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Buckling of FGM elliptical cylindrical shell under follower lateral pressure

  • Moradi, Alireza (Faculty of Civil Engineering and Architecture, Shahid Chamran University of Ahvaz) ;
  • Poorveis, Davood (Faculty of Civil Engineering and Architecture, Shahid Chamran University of Ahvaz) ;
  • Khajehdezfuly, Amin (Faculty of Civil Engineering and Architecture, Shahid Chamran University of Ahvaz)
  • 투고 : 2021.07.16
  • 심사 : 2022.10.20
  • 발행 : 2022.10.25

초록

A review of previous studies shows that although there is a considerable difference between buckling loads of structures under follower and non-follower lateral loads, only the buckling load of FGM elliptical cylindrical shell under non-follower lateral load was investigated in the literature. This study is the first to obtain the buckling load of elliptical FGM cylindrical shells under follower lateral load and also make a comparison between buckling loads of elliptical FGM cylindrical shells under follower and non-follower lateral loads. Moreover, this research is the first one to derive the load potential function of elliptical cylindrical shell. In this regard, the FGM cylindrical elliptical shell was modeled using the semi-analytical finite strip method and based on the First Shear Deformation Theory (FSDT). The shell is discretized by strip elements aligned in the longitudinal direction. The Lagrangian and harmonic shape functions were considered in the circumference and longitudinal directions, respectively. The buckling pressure of the shell under follower and non-follower lateral loads was obtained from eigenvalue problem. The results obtained from the model were compared with those presented in the literature to evaluate the validity of the model. A comparison index was defined to compare the buckling loads of the shell under follower and non-follower lateral load. A parametric study was carried out to investigate the effects of material properties and shell geometry characteristics on the comparison index. For the elliptical cylindrical shells with length-to-radius ratio greater than 16 and major-to-minor axis ratio greater than 0.6, the comparison index reaches to more than 20 percent which is significant. Moreover, the maximum difference is about 30 percent in some cases. The results obtained from the parametric study indicate that the buckling load of long elliptical cylindrical shell under non-follower load is not reliable.

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참고문헌

  1. Abualnour, M., Houari, M.S.A., Tounsi, A., Bedia, E.A.A. and Mahmoud, S.R. (2018), "A novel quasi-3D trigonometric plate theory for free vibration analysis of advanced composite plates", Compos. Struct., 184(3), 688-697. https://doi.org/10.1016/j.compstruct.2017.10.047.
  2. Abuteir, B.W., Harkati, E., Boutagouga, D., Mamouri, S. and Djeghaba, K., (2021), "Thermo-mechanical nonlinear transient dynamic and dynamic-buckling analysis of functionally graded material shell structures using an implicit conservative/decaying time integration scheme", Mech. Adv. Mater. Struct., 15(06), 1-14. https://doi.org/10.1080/15376494.2021.1964115.
  3. Akbas, S.D. (2017), "Vibration and Static Analysis of Functionally Graded Porous Plates", J. Appl. Comput. Mech., 3(03), 199-207. https://doi.org/10.22055/jacm.2017.21540.1107.
  4. Asadi, E. and Qatu, M.S. (2013), "Free vibration of thick laminated cylindrical shells with different boundary conditions using general differential quadrature", J. Vib. Control, 19(3), 356-366. https://doi.org/10.1177%2F1077546311432000. https://doi.org/10.1177%2F1077546311432000
  5. Asadi, E., Wang, W. and Qatu, M.S. (2012), "Static and vibration analyses of thick deep laminated cylindrical shells using 3D and various shear deformation theories", Compos. Struct., 94(2), 494-500. https://doi.org/10.1016/j.compstruct.2011.08.011.
  6. Basaglia, C., Camotim, D. and Silvestre, N. (2019), "GBT-based buckling analysis of steel cylindrical shells under combinations of compression and external pressure", Thin-Walled Struct., 144(5), 106274-11. https://doi.org/10.1016/j.tws.2019.106274.
  7. Daikh, A.A., Bachiri, A., Houari, M.S.A. and Tounsi, A. (2022), "Size dependent free vibration and buckling of multilayered carbon nanotubes reinforced composite nanoplates in thermal environment", Mech. Based Des. Struct. 50(4), 1371-1399. https://doi.org/10.1080/15397734.2020.1752232.
