Steel and Composite Structures

  • 제38권2호
  • /
  • Pages.189-211
  • /
  • 2021
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  • 1229-9367(pISSN)
  • /
  • 1598-6233(eISSN)
테크노프레스 (Techno-Press)
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DOI QR코드

DOI QR Code

Thermoelastoplastic response of FGM linearly hardening rotating thick cylindrical pressure vessels

  • Ebrahimi, Tayebeh (Department of Mechanical Engineering, Yasouj University) ;
  • Nejad, Mohammad Zamani (Department of Mechanical Engineering, Yasouj University) ;
  • Jahankohan, Hamid (Department of Mechanical Engineering, Yasouj University) ;
  • Hadi, Amin (Cellular and Molecular Research Center, School of Medicine, Yasuj University of Medical Sciences)
  • 투고 : 2020.05.16
  • 심사 : 2020.12.21
  • 발행 : 2021.01.25
⟨ 이전 논문 다음 논문 ⟩

초록

An analytical solution is presented to analyze the thermoelastoplastic response of a rotating thick-walled cylindrical pressure vessel made of functionally graded material (FGM). The analysis is based on Tresca's yield condition, its associated flow rule and linear strain hardening material behaviour. The uncoupled theory of thermoelasticity is used, and the plane strain condition is assumed. The material properties except for Poisson's ratio, are assumed to vary nonlinearly in the radial direction. Elastic, partially plastic, fully plastic, and residual stress states are investigated. The heat conduction equation for the one-dimensional problem in cylindrical coordinates is used to obtain temperature distribution in the vessel. It is assumed that the inner surface is exposed to an airstream and that the outer surface is exposed to a uniform heat flux. Tresca's yield criterion and its associated flow rule are used to formulate six different plastic regions for a linearly hardening condition. All these stages are studied in detail. It is shown that the thermoelastoplastic stress response of a rotating FGM pressure vessel is affected significantly by the nonhomogeneity of the material and temperature gradient. The results are validated with those of other researchers for appropriate values of the system parameters and excellent agreement is observed.

키워드

과제정보

The research described in this paper was financially supported by the Natural Science Foundation.

