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Thermoelastic analysis of rotating FGM thick-walled cylindrical pressure vessels under bi-directional thermal loading using disk-form multilayer

  • Received : 2023.01.29
  • Accepted : 2024.03.25
  • Published : 2024.04.25
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Abstract

In this research, a semi-analytical solution is presented for computing mechanical displacements and thermal stresses in rotating thick cylindrical pressure vessels made of functionally graded material (FGM). The modulus of elasticity, linear thermal expansion coefficient, and density of the cylinder are assumed to change along the axial direction as a power-law function. It is also assumed that Poisson's ratio and thermal conductivity are constant. This cylinder was subjected to non-uniform internal pressure and thermal loading. Thermal loading varies in two directions. The governing equations are derived by the first-order shear deformation theory (FSDT). Using the multilayer method, a functionally graded (FG) cylinder with variable thickness is divided into n homogenous disks, and n sets of differential equations are obtained. Applying the boundary conditions and continuity conditions between the layers, the solution of this set of equations is obtained. To the best of the researchers' knowledge, in the literature, there is no study carried out bi-directional thermoelastic analysis of clamped-clamped rotating FGM thick-walled cylindrical pressure vessels under variable pressure in the longitudinal direction.

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References

  1. Akbarzadeh Khorshidi, M. and Soltani, D. (2020), "Analysis of functionally graded thick-walled cylinders with high order shear deformation theories under non-uniform pressure", SN Appl. Sci., 2(8),1-19. https://doi.org/10.1007/s42452-020-3179-0.
  2. Arefi, M. (2015), "Two-dimensional thermoelastic analysis of a functionally graded cylinder for different functionalities by using the higher-order shear deformation theory", J. Appl. Mech. Tech. Phy., 56(3), 494-501. https://doi.org/10.1134/S0021894415030207.
  3. Barati, A., Hadi, A., Nejad, M.Z. and Noroozi, R. (2022), "On vibration of bi-directional functionally graded nanobeams under magnetic field", Mech. Based. Des. Struc., 50(2), 468-485. https://doi.org/10.1080/15397734.2020.1719507.
  4. Chen, Y.Z. (2021), "A novel numerical solution for a functionally graded hollow cylinder with arbitrary elastic property along the radial direction", Int. J. Pres. Ves, Pip., 191(December 2020), 104301. https://doi.org/10.1016/j.ijpvp.2021.104301.
  5. Dai, H.L., Rao, Y.N. and Dai, T. (2016), "A review of recent researches on FGM cylindrical structures under coupled physical interactions, 2000-2015", Compos. Struct., 152, 199-225. https://doi.org/10.1016/j.compstruct.2016.05.042.
  6. Dehghan, M., Nejad, M.Z. and Moosaie, A. (2016), "Thermoelectro-elastic analysis of functionally graded piezoelectric shells of revolution: Governing equations and solutions for some simple cases", Int. J. Eng. Sci., 104, 34-61 https://doi.org/10.1016/j.ijengsci.2016.04.007
  7. Dehshahri, K., Nejad, M.Z., Ziaee, S., Niknejad, A. and Hadi, A. (2020), "Free vibrations analysis of arbitrary three-dimensionally FGM nanoplates", Adv. Nano Res., 8(2), 115-134. https://doi.org/10.12989/anr.2020.8.2.115.
  8. Ebrahimi, T., Nejad, M.Z., Jahankohan, H. and Hadi, A. (2021), "Thermoelastoplastic response of FGM linearly hardening rotating thick cylindrical pressure vessels", Steel. Compos. Struct., 38(2), 189-211. https://doi.org/10.12989/scs.2021.38.2.189.
  9. Eker, M., Yarimpabuc, D., Yildirim, A. and C elebi, K. (2020), "Elastic solutions based on the Mori-Tanaka scheme for pressurized functionally graded cylinder", J. Appl. Math. Comput. Mech., 19(4), 57-68. https://doi.org/10.17512/jamcm.2020.4.05.