  8. Daikh, A.A., Drai, A., Houari, M.S.A. and Eltaher M.A. (2020), "Static analysis of multilayer nonlocal strain gradient nanobeam reinforced by carbon nanotubes", Steel Compos. Struct., 36(6), 643-656. http://dx.doi.org/10.12989/scs.2020.36.6.643.
  9. Dey, T. and Ramachandra, L.S. (2014), "Nonlinear stability analysis of laminated composite simply supported circular cylindrical shells subjected to partial axial loading", J. Eng. Mech., 140(8), 04014058-13. https://doi.org/10.1061/(ASCE)EM.1943-7889.0000764.
  10. Fernandez, F., Lewicki, J.P. and Tortorelli, D.A. (2021), "Optimal toolpath design of additive manufactured composite cylindrical structures", Comput. Methods Appl. Mech. Eng., 376(10), 113673. https://doi.org/10.1016/j.cma.2021.113673.
  11. Foroutana, K. and Ahmadi, H. (2020), "Simultaneous resonances of SSMFG cylindrical shells resting on viscoelastic foundations", Steel Compos. Struct., 37(1), 51-73. http://dx.doi.org/10.12989/scs.2020.37.1.051.
  12. Guo, Y., Serhat, G., Perez, M.G. and Knippers, J. (2022), "Maximizing buckling load of elliptical composite cylinders using lamination parameters", Eng. Struct., 262(05), 114342. https://doi.org/10.1016/j.engstruct.2022.114342.
  13. Hirane, H., Belarbi, MO., Houari, M.S.A. and Tounsi, A. (2021), "On the layerwise finite element formulation for static and free vibration analysis of functionally graded sandwich plates". Eng. Comput., 34(6), 1-29. https://doi.org/10.1007/s00366-020-01250-1.
  14. Houmat, A. (2021), "Three-dimensional free flexural vibrations of fluid-filled functionally graded circular cylindrical shell with curvilinear radius variation", Compos. Struct., 272(06), 114263. https://doi.org/10.1016/j.compstruct.2021.114263.
  15. Katariya, P.V. and Panda, S.K. (2020), "Numerical analysis of thermal post-buckling strength of laminated skew sandwich composite shell panel structure including stretching effect", Steel Compos. Struct., 34(2), 279-288. http://dx.doi.org/10.12989/scs.2020.34.2.279.
  16. Khayat, M., Poorveis, D. and Moradi, S. (2017a), "Semi-analytical approach in buckling analysis of functionally graded shells of revolution subjected to displacement dependent pressure", J. Press. Vessel Technol., 139(6), 061202-21. https://doi.org/10.1115/1.4037042.
  17. Khayat, M., Poorveis, D. and Moradi, S. (2017b), "Buckling analysis of functionally graded truncated conical shells under external displacement-dependent pressure", Steel Compos. Struct., 23(1), 1-6. http://dx.doi.org/10.12989/scs.2017.23.1.001.
  18. Khayat, M., Dehghan, S.M., Najafgholipour, M.A. and Baghlani, A. (2018), "Free vibration analysis of functionally graded cylindrical shells with different shell theories using semianalytical method", Steel Compos. Struct, 28(6), 735-748. http://dx.doi.org/10.12989/scs.2018.28.6.735.
  19. Khayat, M., Poorveis, D. and Moradi, S., (2016a), "Buckling analysis of laminated composite cylindrical shell subjected to lateral displacement-dependent pressure using semi-analytical finite strip method", Steel Compos. Struct., 22(2), 301-321. https://doi.org/10.12989/scs.2016.22.2.301.
  20. Khayat, M., Poorveis, D., Moradi, S. and Hemmati, M. (2016b), "Buckling of thick deep laminated composite shell of revolution under follower forces", Struct. Eng. Mech., 58(1), 59-91. https://doi.org/10.12989/sem.2016.58.1.059.
