DOI QR코드

DOI QR Code

Exact thermoelastoplastic analysis of FGM rotating hollow disks in a linear elastic-fully plastic condition

  • Nadia Alavi (Department of Mechanical Engineering, Yasouj University) ;
  • Mohammad Zamani Nejad (Department of Mechanical Engineering, Yasouj University) ;
  • Amin Hadi (Cellular and Molecular Research Center, Yasuj University of Medical Sciences) ;
  • Anahita Nikeghbalyan (Department of Mechanical Engineering, Yasouj University)
  • Received : 2023.03.15
  • Accepted : 2024.04.03
  • Published : 2024.05.25

Abstract

In the present study, thermoelsatoplastic stresses and displacement for rotating hollow disks made of functionally graded materials (FGMs) has been investigated. The linear elastic-fully plastic condition is considered. The material properties except Poisson's ratio are assumed to vary in the radial direction as a power-law function. The heat conduction equation for the one-dimensional problem in cylindrical coordinates is used to obtain temperature distribution in the disk. The plastic model is based on the Tresca yield criterion and its associated flow rules under the assumption of perfectly plastic material behavior. Exact solutions of field equations for elastic and plastic deformations are obtained. It is shown that the elastoplastic response of the functionally graded (FG) disk is affected notably by the radial variation of material properties. It is also shown that, depending on material properties and disk dimensions, different modes of plastic deformation may occur.