  10. Emadi, M., Nejad, M.Z., Ziaee, S. and Hadi, A. (2021), "Buckling analysis of arbitrary two-directional functionally graded nanoplate based on nonlocal elasticity theory using generalized differential quadrature method", Steel. Compos. Struct., 39(5), 565-581. https://doi.org/10.12989/scs.2021.39.5.565.
  11. Evci, C. and Gulgec, M. (2018), "Functionally graded hollow cylinder under pressure and thermal loading: Effect of material parameters on stress and temperature distributions", Int. J. Eng. Sci., 123, 92-108. https://doi.org/10.1016/j.ijengsci.2017.11.019.
  12. Fatehi, P. and Nejad, M. Z. (2014), "Effects of material gradients on onset of yield in FGM rotating thick cylindrical shells", Int. J. Appl. Mech., 6(04), 1450038. https://doi.org/10.1142/S1758825114500380.
  13. Ghannad, M. and Nejad, M.Z. (2010), "Elastic analysis of pressurized thick hollow cylindrical shells with clampedclamped ends", Mechanika, 85(5), 11-18.
  14. Ghannad, M. and Yaghoobi, M.P. (2017), "2D Thermo elastic behavior of an FG cylinder under thermomechanical loads using a first order temperature theory", Int. J. Pres. Ves. Pip., 149, 75-92. https://doi.org/10.1016/j.ijpvp.2016.12.002.
  15. Ghannad, M., Nejad, M.Z. and Rahimi, G.H. (2009), "Elastic solution of axisymmetric thick truncated conical shells based on first-order shear deformation theory", Mechanika, 79(5), 13-20.
  16. Ghannad, M., Nejad, M.Z., Rahimi, G.H. and Sabouri, H. (2012), "Elastic analysis of pressurized thick truncated conical shells made of functionally graded materials", Struct, Eng, Mech., 43(1), 105-126. https://doi.org/10.12989/sem.2012.43.1.105.
  17. Gharibi, M., Nejad, M.Z. and Hadi, A. (2017), "Elastic analysis of functionally graded rotating thick cylindrical pressure vessels with exponentially-varying properties using power series method of Frobenius", J. Comput. Appl. Mech., 48(1), 89-98. https://doi.org/10.22059/JCAMECH.2017.233633.143.
  18. Gharooni, H., Ghannad, M. and Nejad, M.Z. (2016), "Thermoelastic analysis of clamped-clamped thick FGM cylinders by using third-order shear deformation theory", Lat. Am. J. Solids. Struct., 13(4), 750-774. https://doi.org/10.1590/1679-78252254.
  19. Ghayesh, M.H. and Farajpour, A. (2019a), "A review on the mechanics of functionally graded nanoscale and microscale structures", Int. J. Eng. Sci., 137, 8-36. https://doi.org/10.1016/j.ijengsci.2018.12.001.
  20. Ghayesh, M.H. and Farajpour, A. (2019b), "Vibrations of shear deformable FG viscoelastic microbeams", Microsyst. Technol., 25(4), 1387-1400. https://doi.org/10.1007/s00542-018-4184-8.
  21. Hadi, A, Nejad, M.Z. Rastgoo, A. and Hosseini, M. (2018), "Buckling analysis of FGM Euler-Bernoulli nano-beams with 3D-varying properties based on consistent couple-stress theory", Steel. Compos. Struct., 26(6), 663-672. https://doi.org/10.12989/scs.2018.26.6.663 https://doi.org/10.1515/nleng-2020-0013.
  22. Jabbari, M. and Nejad, M.Z. (2018), "Mechanical and thermal stresses in radially functionally graded hollow cylinders with variable thickness due to symmetric loads", Aust. J. Mech. Eng., 18(sup1), S108-21. https://doi.org/10.1080/14484846.2018.1481562.
  23. Jabbari, M., Nejad, M.Z. and Ghannad, M. (2015), "Thermoelastic analysis of axially functionally graded rotating thick cylindrical pressure vessels with variable thickness under mechanical loading", Int. J. Eng. Sci., 96, 1-18. https://doi.org/10.1016/j.ijengsci.2015.07.005.