  21. Khalfi, Y., Houari, M.S.A. and Tounsi, A. (2014), "A refined and simple shear deformation theory for thermal buckling of solar functionally graded plates on elastic foundation", Int. J. Comput. Methods, 11(5), 1350077-15. https://doi.org/10.1142/S0219876213500771.
  22. Khetir, H., Bouiadjra, M.B., Houari, M.S.A., Tounsi, A. and Mahmoud, S.R. (2017), "A new nonlocal trigonometric shear deformation theory for thermal buckling analysis of embedded nanosize FG plates", Struct. Eng. Mech., 64(4), 391-402. http://dx.doi.org/10.12989/sem.2017.64.4.391.
  23. Kumar, R., Dey, T. and Panda, S.K. (2019), "Instability and vibration analyses of FG cylindrical panels under parabolic axial compressions", Steel Compos. Struct., 31(02), 187-199. https://doi.org/10.12989/scs.2019.31.2.187.
  24. Lin, H., Cao, D. and Shao, C. (2018), "An admissible function for vibration and flutter studies of FG cylindrical shells with arbitrary edge conditions using characteristic orthogonal polynomials", Compos. Struct., 185(03), 748-763. https://doi.org/10.1016/j.compstruct.2017.11.071.
  25. Li, Z.M. and Lin, Z.Q. (2010), "Non-linear buckling and postbuckling of shear deformable anisotropic laminated cylindrical shell subjected to varying external pressure loads", Compos. Struct., 92(2), 553-567. https://doi.org/10.1016/j.compstruct.2009.08.048.
  26. Lopatin, A.V. and Morozov, E.V., (2012), "Buckling of a composite cantilever circular cylindrical shell subjected to uniform external lateral pressure", Compos. Struct., 94(2), 553-562. https://doi.org/10.1016/j.compstruct.2011.08.021.
  27. Mahawar, P. and Sharma, P. (2022), "Free vibration analysis of FGM conical shell", Proceedings of Advances in Mechanical and Materials Technology, Lecture Notes in Mechanical Engineering. Springer, Singapore, 83-91, https://doi.org/10.1007/978-981-16-2794-1_7.
  28. Majidi-Mozafari, K., Bahaadini, R. and Saidi, A.R. (2021), "Aeroelastic flutter analysis of functionally graded spinning cylindrical shells reinforced with graphene nanoplatelets in supersonic flow", Mater. Res. Express., 8(11), 115012. https://doi.org/10.1088/2053-1591/ac2ce4.
  29. Mirfakhraei, P. and Redekop, P. (1998), "Buckling of circular cylindrical shells by the differential quadrature method", Int. J. Press. Vessel. Pip., 75(4), 347-353. https://doi.org/10.1016/S0308-0161(98)00032-5.
  30. Mirjavadi, S.S., Forsat, M., Barati, M.R. and Hamouda, A.M.S. (2020), "Post-buckling of higher-order stiffened metal foam curved shells with porosity distributions and geometrical imperfection", Steel Compos. Struct., 35(4), 567-578. http://dx.doi.org/10.12989/scs.2020.35.4.567.
  31. Mota, A.F., Loja, M.A.R., Barbosa, J.I. and Rodrigues, J.A. (2020), "Porous Functionally Graded Plates: An Assessment of the Influence of Shear Correction Factor on Static Behavior", Math. Comput. Appl., 25(03), 1-26. https://doi.org/10.3390/mca25020025.
  32. Na, K., Kim, J. and Park, J. (2019), "Dynamic Stability Analyses of the Liquid-Filled Cylindrical Shells with Lumped Masses Under a Follower Force", Int. J. Aeronaut. Space Sci., 20(1), 664-672. https://doi.org/10.1007/s42405-019-00203-3.
  33. Nejati, M., Dimitri, R., Tornabene, F. and Hossein Yas, M. (2017), "Thermal buckling of nanocomposite stiffened cylindrical shells reinforced by Functionally Graded Wavy Carbon Nano-Tubes with temperature-dependent properties", Appl. Sci., 7(12), 1-24. https://doi.org/10.3390/app7121223.
  34. Park, S.H. and Kim, J.H. (2000), "Dynamic stability of a completely free circular cylindrical shell subjected to a follower force", J. Sound Vib., 231(4), 989-1005. https://doi.org/10.1006/jsvi.1999.2319.