Keywords

References

  1. Akis, T. and Eraslan, A. (2006), "The stress response and onset of yield of rotating FGM hollow shafts", Acta Mechanica. 187(1), 169-187. https://doi.org/10.1007/s00707-006-0374-z.
  2. Akis, T. and Eraslan, A.N. (2007), "Exact solution of rotating FGM shaft problem in the elastoplastic state of stress", Arch. Appl. Mech., 77(10), 745-765. https://doi.org/10.1007/s00419-007-0123-3.
  3. Bhowmick, S., Misra, D. and Saha, K.N. (2008), "Approximate solution of limit angular speed for externally loaded rotating solid disk", Int. J. Mech. Sci., 50(2), 163-174. https://doi.org/10.1016/j.ijmecsci.2007.07.004.
  4. Bose, T., Rattan, M. and Chamoli, N. (2017), "Steady state creep of isotropic rotating composite disc under thermal gradation", Int. J. Appl. Mech., 9(06), 1750077. https://doi.org/10.1142/S1758825117500776.
  5. Callioglu, H., Bektas, N.B. and Sayer, M. (2011), "Stress analysis of functionally graded rotating discs: analytical and numerical solutions", Acta Mech. Sinica. 27(6), 950-955. https://doi.org/10.1007/s10409-011-0499-8.
  6. Dai, T. and Dai, H.-L. (2016), "Thermo-elastic analysis of a functionally graded rotating hollow circular disk with variable thickness and angular speed", Appl. Mathem. Modelling. 40(17-18), 7689-7707. https://doi.org/10.1016/j.apm.2016.03.025.
  7. Ebrahimi, F., Seyfi, A., Nouraei, M. and Haghi, P. (2022), "Influence of magnetic field on the wave propagation response of functionally graded (FG) beam lying on elastic foundation in thermal environment", Waves Random Complex Media. 32(5), 2158-2176. https://doi.org/10.1080/17455030.2020.1847359.
  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. Emadi, M., Nejad, M.Z., Ziaee, S. and Hadi, A. (2021), "Buckling analysis of arbitrary two-directional functionally graded nano-plate 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.
  10. Eraslan, A. and Akis, T. (2006), "On the plane strain and plane stress solutions of functionally graded rotating solid shaft and solid disk problems", Acta Mechanica. 181(1), 43-63. https://doi.org/10.1007/s00707-005-0276-5.
  11. Eraslan, A.N. and Orcan, Y. (2002), "Elastic-plastic deformation of a rotating solid disk of exponentially varying thickness", Mech. Mater., 34(7), 423-432. https://doi.org/10.1016/S0167-6636(02)00117-5.
  12. Eyvazian, A., Zhang, C., Civalek, O ., Khan, A., Sebaey, T.A. and Farouk, N. (2022), "Wave propagation analysis of sandwich FGM nanoplate surrounded by viscoelastic foundation", Arch. Civil Mech. Eng., 22(4), 1-10. https://doi.org/10.1007/s43452-022-00474-w. 
  13. 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.
  14. Ghannad, M., Rahimi, G.H. and Nejad, M.Z. (2013), "Elastic analysis of pressurized thick cylindrical shells with variable thickness made of functionally graded materials", Compos. Part B-Eng., 45(1), 388-396. https://doi.org/10.1016/j.compositesb.2012.09.043.
  15. Ghayesh, M.H. and Farajpour, A. (2019), "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.
  16. Guven, U. (1993), "On the stresses in an elastic-plastic annular disk of variable thickness under external pressure", Int. J. Solids Struct., 30(5), 651-658. https://doi.org/10.1016/0020-7683(93)90027-5.
  17. Hadi, A., Nejad, M.Z. and Hosseini, M. (2018), "Vibrations of three-dimensionally graded nanobeams", Int. J. Eng. Sci., 128, 12-23. https://doi.org/10.1016/j.ijengsci.2018.03.004.
  18. 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.
  19. Horgan, C. and Chan, A. (1999), "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.
  20. Jabbari, M., Nejad, M.Z. and Ghannad, M. (2015), "Thermo-elastic 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.
  21. Jahromi, B.H., Nayeb-Hashemi, H. and Vaziri, A. (2012), "Elasto-plastic stresses in a functionally graded rotating disk", J. Eng. Mater. Technol., 134(2), 021004. https://doi.org/10.1115/1.4006023.
  22. Jankowski, P., Zur, K.K. and Farajpour, A. (2022), "Analytical and meshless DQM approaches to free vibration analysis of symmetric FGM porous nanobeams with piezoelectric effect", Eng. Anal. Bound. Elements. 136, 266-289. https://doi.org/10.1016/j.enganabound.2022.01.007.
  23. Karami, B., Shahsavari, D., Janghorban, M. and Li, L. (2019), "On the resonance of functionally graded nanoplates using bi-Helmholtz nonlocal strain gradient theory", Int. J. Eng. Sci., 144, 103143. https://doi.org/10.1016/j.ijengsci.2019.103143.
  24. 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.
  25. 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.
  26. Kholdi, M., Rahimi, G., Loghman, A., Ashrafi, H. and Arefi, M. (2021), "Analysis of thick-walled spherical shells subjected to various temperature gradients: thermo-elasto-plastic and residual stress studies", Int. J. Appl. Mech., 13(09), 2150105. https://doi.org/10.1142/S1758825121501052.
  27. 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.
  28. Li, L., Li, X. and Hu, Y. (2016), "Free vibration analysis of nonlocal strain gradient beams made of functionally graded material", Int. J. Eng. Sci., 102, 77-92. https://doi.org/10.1016/j.ijengsci.2016.02.010
  29. Mahdavi, E., Ghasemi, A. and Alashti, R.A. (2016), "Elastic-plastic analysis of functionally graded rotating disks with variable thickness and temperature-dependent material properties under mechanical loading and unloading", Aeros. Sci. Technol., 59, 57-68. https://doi.org/10.1016/j.ast.2016.10.011.
  30. Mazarei, Z., Nejad, M.Z. and Hadi, A. (2016), "Thermo-elasto-plastic analysis of thick-walled spherical pressure vessels made of functionally graded materials", Int. J. Appl. Mech., 8(04), 1650054. https://doi.org/10.1142/S175882511650054X.
  31. Mohammadi, M., Hosseini, M., Shishesaz, M., Hadi, A. and Rastgoo, A. (2019), "Primary and secondary resonance analysis of porous functionally graded nanobeam resting on a nonlinear foundation subjected to mechanical and electrical loads", Europ. J. Mech.-A/Solids. 77, 103793. https://doi.org/10.1016/j.euromechsol.2019.05.008.
  32. Movahedfar, V., Kheirikhah, M.M., Mohammadi, Y. and Ebrahimi, F. (2022), "Modified strain gradient theory for nonlinear vibration analysis of functionally graded piezoelectric doubly curved microshells", Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science. 236(8), 4219-4231. https://doi.org/10.1177/09544062211045886.
