Advertisement

Acta Mechanica

, Volume 230, Issue 6, pp 2145–2169 | Cite as

On the nonlinear bending and post-buckling behavior of laminated sandwich cylindrical shells with FG or isogrid lattice cores

  • Famida FallahEmail author
  • Ehsan Taati
Original Paper

Abstract

The nonlinear governing equations of three shell theories (Donnell, Love, and Sanders) with first-order approximation and von Kármán’s geometric nonlinearity for laminated sandwich cylindrical shells with isotropic, functionally graded (FG) or isogrid lattice layers are decoupled. This uncoupling makes it possible to present a semi-analytical solution for the nonlinear bending and post-buckling behavior of short and long doubly simply supported, doubly clamped, and cantilever laminated sandwich cylindrical shells subjected to various types of thermo-mechanical loadings. The results for deflection, stress, critical axial traction, and mode shapes in FG shells are verified with those obtained from ABAQUS code. Finally, the case studies are presented for FG shells and laminated sandwich shells with different layups such as \([\hbox {Al; ZrO}_2]\), \([\hbox {Al; FG core; ZrO}_2]\), \([\hbox {Al; Gr; ZrO}_2]\), \([\hbox {Al; Gr; FG core; ZrO}_2]\), \([\hbox {Al; isogrid lattice core; Al}]\). The closed-form solutions presented here for the kinetic parameters and critical axial loading in a nonlinear analysis can be used in the conceptual design of laminated sandwich cylindrical shells with arbitrary layups and boundary conditions. Furthermore, introducing an equivalent Young’s modulus through the shell thickness, a simple formula is presented for the calculation of critical load in long shells with simple and clamped ends under axial loading with a maximum error of 10%. Moreover, findings show that the boundary-layer type behavior is seen only in long cylindrical shells in the pre-buckling region. Under thermal loading, snap-through buckling is observed in clamped shells. However, in simply supported shells by increasing the temperature, the transverse deflection increases, and while \(\Delta T-w/h\) curves do not show any buckling phenomenon, the \(N^{0}/N_{\mathrm{cr}}^{*} -\Delta T\) curves show such a behavior.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Notes

