSciNetCrossRefzbMATHGoogle Scholar
  9. 9.
    Zidi M, Tounsi A, Houari MSA, Adda Bedia EA, Anwar Bég O (2014) Bending analysis of FGM plates under hygro-thermo-mechanical loading using a four variable refined plate theory. Aerosp Sci Technol 34:24–34. CrossRefGoogle Scholar
  10. 10.
    Akavci SS (2016) Mechanical behavior of functionally graded sandwich plates on elastic foundation. Compos B Eng 96:136–152. CrossRefGoogle Scholar
  11. 11.
    Tung HV, Duc ND (2014) Nonlinear response of shear deformable FGM curved panels resting on elastic foundations and subjected to mechanical and thermal loading conditions. Appl Math Model 38(11):2848–2866. MathSciNetCrossRefzbMATHGoogle Scholar
  12. 12.
    Eskandari H (2016) Stress intensity factor of semi-elliptical surface crack in a thermo-mechanically loaded cylinder with hoop wrapped FGM layer. J Braz Soc Mech Sci Eng 38(8):2563–2570. CrossRefGoogle Scholar
  13. 13.
    Fesharaki JJ, Loghman A, Yazdipoor M, Golabi S (2014) Semi-analytical solution of time-dependent thermomechanical creep behavior of FGM hollow spheres. Mech Time-Depend Mater 18(1):41–53. CrossRefGoogle Scholar
  14. 14.
    Fesharaki JJ, Si Golabi (2016) A novel method to specify pattern recognition of actuators for stress reduction based on particle swarm optimization method. Smart Struct Syst 17(5):725–742CrossRefGoogle Scholar
  15. 15.
    Hosseini M, Dini A, Eftekhari M (2017) Strain gradient effects on the thermoelastic analysis of a functionally graded micro-rotating cylinder using generalized differential quadrature method. Acta Mech 228(5):1563–1580. MathSciNetCrossRefzbMATHGoogle Scholar
  16. 16.
    Alibeigloo A (2017) Thermo elasticity solution of functionally graded, solid, circular, and annular plates integrated with piezoelectric layers using the differential quadrature method. Mech Adv Mater Struct. CrossRefGoogle Scholar
  17. 17.
    Alibeigloo A (2016) Thermo elasticity solution of sandwich circular plate with functionally graded core using generalized differential quadrature method. Compos Struct 136:229–240. CrossRefGoogle Scholar
  18. 18.
    Karami B, Janghorban M, Tounsi A (2018) Variational approach for wave dispersion in anisotropic doubly-curved nanoshells based on a new nonlocal strain gradient higher order shell theory. Thin-Walled Struct 129:251–264. CrossRefGoogle Scholar
  19. 19.
    Atrian A, Jafari Fesharaki J, Nourbakhsh SH (2015) Thermo-electromechanical behavior of functionally graded piezoelectric hollow cylinder under non-axisymmetric loads. Appl Math Mech 36(7):939–954. MathSciNetCrossRefzbMATHGoogle Scholar
  20. 20.
    Sobhani Aragh B, Yas MH (2010) Three-dimensional analysis of thermal stresses in four-parameter continuous grading fiber reinforced cylindrical panels. Int J Mech Sci 52(8):1047–1063. CrossRefGoogle Scholar
  21. 21.
    Karami G, Malekzadeh P (2002) Static and stability analyses of arbitrary straight-sided quadrilateral thin plates by DQM. Int J Solids Struct 39(19):4927–4947. CrossRefzbMATHGoogle Scholar
  22. 22.
    Alinaghizadeh F, Shariati M (2015) Static analysis of variable thickness two-directional functionally graded annular sector plates fully or partially resting on elastic foundations by the GDQ method. J Braz Soc Mech Sci Eng 37(6):1819–1838. CrossRefGoogle Scholar
  23. 23.
    Malekzadeh P, Safaeian Hamzehkolaei N (2016) Temperature-dependent discrete layer-differential quadrature bending analysis of the multi-layered functionally graded annular plates rested on a two-parameter elastic foundation. Mech Adv Mater Struct 23(1):43–58. CrossRefGoogle Scholar