  33. Najafzadeh, M., Adeli, M.M., Zarezadeh, E. and Hadi, A. (2022), "Torsional vibration of the porous nanotube with an arbitrary cross-section based on couple stress theory under magnetic field", Mech. Based Des. Struct. Machines. 50(2), 1-15. https://doi.org/10.1080/15397734.2020.1733602.
  34. Nejad, M.Z. and Fatehi, P. (2015), "Exact elasto-plastic analysis of rotating thick-walled cylindrical pressure vessels made of functionally graded materials", Int. J. Eng. Sci., 86, 26-43. https://doi.org/10.1016/j.ijengsci.2014.10.002.
  35. Nejad, M.Z. and Hadi, A. (2016), "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.
  36. Nejad, M.Z. and Hadi, A. (2016), "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.
  37. Nejad, M.Z. and Kashkoli, M.D. (2014), "Time-dependent thermo-creep analysis of rotating FGM thick-walled cylindrical pressure vessels under heat flux", Int. J. Eng. Sci., 82, 222-237. https://doi.org/10.1016/j.ijengsci.2014.06.006.
  38. Nejad, M.Z., Alamzadeh, N. and Hadi, A. (2018), "Thermoelastoplastic analysis of FGM rotating thick cylindrical pressure vessels in linear elastic-fully plastic condition", Compos. Part B-Eng., 154, 410-422. https://doi.org/10.1016/j.compositesb.2018.09.022.
  39. Nejad, M.Z., Hadi, A. and Farajpour, A. (2017), "Consistent couple-stress theory for free vibration analysis of Euler-Bernoulli nano-beams made of arbitrary bi-directional functionally graded materials", Struct. Eng. Mech., 63(2), 161-169. https://doi.org/10.12989/sem.2017.63.2.161.
  40. 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.
  41. Nejad, M.Z., Hadi, A., Omidvari, A. and Rastgoo, A. (2018), "Bending analysis of bi-directional functionally graded Euler-Bernoulli nano-beams using integral form of Eringen's nonlocal elasticity theory", Struct. Eng. Mech., 67(4), 417-425. https://doi.org/10.12989/sem.2018.67.4.417. 
  42. 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.
  43. 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.
  44. Nejad, M.Z., Rahimi, G. and Ghannad, M. (2009), "Set of field equations for thick shell of revolution made of functionally graded materials in curvilinear coordinate system", Mechanika. 77(3), 18-26.
  45. Nejad, M.Z., Rastgoo, A. and Hadi, A. (2014), "Effect of exponentially-varying properties on displacements and stresses in pressurized functionally graded thick spherical shells with using iterative technique", J. Solid Mech., 6(4), 366-377.
  46. Nejad, M.Z., Rastgoo, A. and Hadi, A. (2014), "Exact elasto-plastic 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.
  47. Noroozi, R., Barati, A., Kazemi, A., Norouzi, S. and Hadi, A. (2020), "Torsional vibration analysis of bi-directional FG nano-cone with arbitrary cross-section based on nonlocal strain gradient elasticity", Adv. Nano Res., 8(1), 13-24. https://doi.org/10.12989/anr.2020.8.1.013.
  48. Orcan, Y. and Eraslan, A.N. (2002), "Elastic-plastic stresses in linearly hardening rotating solid disks of variable thickness", Mech. Res. Commun., 29(4), 269-281. https://doi.org/10.1016/S0093-6413(02)00261-6.
  49. Park, K.-J. and Kim, Y.-W. (2016), "Vibration characteristics of fluid-conveying FGM cylindrical shells resting on Pasternak elastic foundation with an oblique edge", Thin-Wall. Struc., 106, 407-419. https://doi.org/10.1016/j.tws.2016.05.011.
  50. Peng, X.-L. and Li, X.-F. (2012a), "Effects of gradient on stress distribution in rotating functionally graded solid disks", J. Mech. Sci. Technol., 26(5), 1483-1492. https://doi.org/10.1007/s12206-012-0339-1.
  51. Peng, X.-L. and Li, X.-F. (2012b), "Elastic analysis of rotating functionally graded polar orthotropic disks", Int. J. Mech. Sci., 60(1), 84-91. https://doi.org/10.1016/j.ijmecsci.2012.04.014.
  52. Sofiyev, A. (2018), "Application of the FOSDT to the solution of buckling problem of FGM sandwich conical shells under hydrostatic pressure", Compos. Part B-Eng., 144, 88-98. https://doi.org/10.1016/j.compositesb.2018.01.025.
  53. Sofiyev, A. (2019), "About an approach to the determination of the critical time of viscoelastic functionally graded cylindrical shells", Compos. Part B-Eng., 156, 156-165. https://doi.org/10.1016/j.compositesb.2018.08.073.
  54. Soltani, M., Soltani, A. and Civalek, O. (2022), "Interaction of the lateral buckling strength with the axial load for FG micro-sized I-section beam-columns", Thin-Wall. Struct., 179, 109616. https://doi.org/10.1016/j.tws.2022.109616.
  55. 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.
  56. You, L. and Zhang, J. (1999), "Elastic-plastic stresses in a rotating solid disk", Int. J. Mech. Sci., 41(3), 269-282. https://doi.org/10.1016/S0020-7403(98)00049-6.
  57. You, L., Wang, J. and Tang, B. (2009), "Deformations and stresses in annular disks made of functionally graded materials subjected to internal and/or external pressure", Meccanica. 44(3), 283-292. https://doi.org/10.1007/s11012-008-9174-y.
  58. Zarezadeh, E., Hosseini, V. and Hadi, A. (2020), "Torsional vibration of functionally graded nano-rod under magnetic field supported by a generalized torsional foundation based on nonlocal elasticity theory", Mech. Based Des. Struct. Machines. 48(4), 480-495. https://doi.org/10.1080/15397734.2019.1642766.
  59. Zhang, Y.-W. and She, G.-L. (2022), "Wave propagation and vibration of FG pipes conveying hot fluid", Steel Compos. Struct., 42(3), 397-405. https://doi.org/10.12989/scs.2022.42.3.397.
  60. Zhao, J.-L., Chen, X., She, G.-L., Jing, Y., Bai, R.-Q., Yi, J., Pu, H.-Y. and Luo, J. (2022), "Vibration characteristics of functionally graded carbon nanotube-reinforced composite double-beams in thermal environments", Steel Compos. Struct., 43(6), 797-808. https://doi.org/10.12989/scs.2022.43.6.797.
  61. Zheng, Y., Bahaloo, H., Mousanezhad, D., Mahdi, E., Vaziri, A. and Nayeb-Hashemi, H. (2016), "Stress analysis in functionally graded rotating disks with non-uniform thickness and variable angular velocity", Int. J. Mech. Sci., 119, 283-293. https://doi.org/10.1016/j.ijmecsci.2016.10.018.