DOI QR코드

DOI QR Code

Nonlinear buckling analysis of FGP shallow spherical shells under thermomechanical condition

  • Ahmadi, Habib (Faculty of Mechanical and Mechatronics Engineering, Shahrood University of Technology) ;
  • Foroutan, Kamran (Faculty of Mechanical and Mechatronics Engineering, Shahrood University of Technology)
  • 투고 : 2020.08.05
  • 심사 : 2021.06.08
  • 발행 : 2021.08.25

초록

In this study, an analytical method is presented to investigate the nonlinear buckling analysis of functionally graded porous (FGP) shallow spherical shells exposed to external excitation in a thermal environment resting on elastic foundations. The elastic foundations of the FGP shell are consist of a two-term Winkler-Pasternak's model. Using the classical theory of shells and considering nonlinear von Kármán-Donnell relations and Hook law, the governing equations of thin FG porous spherical shells are extracted. Galerkin's method is utilized to discretize the governing equation of shallow spherical shell. Regarding the discretized equations of motion, the explicit expressions for dynamic and static critical buckling loading are determined under thermomechanical effect. Two types of distributions for FG porous, including the uniform and symmetric porosity, are considered. To investigate the dynamic buckling exposed to external pressure and thermal effect, the equations of motion of FGP shallow spherical shells are examined via a numerical method named Runge-Kutta approach, and then with a procedure presented by Budiansky-Roth, the critical load for the nonlinear dynamic buckling is obtained. The influence of thermal environment changes, porosity coefficients, various porosity distributions, elastic foundations, and geometrical characteristics on the nonlinear static and dynamic buckling response of FGP shallow spherical shell is examined.