  24. Jabbari, M., Nejad, M.Z. and Ghannad, M. (2016), "Thermoelastic analysis of axially functionally graded rotating thick truncated conical shells with varying thickness", Compos. Part B: Engineering, 96, 20-34. https://doi.org/10.1016/j.compositesb.2016.04.026.
  25. Jabbari, M., Sohrabpour, S. and Eslami, M.R. (2003), "General solution for mechanical and thermal stresses in a functionally graded hollow cylinder due to nonaxisymmetric steady-state loads", Int. J. Appl. Mech., 70(1), 111-118. https://doi.org/10.1115/1.1509484.
  26. Kashkoli, M.D. and Nejad, M.Z. (2018), "Time-dependent creep analysis and life assessment of 304 L austenitic stainless steel thick pressurized truncated conical shells", Steel. Compos. Struct., 28(3), 349-362. https://doi.org/10.12989/scs.2018.28.3.349.
  27. Kashkoli, M.D., Tahan, K.N. and Nejad, M.Z. (2017), "Time-dependent thermomechanical creep behavior of FGM thick hollow cylindrical shells under non-uniform internal pressure", Int. J. Appl. Mech., 9(06), 1750086. https://doi.org/10.1142/S1758825117500867.
  28. Kashkoli, M.D., Tahan, K.N. and Nejad, M.Z. (2018), "Thermomechanical creep analysis of FGM thick cylindrical pressure vessels with variable thickness", Int. J. Appl. Mech., 10(01), 1850008. https://doi.org/10.1142/S1758825118500084.
  29. Kashkoli, M.D., Tahan, K.N. and Nejad, M.Z. (2019), "Creep damage and life assessment of thick cylindrical pressure vessels with variable thickness made of 304L austenitic stainless steel", Steel. Compos. Struct., 32(6), 701-715. https://doi.org/10.12989/scs.2019.32.6.701.
  30. Khoshgoftar, M.J., Mirzaali, M.J. and Rahimi, G.H. (2015), "Thermoelastic analysis of non-uniform pressurized functionally graded cylinder with variable thickness using first order shear deformation theory (fsdt) and perturbation method", Chin. J. Mech. Eng.-En., 28(6), 1149-1156. https://doi.org/10.3901/CJME.2015.0429.048.
  31. Li, L. and Hu, Y. (2016), "Nonlinear bending and free vibration analyses of nonlocal strain gradient beams made of functionally graded material", Int. J. Eng. Sci., 107, 77-97. https://doi.org/10.1016/j.ijengsci.2016.07.011.
  32. Li, L., Li, X. and Hu, Y. (2018), "Nonlinear bending of a two-dimensionally functionally graded beam", Compos. Struct.,184, 1049-1061. https://doi.org/10.1016/j.compstruct.2017.10.087
  33. Mahapatra, T.R., Kar, V.R., Panda, S.K. and Mehar, K. (2017), "Nonlinear thermoelastic deflection of temperature dependent FGM curved shallow shell under nonlinear thermal loading", J. Therm. Stresses., 40 (9), 1184-1199. https://doi.org/10.1080/01495739.2017.1302788.
  34. Manthena, V.R. and Kedar, G.D. (2018), "Mathematical modeling of thermoelastic state of a functionally graded thermally sensitive thick hollow cylinder with internal heat generation", Int. J. Thermodynamics, 21(4), 202-212. https://doi.org/10.5541/ijot.434180.
  35. Mazarei, Z., Nejad, M.Z. and Hadi, A. (2016), "Thermo-elastoplastic analysis of thick-walled spherical pressure vessels made of functionally graded materials", Int. J. Appl. Mech., 8(4), 1-25. https://doi.org/10.1142/S175882511650054X.
  36. Mohammadi, K., Mahinzare, M., Ghorbani, KH. and Ghadiri, M. (2018), "Cylindrical functionally graded shell model based on the first order shear deformation nonlocal strain gradient elasticity theory", Microsyst. Technol., 24(2), 1133-1146. https://doi.org/10.1007/s00542-017-3476-8.