  35. Park, S.H. and Kim, J.H. (2012), "Dynamic stability of a free-free cylindrical shell under a follower force", AIAA J., 38(6), 1070-1077. https://doi.org/10.2514/2.1069.
  36. Park, S.H. and Kim, J.H. (2002), "Dynamic stability of a stiffedged cylindrical shell subjected to a follower force", Comput. Struct., 80(3), 227-233. https://doi.org/10.1016/S0045-7949(02)00007-X.
  37. Rouhi, M., Ghayoor, H., Hoa, S.V., Hojjati, M. and Weaver, P.M. (2016), "Stiffness tailoring of elliptical composite cylinders for axial buckling performance", Compos. Struct., 150(4), 115-123. https://doi.org/10.1016/j.compstruct.2016.05.007.
  38. Reddy, J.N. (2000), "Analysis of functionally graded plates", Int. J. Numer. Methods Eng., 47(1-3), 663-684. https://doi.org/10.1002/(SICI)1097-0207(20000110/30)47:1/3.
  39. Sahan, M.F. (2015), "Transient analysis of cross-ply laminated shells using FSDT: Alternative formulation", Steel Compos. Struct., 18(4), 889-907. http://dx.doi.org/10.12989/scs.2015.18.4.889.
  40. Sayyad, A.S. and Ghugal, Y.M. (2021), "Static and free vibration analysis of doubly-curved functionally graded material shells", Compos. Struct., 269(02), 114045. https://doi.org/10.1016/j.compstruct.2021.114045.
  41. Shahali, P., Haddadpour, H. and Shakhesi, S. (2022), "Dynamic analysis of electrorheological fluid sandwich cylindrical shells with functionally graded face sheets using a semi-analytical approach", Compos. Struct., 295(03), 115715. https://doi.org/10.1016/j.compstruct.2022.115715.
  42. Shamass, R., Alfano, G. and Guarracino, F. (2015), "An Analytical Insight into the Buckling Paradox for Circular Cylindrical Shells under Axial and Lateral Loading", Math. Probl. Eng., 2015(1), 1-10. https://doi.org/10.1155/2015/514267.
  43. Sheng, G.G. and Wang, X. (2018), "The dynamic stability and nonlinear vibration analysis of stiffened functionally graded cylindrical shells", Appl. Math. Model., 56(04), 389-403. https://doi.org/10.1016/j.apm.2017.12.021.
  44. Silvestre, N. (2008), "Buckling behaviour of elliptical cylindrical shells and tubes under compression", Int. J. Solids Struct., 45(16), 4427-4447. https://doi.org/10.1016/j.ijsolstr.2008.03.019.
  45. Silvestre, N. and Gardner, L. (2011), "Elastic local post-buckling of elliptical tubes", J. Constr. Steel Res., 67(3), 281-292. https://doi.org/10.1016/j.jcsr.2010.11.004.
  46. Sofiyev, A.H., Tornabene, F., Dimitri, F. and Kuruoglu, N. (2020), "Buckling behavior of FG-CNT reinforced composite conical shells subjected to a combined loading", Nanomaterials, 10(3), 1-19. https://doi.org/10.3390/nano10030419.
  47. Sofiyev, A.H. and Kuruoglu, N. (2016), "Domains of dynamic instability of FGM conical shells under time dependent periodic loads", Compos. Struct., 136(05), 139-148. https://doi.org/10.1016/j.compstruct.2015.09.060.
  48. Sofiyev, A.H. and Kuruoglu, N. (2015), "Parametric instability of shear deformable sandwich cylindrical shells containing an FGM core under static and time dependent periodic axial loads", Int. J. Mech. Sci., 102(07), 114-123. https://doi.org/10.1016/j.ijmecsci.2015.07.025.
  49. Sofiyev, A.H. (2016), "Parametric vibration of FGM conical shells under periodic lateral pressure within the shear deformation theory", Compos. B. Eng., 89(02), 282-294. https://doi.org/10.1016/j.compositesb.2015.11.017.