참고문헌

  1. Abouelregal, A. and Zenkour, A. (2019), "Vibration of FG viscoelastic nanobeams due to a periodic heat flux via fractional derivative model", J. Comput. Appl. Mech.. 50(1), 148-156. 10.22059/JCAMECH.2019.277115.367.
  2. Afshin, A., Nejad, M.Z. and Dastani, K. (2017), "Transient thermoelastic analysis of FGM rotating thick cylindrical pressure vessels under arbitrary boundary and initial conditions", J. Comput. Appl. Mech.. 48(1), 15-26. 10.22059/JCAMECH.2017.233643.144.
  3. Ahmadi, S.R., Sheikhlou, M. and Gharebagh, V.M. (2011), "Thermo-elastic/plastic semi-analytical solution of incompressible functionally graded spherical pressure vessel under thermo-mechanical loading", Acta Mechanica. 222(1-2), 161. https://doi.org/10.1007/s00707-011-0512-0.
  4. Akis, T. (2009), "Elastoplastic analysis of functionally graded spherical pressure vessels", Comput. Mater. Sci., 46(2), 545-554. https://doi.org/10.1016/j.commatsci.2009.04.017.
  5. Akis, T. and Eraslan, A. (2006), "The stress response and onset of yield of rotating FGM hollow shafts", Acta Mechanica. 187(1-4), 169-187. https://doi.org/10.1007/s00707-006-0374-z.
  6. Akis, T. and Eraslan, A.N. (2007), "Exact solution of rotating FGM shaft problem in the elastoplastic state of stress", Archive Appl. Mech., 77(10), 745-765. https://doi.org/10.1007/s00419-007-0123-3.
  7. Alikarami, S. and Parvizi, A. (2017), "Elasto-plastic analysis and finite element simulation of thick-walled functionally graded cylinder subjected to combined pressure and thermal loading", Sci. Eng Compos. Mater., 24(4), 609-620. https://doi.org/10.1515/secm-2015-0010
  8. Aminipour, H., Janghorban, M. and Li, L. (2020), "Wave dispersion in nonlocal anisotropic macro/nanoplates made of functionally graded materials", Waves in Random and Complex Media, 1-45. https://doi.org/10.1080/17455030.2020.1713422.
  9. Ataee, A. and Noroozi, R. (2018), "Behavioral Optimization of Pseudo-Neutral Hole in Hyperelastic Membranes Using Functionally graded Cables", J. Comput. Appl. Mech., 49(2), 282-291. 10.22059/JCAMECH.2018.268899.338.
  10. Atai, A.A. and Lak, D. (2017), "Analytic solution of effect of electric field on elasto-plastic response of a functionally graded piezoelectric hollow cylinder", Int. J. Press. Vess. Piping, 155, 1-14. https://doi.org/10.1016/j.ijpvp.2017.06.007.
  11. Barati, A., Hadi, A., Nejad, M.Z. and Noroozi, R. (2020), "On vibration of bi-directional functionally graded nanobeams under magnetic field", Mech. Based Design Struct. Machines, 1-18. doi: 10.1080/15397734.2020.1719507
  12. Burzynski, S., Chroscielewski, J., Daszkiewicz, K. and Witkowski, W. (2018), "Elastoplastic nonlinear FEM analysis of FGM shells of Cosserat type", Compos. Part B-Eng., 154, 478-491. https://doi.org/10.1016/j.compositesb.2018.07.055.
  13. Damadam, M., Moheimani, R. and Dalir, H. (2018), "Bree's diagram of a functionally graded thick-walled cylinder under thermo-mechanical loading considering nonlinear kinematic hardening", Case Studies in Therm. Eng., 12, 644-654. https://doi.org/10.1016/j.csite.2018.08.004.
  14. Daneshmehr, A., Rajabpoor, A. and Hadi, A. (2015), "Size dependent free vibration analysis of nanoplates made of functionally graded materials based on nonlocal elasticity theory with high order theories", Int. J. Eng. Sci., 95 23-35. https://doi.org/10.1016/j.ijengsci.2015.05.011.
  15. Darijani, H., Kargarnovin, M. and Naghdabadi, R. (2009), "Design of spherical vessels under steady-state thermal loading using thermo-elasto-plastic concept", Int. J. Press. Vess. Piping, 86(2-3), 143-152. https://doi.org/10.1016/j.ijpvp.2008.12.001.
  16. Dehghan, M., Nejad, M.Z. and Moosaie, A. (2016), "Thermo-electro-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.
  17. Dehshahri, K., Nejad, M.Z., Ziaee, S., Niknejad, A. and Hadi, A. (2020), "Free vibrations analysis of arbitrary three-dimensionally FGM nanoplates", Ad. Nano Res., 8(2), 115-134. https://doi.org/10.12989/anr.2020.8.2.115.
  18. 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(1-2), 43-63. https://doi.org/10.1007/s00707-005-0276-5.
  19. Eslami, M.R., Hetnarski, R.B., Ignaczak, J., Noda, N., Sumi, N. and Tanigawa, Y. (2013), Theory of elasticity and thermal stresses, Springer