키워드

참고문헌

  1. Ahmadi, H. and Foroutan, K. (2019), "Combination resonance analysis of FG porous cylindrical shell under two-term excitation", Steel Compos. Struct., 32(2), 253-264. http://dx.doi.org/10.12989/scs.2019.32.2.253.
  2. Ahmadi, H. and Foroutan, K. (2020), "Nonlinear static and dynamic thermal buckling analysis of imperfect multilayer FG cylindrical shells with an FG porous core resting on nonlinear elastic foundation", J. Therm. Stresses, 1-21. https://doi.org/10.1080/01495739.2020.1727802.
  3. Anh, V.T.T., Bich, D.H. and Duc, N.D. (2015), "Nonlinear stability analysis of thin FGM annular spherical shells on elastic foundations under external pressure and thermal loads", Eur. J. Mech. A-Solid, 50, 28-38. https://doi.org/10.1016/j.euromechsol.2014.10.004.
  4. Ansari, R., Torabi, J. and Shojaei, M.F. (2016), "Vibrational analysis of functionally graded carbon nanotube-reinforced composite spherical shells resting on elastic foundation using the variational differential quadrature method", Eur. J. Mech. A-Solid., 60, 166-182. https://doi.org/10.1016/j.euromechsol.2016.07.003.
  5. Babaei, H., Eslami M.R. and Khorshidvand, A.R. (2020), "Thermal buckling and postbuckling responses of geometrically imperfect FG porous beams based on physical neutral plane", J. Therm. Stresses, 43(1), 109-131. https://doi.org/10.1080/01495739.2019.1660600.
  6. Belica, T., Malinowski, M. and Magnucki, K. (2011), "Dynamic stability of an isotropic metal foam cylindrical shell subjected to external pressure and axial compression", J. Appl. Mech., 78(4), 041003. https://doi.org/10.1115/1.4003768.
  7. Bich, D.H. and Dung, D.V. (2012), "Nonlinear static and dynamic buckling analysis of functionally graded shallow spherical shells including temperature effects", Compos. Struct., 94(9), 2952-2960. https://doi.org/10.1016/j.compstruct.2012.04.012 Get.
  8. Bich, D.H. and Hoang, V.T. (2011), "Non-linear axisymmetric response of functionally graded shallow spherical shells under uniform external pressure including temperature effects", Int. J. Nonlinear Mech., 46(9) 1195-1204. https://doi.org/10.1016/j.ijnonlinmec.2011.05.015Get.
  9. Boroujerdy, M.S. and Eslami, M.R. (2015), "Unsymmetrical buckling of piezo-FGM shallow clamped spherical shells under thermal loading", J. Therm. Stresses, 38(11) 1290-1307. https://doi.org/10.1080/01495739.2015.1073532.
  10. Birman V. (1997), "Theory and comparison of the effect of composite and shape memory along stiffness on stability of composite shells and plates", Int. J. Mech. Sci., 39(10), 119-149. https://doi.org/10.1016/S0020-7403(97)00008-8.
  11. Budiansky, B. (1962), "Axisymmetric dynamic buckling of clamped shallow spherical shells", NASA TN 1510, 597-606.
  12. Duc, N.D. (2013), "Nonlinear dynamic response of imperfect eccentrically stiffened FGM double curved shallow shells on elastic foundation", Compos. Struct., 99, 88-96. https://doi.org/10.1016/j.compstruct.2012.11.017.
  13. Duc. N.D. and Thang, P.T. (2015), "Nonlinear dynamic response and vibration of shear deformable imperfect eccentrically stiffened S-FGM circular cylindrical shells surrounded on elastic foundations", Aerosp. Sci. Technol., 40, 115-127. https://doi.org/10.1016/j.ast.2014.11.005.
  14. Eslami, M.R., Ghorbani, H.R. and Shakeri, M. (2001), "Thermoelastic buckling of thin spherical shells", J. Therm. Stresses, 24(12), 1177-1198. https://doi.org/10.1080/014957301753251746.
  15. Foroutan, K., Shaterzadeh, A.R. and Ahmadi, H. (2020), "Nonlinear static and dynamic hygrothermal buckling analysis of imperfect functionally graded porous cylindrical shells", Appl. Math. Model., 77, 539-553. https://doi.org/10.1016/j.apm.2019.07.062.
  16. Galeban, M.R., Mojahedin, A., Taghavi, Y. and Jabbari, M. (2016), "Free vibration of functionally graded thin beams made of saturated porous materials", Steel Compos. Struct., 21(5), 999-1016. http://dx.doi.org/10.12989/scs.2016.21.5.999.
  17. Gao, K., Gao, W., Wu, B., Wu, D. and Song, C. (2018), "Nonlinear primary resonance of functionally graded porous cylindrical shells using the method of multiple scales", Thin Wall. Struct., 125, 281-293. https://doi.org/10.1016/j.tws.2017.12.039.
  18. Ganapathi, M. and Varadan, T.K. (1995), "Dynamic buckling of laminated anisotropic spherical caps", J. Appl. Mech. Mar., 62(1), 13-19. https://doi.org/10.1115/1.2895879.
  19. Ganapathi, M. and Varadan, T.K. (1982), "Dynamic buckling of orthotropic shallow spherical shells", Comput. Struct., 15(5), 517-520. https://doi.org/10.1016/0045-7949(82)90003-7.
  20. Ghadiri, M. and SafarPour, H. (2017), "Free vibration analysis of size-dependent functionally graded porous cylindrical microshells in thermal environment", J. Therm. Stresses, 40(1), 55-71. https://doi.org/10.1080/01495739.2016.1229145.
  21. Huang, N.C. (1964), "Unsymmetrical buckling of thin shallow spherical shells", J. Appl. Mech., 31(3), 447-457. https://doi.org/10.1115/1.3629662.
  22. Kar, V.R. and Panda, S.K. (2015), "Nonlinear flexural vibration of shear deformable functionally graded spherical shell panel", Steel Compos. Struct., 18(3), 693-709. http://dx.doi.org/10.12989/scs.2015.18.3.693.
  23. 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. http://dx.doi.org/10.12989/scs.2018.29.3.349.
  24. Lakes, R. (1996), "Cellular solid structures with unbounded thermal expansion", J. Mater. Sci. Lett., 15(6), 475-477. https://doi.org/10.1007/BF00275406.
  25. Loy, C.T., Lam, K.Y. and Reddy, J.N. (1999), "Vibration of functionally graded cylindrical shells", Int. J. Mech. Sci., 41(3), 309-324. https://doi.org/10.1016/S0020-7403(98)00054-X.