  37. Najibi, A. and Shojaeefard, M.H. (2016), "Elastic mechanical stress analysis in a 2d-FGM thick finite length hollow cylinder with newly developed material model", Acta. Mech. Solida. Sin., 29(2), 178-191. https://doi.org/10.1016/S0894-9166(16)30106-9.
  38. Nejad M.Z., Abedi, M., Lotfian, MH. and Ghannad, M. (2016), "Exact and numerical elastic analysis for the FGM thick-walled cylindrical pressure vessels with exponentially-varying properties", Arch. Metall. Mater., 61(3), 1303-1308. https://doi.org/10.1515/amm-2016-0267.
  39. Nejad, M.Z. and Hadi, A. (2016-a), "Eringen's non-local elasticity theory for bending analysis of bi-directional functionally graded Euler-Bernoulli nano-beams", Int. J. Eng. Sci., 106, 1-9. https://doi.org/10.1016/j.ijengsci.2016.05.005
  40. Nejad, M.Z. and Hadi, A. (2016-b), "Non-local analysis of free vibration of bi-directional functionally graded Euler-Bernoulli nano-beams", Int. J. Eng. Sci., 105, 1-11 https://doi.org/10.1016/j.ijengsci.2016.04.011.
  41. Nejad, M.Z. and Rahimi, G.H. (2009), "Deformations and stresses in rotating FGM pressurized thick hollow cylinder under thermal load", Sci. Res. Essays., 4(3), 131-140.
  42. Nejad, M.Z. and Rahimi, G.H. (2010), "Elastic analysis of FGM rotating cylindrical pressure vessels", J. Chin. Inst. Eng., 33(4), 525-530. https://doi.org/10.1080/02533839.2010.9671640.
  43. Nejad, M.Z., Hadi, A. and Rastgoo, A. (2016), "Buckling analysis of arbitrary two-directional functionally graded euler-bernoulli nano-beams based on nonlocal elasticity theory", Int. J. Eng. Sci., 103, 1-10. https://doi.org/10.1016/j.ijengsci.2016.03.001.
  44. Nejad, M.Z., Jabbari, M. and Ghannad, M. (2015), "Elastic analysis of FGM rotating thick truncated conical shells with axially-varying properties under non-uniform pressure loading", Compos. Struct., 122, 561-569. https://doi.org/10.1016/j.compstruct.2014.12.028.
  45. Nejad, M.Z., Jabbari, M. and Ghannad, M. (2015), "Elastic analysis of axially functionally graded rotating thick cylinder with variable thickness under non-uniform arbitrarily pressure loading", Int. J. Eng. Sci., 89, 86-99. https://doi.org/10.1016/j.ijengsci.2014.12.004.
  46. Nejad, M.Z., Jabbari, M. and 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, 215-231. https://doi.org/10.1007/s00707-016-1709-z
  47. Nejad, M.Z., Jabbari, M. and Hadi, A. (2017), "A review of functionally graded thick cylindrical and conical shells", J. Comput Appl. Mech., 48(2), 357-370. https://doi.org/10.22059/JCAMECH.2017.247963.220.
  48. Nejad, M.Z., Rastgoo, A. and Hadi, A. (2015), "Exact elastoplastic analysis of rotating disks made of functionally graded materials", Int. J. Eng. Sci., 85, 47-57. https://doi.org/10.1016/j.ijengsci.2014.07.009.
  49. Omidi Bidgoli, M., Loghman, A. and Arefi, M. (2019), "Three-dimensional thermo-elastic analysis of a rotating cylindrical functionally graded shell subjected to mechanical and thermal loads based on the fsdt formulation", J. Appl. Mech. Tech. Phy., 60(5), 899-907. https://doi.org/10.1134/S0021894419050134.
  50. Parhizkar Yaghoobi, M. and Ghannad, M. (2020), "An analytical solution for heat conduction of FGM cylinders with varying thickness subjected to non-uniform heat flux using a first-order temperature theory and perturbation technique", Int. Commun. Heat. Mass., 116, 104684. https://doi.org/10.1016/j.icheatmasstransfer.2020.104684.