  20. 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(4), Article Number: 1450038.
  21. Figueiredo, F., Borges, L. and Rochinha, F. (2008). "Elasto‐plastic stress analysis of thick‐walled FGM pipes", AIP Conference Proceedings.
  22. Ghannad, M. and Nejad, M.Z. (2010), "Elastic analysis of pressurized thick hollow cylindrical shells with clampedclamped ends", Mechanika. 85(5), 11-18.
  23. Ghannad, M., Nejad, M.Z. and Rahimi, G. (2009), "Elastic solution of axisymmetric thick truncated conical shells based on first-order shear deformation theory", Mechanika. 79(5), 13-20.
  24. Ghannad, M., Nejad, M.Z., Rahimi, G. 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.
  25. 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-Engineering. 45(1), 388-396. https://doi.org/10.1016/j.compositesb.2012.09.043.
  26. 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. 10.22059/JCAMECH.2017.233633.143.
  27. 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.
  28. Ghayesh, M.H. and Farajpour, A. (2019), "Vibrations of shear deformable FG viscoelastic microbeams", Microsystem Technologies, 25(4), 1387-1400. https://doi.org/10.1007/s00542-018-4184-8.
  29. Ghayesh, M.H., Farajpour, A. and Farokhi, H. (2019), "Asymmetric Oscillations of AFG Microscale Nonuniform Deformable Timoshenko Beams", Vibration. 2(2), 201-221. https://doi.org/10.3390/vibration2020013.
  30. Goodarzi, M., Bahrami, M.N. and Tavaf, V. (2017), "Refined plate theory for free vibration analysis of FG nanoplates using the nonlocal continuum plate model", J. Comput. Appl. Mech., 48(1), 123-136. 10.22059/JCAMECH.2017.236217.155.
  31. 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.
  32. 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.
  33. Heydari, A. (2019), "Elasto-Plastic Analysis of Cylindrical Vessel with Arbitrary Material Gradation Subjected to Thermo-Mechanical Loading Via DTM", Arabian J. Sci. Eng., 1-17. https://doi.org/10.1007/s13369-019-03910-x.
  34. 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.
  35. Hosseini, M., Shishesaz, M. and Hadi, A. (2019), "Thermoelastic analysis of rotating functionally graded micro/nanodisks of variable thickness", Thin-Wall. Struct., 134 508-523. https://doi.org/10.1016/j.tws.2018.10.030.
  36. Hosseini, M., Shishesaz, M., Tahan, K.N. and Hadi, A. (2016), "Stress analysis of rotating nano-disks of variable thickness made of functionally graded materials", Int. J. Eng. Sci., 109 29-53. https://doi.org/10.1016/j.ijengsci.2016.09.002.
  37. Jabbari, M., Ghannad, M. and Nejad, M.Z. (2016), "Effect of thickness profile and FG function on rotating disks under thermal and mechanical loading", J. Mechanics. 32(1), 35-46. https://doi.org/10.1017/jmech.2015.95.
  38. Jabbari, M. and Nejad, M.Z. (2020), "Mechanical and thermal stresses in radially functionally graded hollow cylinders with variable thickness due to symmetric loads", Australian J. Mech. Eng., 18, 108-121. https://doi.org/10.1080/14484846.2018.1481562.
  39. 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.
  40. 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-Eng., 96, 20-34. https://doi.org/10.1016/j.compositesb.2016.04.026.
  41. 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.
  42. Kalali, A.T., Moud, S.H. and Hassani, B. (2016), "Elasto-plastic stress analysis in rotating disks and pressure vessels made of functionally graded materials", Latin Am. J. Solid. Struct., 13(5), 819-834. https://doi.org/10.1590/1679-78252420.
  43. Karami, B., Shahsavari, D., Janghorban, M. and Li, L. (2019), "Influence of homogenization schemes on vibration of functionally graded curved microbeams", Compos. Struct., 216, 67-79. https://doi.org/10.1016/j.compstruct.2019.02.089.
  44. Karami, B., Shahsavari, D., Janghorban, M. and Li, L. (2019), "On the resonance of functionally graded nanoplates using biHelmholtz nonlocal strain gradient theory", Int. J. Eng. Sci., 144, 103143. https://doi.org/10.1016/j.ijengsci.2019.103143.
  45. Karami, B., Shahsavari, D., Janghorban, M. and Li, L. (2020), "Free vibration analysis of FG nanoplate with poriferous imperfection in hygrothermal environment", Struct. Eng. Mech., 73(2), 191-207. https://doi.org/10.12989/sem.2020.73.2.191.