  26. Magnucki, K., Malinowski, M. and Kasprzak, J. (2006), "Bending and buckling of a rectangular porous plate", Steel Compos. Struct., 6(4), 319-333. http://dx.doi.org/10.12989/scs.2006.6.4.319.
  27. 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.
  28. Mushtari X.M. and Galimov K.Z. (1957), Nonlinear theory of elastic shells, Tatknigoizdat, Kazan.
  29. Oghibalov, P.M. (1963), Dynamics and stability of shells, Moscow.
  30. Prakash, T., Sundararajan, N. and Ganapathi, M. (2007), "On the nonlinear axisymmetric dynamic buckling behavior of clamped functionally graded spherical caps", J. Sound Vib., 299(1-2) 36-43. https://doi.org/10.1016/j.jsv.2006.06.060.
  31. Quan, T.Q. and Duc, N.D. (2016), "Nonlinear vibration and dynamic response of shear deformable imperfect functionally graded double-curved shallow shells resting on elastic foundations in thermal environments", J. Therm. Stresses. 39(4), 437-459. https://doi.org/10.1080/01495739.2016.1158601.
  32. Shahsiah, R., Eslami, M.R. and Naj, R. (2006), "Thermal instability of functionally graded shallow spherical shell", J. Therm. Stresses, 29(8), 771-790. https://doi.org/10.1080/01495730600705406.
  33. Sun, J., Xu, X. and Lim, C.W. (2014), "Buckling of functionally graded cylindrical shells under combined thermal and compressive loads", J. Therm. Stresses, 37(3), 340-362. https://doi.org/10.1080/01495739.2013.869143.
  34. Tillman, S.C. (1970), "On the buckling behaviour of shallow spherical caps under a uniform pressure load", Int. J. Solids Struct., 6(1), 37-52. https://doi.org/10.1016/0020-7683(70)90080-6.
  35. Uysal, M.U. (2016), "Buckling behaviours of functionally graded polymeric thin-walled hemispherical shells", Steel Compos. Struct., 21(4), 849-862. http://dx.doi.org/10.12989/scs.2016.21.4.849.
  36. Wang, Y.Q., Liu, Y.F. and Yang, T.H. (2019b), "Nonlinear thermo-electro-mechanical vibration of functionally graded piezoelectric nanoshells on Winkler-Pasternak foundations via nonlocal Donnell's nonlinear shell theory", Int. J. Struct. Stab. Dynam., 19(9), 1950100. https://doi.org/10.1142/S0219455419500998.
  37. Wang, Y.Q., Liu, Y.F. and Zu, J.W. (2019a), "Nonlinear vibration of magnetoelectroelastic nanoscale shells embedded in elastic media in thermoelectromagnetic fields", J. Intel. Mat. Syst. Str., 30(15), 2331-2347. https://doi.org/10.1177/1045389X19862382.
  38. Wang, Y.Q., Liu, Y.F. and Zu, J.W. (2019e), "On scale-dependent vibration of circular cylindrical nanoporous metal foam shells", Microsyst. Technol., 25(7), 2661-2674. https://doi.org/10.1007/s00542-018-4262-y.
  39. Wang, Y.Q. and Teng, M.W. (2019), "Vibration analysis of circular and annular plates made of 3D graphene foams via Chebyshev-Ritz method", Aerosp. Sci. Technol., 95, 105440. https://doi.org/10.1016/j.ast.2019.105440.
  40. Wang, Y. and Wu, D. (2017), "Free vibration of functionally graded porous cylindrical shell using a sinusoidal shear deformation theory", Aerosp. Sci. Technol., 66, 83-91. https://doi.org/10.1016/j.ast.2017.03.003.
  41. Wang, Y.Q., Ye,C. and Zhu, J. (2020), "Chebyshev collocation technique for vibration analysis of sandwich cylindrical shells with metal foam core", ZAMM-J. Appl. Math. Mech., 100(5), e201900199. https://doi.org/10.1002/zamm.201900199.
  42. Wang, Y., Ye, C. and Zu, J.W. (2018), "Identifying the temperature effect on the vibrations of functionally graded cylindrical shells with porosities", Appl. Math. Mech., 39(11), 1587-1604. https://doi.org/10.1007/s10483-018-2388-6.
  43. Wang, Y.Q., Ye, C. and Zu, J.W. (2019d), "Vibration analysis of circular cylindrical shells made of metal foams under various boundary conditions", Int. J. Mech. Mater. Des., 15(2), 333-344. https://doi.org/10.1007/s10999-018-9415-8.
  44. Wang, Y.Q. and Zhao, H.L. (2019), "Free vibration analysis of metal foam core sandwich beams on elastic foundation using Chebyshev collocation method," Arch. Appl. Mech., 89(11), 2335-2349. https://doi.org/10.1007/s00419-019-01579-0.
  45. Wang, Y.Q., Zhao, H.L., Yang, T.H. and Zu, J.W. (2019c), "Thermo-hygro-mechanical bending and vibration of functionally graded material microbeams with microporosity defect", J. Therm. Stresses, 42(7), 815-834. https://doi.org/10.1080/01495739.2019.1587325.
  46. Wang, Y.Q. and Zhang, Z.Y. (2019), "Bending and buckling of three-dimensional graphene foam plates," Results Phys., 13, 102136. https://doi.org/10.1016/j.rinp.2019.02.072.
  47. Wang, Y.Q. and Zu, J.W. (2017), "Vibration behaviors of functionally graded rectangular plates with porosities and moving in thermal environment," Aerosp. Sci. Technol., 69, 550-562. https://doi.org/10.1016/j.ast.2017.07.023.
  48. Wunderlich, W. and Ursula, A. (2002), "Buckling behaviour of imperfect spherical shells", Int. J. Nonlin. Mech., 37(4-5), 589-604. https://doi.org/10.1016/0263-8231(95)00003-V.
  49. Yas, M.H. and Rahimi, S. (2020), "Thermal vibration of functionally graded porous nanocomposite beams reinforced by graphene platelets", Appl. Math. Mech., 1-18. https://doi.org/10.1007/s10483-020-2634-6.
  50. Ye, Z.M. (1997), "The non-linear vibration and dynamic instability of thin shallow shells", J. Sound Vib., 202(3), 303-311. https://doi.org/10.1006/jsvi.1996.0827.
  51. Zhou, C., Zhang, Z., Zhang, J., Fang, Y. and Tahouneh, V. (2020), "Vibration analysis of FG porous rectangular plates reinforced by graphene platelets", Steel Compos. Struct., 34(2), 215-226. http://dx.doi.org/10.12989/scs.2020.34.2.215.