  51. Ramezani, F., Nejad, M.Z. and Ghannad, M. (2023), "Thermoelastic analysis of rotating thick-walled cylindrical pressure vessels with linear variable thickness under bidirectional temperature", J. Comput. Appl. Mech., 54(4), 515-532. https://doi.org/10.22059/JCAMECH.2023.365220.876.
  52. Ramezani, F., Nejad, M.Z. and Ghannad, M. (2024), "Bi-Directional Thermo-Elastic Analysis of Pressurized Thick Cylindrical Shell with Nonlinear Variable Thickness", J. Comput. Appl. Mech., 55(1), 125-143. https://doi.org/10.22059/JCAMECH.2023.367944.899.
  53. Reddy, J N. and Chin, C.D. (1998), "Thermomechanical analysis of functionally graded cylinders and plates", J. Therm. Stresses 21(6), 593-626. https://doi.org/10.1080/ 01495739808956165.
  54. Ruhi, M., Angoshtari, A. and Naghdabadi, R. (2005), "Thermoelastic analysis of thick-walled finite-length 119 cylinders of functionally graded materials", J. Therm. Stresses, 28(4), 391-408. https://doi.org/10.1080/ 01495730590916623.
  55. Sachdeva. C. and Padhee, S.S. (2018), "Functionally graded cylinders: asymptotically exact analytical formulations", Appl. Math. Model., 54, 782-802. https://doi.org/10.1016/j.apm.2017.10.019.
  56. Sarathchandra, D.T., Subbu, S.K. and Venkaiah, N. (2018), "Modeling and analysis of functionally graded cylindrical shell", Mater. Today., Proceedings 5(2), 8587-8595. https://doi.org/10.1016/j.matpr.2017.11.556.
  57. Seddighi, H., Ghannad, M., Loghman, A. and Nejad, M.Z. (2024), "Thermoelastic analysis of variable thickness truncated conical shell subjected to thermomechanical load with internal heat generation using perturbation technique", Mech. Based Des. Struc., 1-31. https://doi.org/10.1080/15397734.2024.2315162.
  58. Sharma, D. and Kaur, R. (2020), "Thermoelastic analysis of FGM hollow cylinder for variable parameters and temperature distributions using fem", Nonlinear Eng., 9(1), 256-264. https://doi.org/10.1515/nleng-2020-0013
  59. She, G.L., Yuan, F.G. and Ren, Y.R. (2017), "Nonlinear analysis of bending, thermal buckling and post-buckling for functionally graded tubes by using a refined beam theory", Compos. Struct., 165, 74-82. https://doi.org/10.1016/j.compstruct.2017.01.013.
  60. Sofiyev, A.H. and Dikmen, F. (2021), "Buckling analysis of functionally graded shells under mixed boundary conditions subjected to uniform lateral pressure", J Appl. Comput. Mech., 7(1), 345-354. https://doi.org/10.22055/JACM.2020.35564.2684.
  61. Sofiyev, A.H. and Fantuzzi, N. (2022), "Analytical solution of stability and vibration problem of clamped cylindrical shells containing functionally graded layers within shear deformation theory", Alex. Eng. J., 64(2), 141-154. https://doi.org/10.1016/j.aej.2022.08.024.
  62. Taghizadeh, T. and Nejad, M.Z. (2021), "Thermo-elastic creep analysis and life assessment of rotating thick pressurized cylindrical shells using third-order shear deformation theory", J. Comput. Appl. Mech., 52(3), 366-393. https://doi.org/10.22059/JCAMECH.2021.306967.546.
  63. Taghizadeh, T., Nejad, M.Z. and Kashkoli, M.D. (2019), "Thermo-elastic creep analysis and life assessment of thick truncated conical shells with variable thickness", Int. J. Appl. Mech., 11(09), 1950086. https://doi.org/10.1142/S1758825119500868.
  64. Vaziri, S.A., Ghannad, M. and Beg, O.A. (2019), "Exact thermoelastic analysis of a thick cylindrical functionally graded material shell under unsteady heating using first order shear deformation theory" Heat Transfer - Asian Res., 48(5), 1737-1760. https://doi.org/10.1002/htj.21455.