  46. Karami, B., Shahsavari, D., Nazemosadat, S.M.R., Li, L. and Ebrahimi, A. (2018), "Thermal buckling of smart porous functionally graded nanobeam rested on Kerr foundation", Steel Compos. Struct., 29(3), 349-362. https://doi.org/10.12989/scs.2018.29.3.349.
  47. Kashkoli, M., Tahan, K.N. and Nejad, M.Z. (2017), "Time-dependent creep analysis for life assessment of cylindrical vessels using first order shear deformation theory", J. Mech., 33(4), 461-474. https://doi.org/10.1017/jmech.2017.6
  48. 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.
  49. 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(6), Article Number: 1750086.
  50. 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(1), Article Number: 1850008. https://doi.org/10.1142/S1758825118500084.
  51. 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.
  52. Koizumi, M. (1993), The concept of FGM.
  53. 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.
  54. Mahamood, R.M. and Akinlabi, E.T. (2017), Types of functionally graded materials and their areas of application, Springer
  55. 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(4), Article Number: 1650054. https://doi.org/10.1142/S175882511650054X.
  56. 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", Eur. J. Mech.-A/Solids, 77, 103793. https://doi.org/10.1016/j.euromechsol.2019.05.008.
  57. Moheimani, R. and Dalir, H. (2020), "Static and Dynamic Solutions of Functionally Graded Micro/Nanobeams under External Loads Using Non-Local Theory", Vibration. 3(2), 51-69. https://doi.org/10.3390/vibration3020006.
  58. Moradi, A., Yaghootian, A., Jalalvand, M. and Ghanbarzadeh, A. (2018), "Magneto-Thermo mechanical vibration analysis of FG nanoplate embedded on Visco Pasternak foundation", J. Comput. Appl. Mech., 49(2), 395-407. 10.22059/JCAMECH.2018.261764.300.
  59. Najibi, A. and Talebitooti, R. (2017), "Nonlinear transient thermoelastic analysis of a 2D-FGM thick hollow finite length cylinder", Compos. Part B-Eng., 111, 211-227. https://doi.org/10.1016/j.compositesb.2016.11.055.
  60. 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.
  61. 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.
  62. 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
  63. 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.
  64. Nejad, M.Z., Hadi, A. and Farajpour, A. (2017), "Consistent couple-stress theory for free vibration analysis of EulerBernoulli 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.
  65. 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 non-local elasticity theory", Struct. Eng. Mech., 67(4), 417-425. https://doi.org/10.12989/sem.2018.67.4.417.
  66. 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.
  67. 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.
  68. 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.
  69. 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 Mechanica. 228(1), 215-231. https://doi.org/10.1007/s00707-016-1709-z.
  70. 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.
  71. Nejad, M.Z. and Rahimi, G. (2009), "Deformations and stresses in rotating FGM pressurized thick hollow cylinder under thermal load", Scientific Res. Essays. 4(3), 131-140. https://doi.org/10.5897/SRE.9000319.
  72. 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.
  73. Nejad, M.Z. and Rahimi, G.H. (2010), "Elastic analysis of FGM rotating cylindrical pressure vessels", J. Chinese Inst. Engineers. 33(4), 525-530. https://doi.org/10.1080/02533839.2010.9671640.
  74. 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.
  75. 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.
  76. 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. 10.22059/JCAMECH.2017.247963.220.
  77. Ozturk, A. and Gulgec, M. (2011), "Elastic-plastic stress analysis in a long functionally graded solid cylinder with fixed ends subjected to uniform heat generation", Int. J. Eng. Sci., 49(10), 1047-1061. https://doi.org/10.1016/j.ijengsci.2011.06.001.
  78. Peng, X.L. and Li, X.F. (2012), "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.
  79. Pradhan, S. and Phadikar, J. (2009), "Bending, buckling and vibration analyses of nonhomogeneous nanotubes using GDQ and nonlocal elasticity theory", Struct. Eng. Mech., 33(2), 193-213. https://doi.org/10.12989/sem.2009.33.2.193.