  24. 24.
    Mehditabar A, Rahimi GH, Ansari Sadrabadi S (2017) Three-dimensional magneto-thermo-elastic analysis of functionally graded cylindrical shell. Appl Math Mech 38(4):479–494. MathSciNetCrossRefzbMATHGoogle Scholar
  25. 25.
    Alashti RA, Khorsand M (2012) Three-dimensional nonlinear thermo-elastic analysis of functionally graded cylindrical shells with piezoelectric layers by differential quadrature method. Acta Mech 223(12):2565–2590. MathSciNetCrossRefzbMATHGoogle Scholar
  26. 26.
    Adineh M, Kadkhodayan M (2017) Three-dimensional thermo-elastic analysis and dynamic response of a multi-directional functionally graded skew plate on elastic foundation. Compos B Eng 125:227–240. CrossRefGoogle Scholar
  27. 27.
    Jafari Fesharaki J, Jafari Fesharaki V, Yazdipoor M, Razavian B (2012) Two-dimensional solution for electro-mechanical behavior of functionally graded piezoelectric hollow cylinder. Appl Math Model 36(11):5521–5533. MathSciNetCrossRefzbMATHGoogle Scholar
  28. 28.
    Franco Correia VM, Aguilar Madeira JF, Araújo AL, Mota Soares CM (2018) Multiobjective optimization of ceramic-metal functionally graded plates using a higher order model. Compos Struct 183:146–160. CrossRefGoogle Scholar
  29. 29.
    Setoodeh AR, Shojaee M, Malekzadeh P (2018) Application of transformed differential quadrature to free vibration analysis of FG-CNTRC quadrilateral spherical panel with piezoelectric layers. Comput Methods Appl Mech Eng 335:510–537. MathSciNetCrossRefGoogle Scholar
  30. 30.
    He M-X, Sun J-Q (2018) Multi-objective structural-acoustic optimization of beams made of functionally graded materials. Compos Struct 185:221–228. CrossRefGoogle Scholar
  31. 31.
    Jamshidi M, Arghavani J (2018) Optimal material tailoring of functionally graded porous beams for buckling and free vibration behaviors. Mech Res Commun 88:19–24. CrossRefGoogle Scholar
  32. 32.
    Meziane MAA, Abdelaziz HH, Tounsi A (2014) An efficient and simple refined theory for buckling and free vibration of exponentially graded sandwich plates under various boundary conditions. J Sandwich Struct Mater 16(3):293–318. CrossRefGoogle Scholar
  33. 33.
    Hussein OS, Mulani SB (2018) Optimization of in-plane functionally graded panels for buckling strength: unstiffened, stiffened panels, and panels with cutouts. Thin-Walled Struct 122:173–181. CrossRefGoogle Scholar
  34. 34.
    Boussaa D (2009) Optimization of temperature-dependent functionally graded material bodies. Comput Methods Appl Mech Eng 198(37):2827–2838. MathSciNetCrossRefzbMATHGoogle Scholar
  35. 35.
    Shu C (2000) Differential quadrature and its application in engineering. Springer, LondonCrossRefGoogle Scholar
  36. 36.
    Malik M, Bert CW (1994) Differential quadrature solutions for steady-state incompressible and compressible lubrication problems. J Tribol 116(2):296–302. CrossRefGoogle Scholar
  37. 37.
    Horgan CO, Chan AM (1999) The pressurized hollow cylinder or disk problem for functionally graded isotropic linearly elastic materials. J Elast 55(1):43–59. MathSciNetCrossRefzbMATHGoogle Scholar
  38. 38.
    Heinbockel JH (2001) Introduction to tensor calculus and continuum mechanics. Trafford Publishing. ISBN-13: 978-1553691334Google Scholar

Copyright information

© The Brazilian Society of Mechanical Sciences and Engineering 2019

Authors and Affiliations

  1. 1.Department of Mechanical Engineering, Najafabad BranchIslamic Azad UniversityNajafabadIran

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