  50. Soldatos, K.P. (2008), "Nonlinear analysis of transverse shear deformable laminated composite cylindrical shells-part II: buckling of axially compressed cross-ply circular and oval cylinders", J. Press. Vessel Technol., 114(1), 110-114. https://doi.org/10.1115/1.2929000.
  51. Torki, M.E., Taghi Kazemi, M. and Talaeitaba, S.B. (2015), "Effect of axial deformation on flutter of cantilevered FGM cylindrical shells under axial follower forces", Transaction A: Civil Eng., 13(2), 160-170. http://dx.doi.org/10.22068/IJCE.13.2.160.
  52. Torki, M.E., Kazemi, M.E., Reddy, J.N., Haddadpoud, H. and Mohmoudkhani, S. (2014), "Dynamic stability of functionally graded cantilever cylindrical shells under distributed axial follower forces", J. Sound Vib., 333(3), 801-817. https://doi.org/10.1016/j.jsv.2013.09.005.
  53. Tornabene, F., Viola, E. and Inman, D.J. (2009), "2-D Differential Quadrature solution for vibration analysis of functionally graded conical, cylindrical shell and annular plate structures", J. Sound Vib., 328(3), 259-290. https://doi.org/10.1016/j.jsv.2009.07.031.
  54. Tornabene, F., Fantuzzi, N. and Bacciocchi, M. (2014), "Free vibrations of free-form doubly-curved shells made of functionally graded materials using higher-order equivalent single layer theories", Compos. B Eng., 67(1), 490-509. https://doi.org/10.1016/j.compositesb.2014.08.012.
  55. Tzeng Y.C. and Chern, Y.C., (2008), "Stability Analysis of a Circular Cylindrical Shell by the Equilibrium Method", Int. J. Struct. Stab. Dyn., 8(3), 465-485. https://doi.org/10.1142/S0219455408002752.
  56. Van Dung, D. and Hoa, L.K. (2013), "Nonlinear buckling and post-buckling analysis of eccentrically stiffened functionally graded circular cylindrical shells under external pressure", ThinWalled Struct., 63(4), 117-124. https://doi.org/10.1016/j.tws.2012.09.010.
  57. Xie, K. and Chen, M. (2021), "An analytical method for free vibrations of functionally graded cylindrical shells with arbitrary intermediate ring supports", J. Braz. Soc. Mech. Sci. Eng., 43(05), 1-13. https://doi.org/10.1007/s40430-021-02829-5.
  58. Xue, J. and Hoo Fatt, M.S. (2002), "Buckling of a non-uniform, long cylindrical shell subjected to external hydrostatic pressure", Eng. Struct., 24(8), 1027-1034. https://doi.org/10.1016/S0141-0296(02)00029-9.
  59. Yahia, S.A., Atmane, H.A., Houari, M.S.A. and Tounsi, A. (2015), "Wave propagation in functionally graded plates with porosities using various higher-order shear deformation plate theories" Struct. Eng. Mech., 53(6), 1143-1165. http://dx.doi.org/10.12989/sem.2015.53.6.1143.
  60. Yao, Y.C. and Jenkins, W.C. (1970), "Buckling of elliptic cylinders under normal pressure", AIAA J., 8(1), 22-27. https://doi.org/10.2514/3.5600.
  61. Zemri, A., Houari, M.S.A., Bousahla, A.A. and Tounsi, A. (2015), "A mechanical response of functionally graded nanoscale beam: an assessment of a refined nonlocal shear deformation theory beam theory", Struct. Eng. Mech., 54(4), 693-710. http://dx.doi.org/10.12989/sem.2015.54.4.693.
  62. Zheng, Y., Han, B., Chen, J., Zhong, J. and Li, J. (2021), "Maximizing the load carrying capacity of a variable stiffness composite cylinder based on the multi-objective optimization method", Int. J. Comput. Methods, 18(05), 2150001. https://doi.org/10.1142/S0219876221500018.
  63. Zucco, G. and Weaver, P.M. (2020), "Post-buckling behaviour in variable stiffness cylindrical panels under compression loading with modal interaction effects", Int. J. Solids Struct., 203(06), 92-109. https://doi.org/10.1016/j.ijsolstr.2020.06.025.