  80. Sadrabadi, S.A., Rahimi, G., Citarella, R., Karami, J.S., Sepe, R. and Esposito, R. (2017), "Analytical solutions for yield onset achievement in FGM thick walled cylindrical tubes undergoing thermomechanical loads", Compos. Part B-Eng., 116, 211-223. https://doi.org/10.1016/j.compositesb.2017.02.023.
  81. Seyyednosrati, A., Parvizi, A., Afzal, S.A. and Alimirzaloo, V. (2017), "Elasto-plastic solution for thick-walled spherical vessels with an inner FGM layer", J. Comput. Appl. Mech., 10.22059/JCAMECH.2017.239277.173.
  82. She, G.L., Ren, Y.R., Xiao, W.S. and Liu, H. (2018), "Study on thermal buckling and post-buckling behaviors of FGM tubes resting on elastic foundations", Struct. Eng. Mech., 66(6), 729-736. https://doi.org/10.12989/sem.2018.66.6.729.
  83. She, G.L., Ren, Y.R. and Yan, K.M. (2019), "On snap-buckling of porous FG curved nanobeams", Acta Astronautica, 161, 475-484. https://doi.org/10.1016/j.actaastro.2019.04.010.
  84. She, G.L., Yan, K.M., Zhang, Y.L., Liu, H.B. and Ren, Y.R. (2018), "Wave propagation of functionally graded porous nanobeams based on non-local strain gradient theory", The European Phys. J. Plus. 133(9), 368. https://doi.org/10.1140/epjp/i2018-12196-5.
  85. She, G.L., Yuan, F.G., Ren, Y.R., Liu, H.B. and Xiao, W.S. (2018), "Nonlinear bending and vibration analysis of functionally graded porous tubes via a nonlocal strain gradient theory", Compos. Struct., 203, 614-623. https://doi.org/10.1016/j.compstruct.2018.07.063.
  86. Shishesaz, M., Hosseini, M., Tahan, K.N. and Hadi, A. (2017), "Analysis of functionally graded nanodisks under thermoelastic loading based on the strain gradient theory", Acta Mechanica. 228(12), 4141-4168. https://doi.org/10.1007/s00707-017-1939-8.
  87. 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.
  88. 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.
  89. Sofiyev, A., Hui, D., Haciyev, V., Erdem, H., Yuan, G., Schnack, E. and Guldal, V. (2017), "The nonlinear vibration of orthotropic functionally graded cylindrical shells surrounded by an elastic foundation within first order shear deformation theory", Compos. Part B-Eng., 116, 170-185. https://doi.org/10.1016/j.compositesb.2017.02.006.
  90. Sofiyev, A. and Osmancelebioglu, E. (2017), "The free vibration of sandwich truncated conical shells containing functionally graded layers within the shear deformation theory", Compos. Part B-Eng., 120, 197-211. https://doi.org/10.1016/j.compositesb.2017.03.054.
  91. Sofiyev, A., Zerin, Z. and Kuruoglu, N. (2017), "Thermoelastic buckling of FGM conical shells under non-linear temperature rise in the framework of the shear deformation theory", Compos. Part B-Eng., 108, 279-290. https://doi.org/10.1016/j.compositesb.2016.09.102.
  92. Sofiyev, A.H. and Kuruoglu, N. (2016), "Domains of dynamic instability of FGM conical shells under time dependent periodic loads", Compos. Struct., 136, 139-148. https://doi.org/10.1016/j.compstruct.2015.09.060.
  93. 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(9), https://doi.org/10.1142/S1758825119500868.
  94. Tang, H., Hu, Y., Li, L. and Ling, L. (2020), "Active control for ratios of strains in functionally graded piezoelectric composites", Compos. Struct., https://doi.org/10.1016/j.compstruct.2020.111861.
  95. Tang, H., Li, L. and Hu, Y. (2018), "Buckling analysis of two-directionally porous beam", Aerosp. Sci. Technol., 78, 471-479. https://doi.org/10.1016/j.ast.2018.04.045.
  96. Yazdani, H. and Nayebi, A. (2013), "Continuum damage mechanics analysis of thin-walled tube under cyclic bending and internal constant pressure", Int. J. Appl. Mech., 5(4), https://doi.org/10.1142/S1758825113500385.
  97. 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 Design Struct. Machines, 48(4), 480-495. https://doi.org/10.1080/15397734.2019.1642766.
  98. Zargaripoor, A., Daneshmehr, A., Isaac Hosseini, I. and Rajabpoor, A. (2018), "Free vibration analysis of nanoplates made of functionally graded materials based on nonlocal elasticity theory using finite element method", J. Comput. Appl. Mech., 49(1), 86-101. 10.22059/JCAMECH.2018.248906.223.