References

  1. 1.
    Reddy, J.N.: Mechanics of Laminated Composite Plates and Shells: Theory and Analysis. CRC Press, Boca Raton (2004)CrossRefzbMATHGoogle Scholar
  2. 2.
    Shiota, I., Miyamoto, Y. (eds.): Functionally Graded Materials 1996. Elsevier, Amsterdam (1997)Google Scholar
  3. 3.
    Witvrouw, A., Mehta, A.: The use of functionally graded poly-SiGe layers for MEMS applications. Mater. Sci. Forum 492, 255–260 (2005)CrossRefGoogle Scholar
  4. 4.
    Ghayesh, M.H., Farokhi, H., Gholipour, A., Tavallaeinejad, M.: Nonlinear oscillations of functionally graded microplates. Int. J. Eng. Sci. 122, 56–72 (2018)CrossRefzbMATHGoogle Scholar
  5. 5.
    Ghayesh, M.H.: Nonlinear vibration analysis of axially functionally graded shear-deformable tapered beams. Appl. Math. Modell. 59, 583–596 (2018)MathSciNetCrossRefGoogle Scholar
  6. 6.
    Ghayesh, M.H.: Dynamics of functionally graded viscoelastic microbeams. Int. J. Eng. Sci. 124, 115–131 (2018)MathSciNetCrossRefzbMATHGoogle Scholar
  7. 7.
    Ghayesh, M.H.: Functionally graded microbeams: simultaneous presence of imperfection and viscoelasticity. Int. J. Mech. Sci. 140, 339–350 (2018)CrossRefGoogle Scholar
  8. 8.
    Ghayesh, M.H., Farokhi, H., Gholipour, A.: Oscillations of functionally graded microbeams. Int. J. Eng. Sci. 110, 35–53 (2017)MathSciNetCrossRefzbMATHGoogle Scholar
  9. 9.
    Vasiliev, V., Morozov, E.V.: Advanced mechanics of composite materials and structural elements, 3rd edn. Elsevier, Newnes (2013)Google Scholar
  10. 10.
    Galletly, G.D., Aylward, R.W., Bushnell, D.: An experimental and theoretical investigation of elastic and elastic-plastic asymmetric buckling of cylinder-cone combinations subjected to uniform external pressure. Arch. Appl. Mech. 43(6), 345–358 (1974)Google Scholar
  11. 11.
    Bisagni, C.: Experimental buckling of thin composite cylinders in compression. AIAA J. 37, 276–278 (1999)CrossRefGoogle Scholar
  12. 12.
    Teng, J.G., Rotter, J.M. (eds.): Buckling of Thin Metal Shells. CRC Press, Boca Raton (2006)Google Scholar
  13. 13.
    Donnell, E.H., Ohio, A.: A new theory for the buckling of thin cylinders under axial compression and bending. Trans. ASME 56, 795–806 (1934)Google Scholar
  14. 14.
    Sanders, L.J.: Nonlinear theories for thin shells. Q. Appl. Math. 21, 21–36 (1963)MathSciNetCrossRefGoogle Scholar
  15. 15.
    Koiter, W.T.: On the nonlinear theory of thin elastic shells. In: Proceedings Koniklijke Nederlands Akademie van Wetenschappen, pp. 1–54 (1966)Google Scholar
  16. 16.
    Yiotis, A.J., Katsikadelis, J.T.: Buckling of cylindrical shell panels: a MAEM solution. Arch. Appl. Mech. 85(9–10), 1545–1557 (2015)CrossRefzbMATHGoogle Scholar
  17. 17.
    Kazemi, E., Darvizeh, M., Darvizeh, A., Ansari, R.: An investigation of the buckling behavior of composite elliptical cylindrical shells with piezoelectric layers under axial compression. Acta Mech. 223(10), 2225–2242 (2012)MathSciNetCrossRefzbMATHGoogle Scholar
  18. 18.
    Liang, K., Ruess, M.: Nonlinear buckling analysis of the conical and cylindrical shells using the SGL strain based reduced order model and the PHC method. Aerosp. Sci. Technol. 55, 103–110 (2016)CrossRefGoogle Scholar
  19. 19.
    Mikhasev, G., Botogova, M.: Effect of edge shears and diaphragms on buckling of thin laminated medium-length cylindrical shells with low effective shear modulus under external pressure. Acta Mech. 228(6), 2119–2140 (2017)MathSciNetCrossRefzbMATHGoogle Scholar
  20. 20.
    Bagheri, M., Jafari, A.A., Sadeghifar, M.: A genetic algorithm optimization of ring-stiffened cylindrical shells for axial and radial buckling loads. Arch. Appl. Mech. 81(11), 1639–1649 (2011)CrossRefzbMATHGoogle Scholar
  21. 21.
    Ghayesh, M.H., Farokhi, H.: Chaotic motion of a parametrically excited microbeam. Int. J. Eng. Sci. 96, 34–45 (2015)MathSciNetCrossRefzbMATHGoogle Scholar
  22. 22.
    Ghayesh, M.H., Farokhi, H., Hussain, S.: Viscoelastically coupled size-dependent dynamics of microbeams. Int. J. Eng. Sci. 109, 243–255 (2016)MathSciNetCrossRefzbMATHGoogle Scholar
  23. 23.
    Ghayesh, M.H., Farokhi, H.: Nonlinear dynamics of microplates. Int. J. Eng. Sci. 86, 60–73 (2015)MathSciNetCrossRefzbMATHGoogle Scholar
  24. 24.
    Ghayesh, M.H., Amabili, M., Farokhi, H.: Nonlinear forced vibrations of a microbeam based on the strain gradient elasticity theory. Int. J. Eng. Sci. 63, 52–60 (2013)MathSciNetCrossRefzbMATHGoogle Scholar
  25. 25.
    Farokhi, H., Ghayesh, M.H.: Supercritical nonlinear parametric dynamics of Timoshenko microbeams. Commun. Nonlinear Sci. Numer. Simul. 59, 592–605 (2018)MathSciNetCrossRefGoogle Scholar
  26. 26.
    Shen, H.S.: Postbuckling analysis of axially-loaded functionally graded cylindrical shells in thermal environments. Compos. Sci. Technol. 62, 977–987 (2002)CrossRefGoogle Scholar
  27. 27.
    Shen, H.S.: Postbuckling analysis of pressure-loaded functionally graded cylindrical shells in thermal environments. Eng. Struct. 25, 487–497 (2003)CrossRefGoogle Scholar
  28. 28.
    Shen, H.S.: Thermal postbuckling behavior of functionally graded cylindrical shells with temperature-dependent properties. Int. J. Solids Struct. 41, 1961–1974 (2004)CrossRefzbMATHGoogle Scholar
  29. 29.
    Shen, H.S., Noda, N.: Postbuckling of FGM cylindrical shells under combined axial and radial mechanical loads in thermal environments. Int. J. Solids Struct. 42, 4641–4662 (2005)CrossRefzbMATHGoogle Scholar
  30. 30.
    Shen, H.S.: Thermal postbuckling of shear deformable FGM cylindrical shells with temperature-dependent properties. Mech. Adv. Mater. Struct. 14, 439–452 (2007)CrossRefGoogle Scholar
  31. 31.
    Shen, H.S.: Postbuckling of axially loaded FGM hybrid cylindrical shells in thermal environments. Compos. Sci. Technol. 65, 1675–1690 (2005)CrossRefGoogle Scholar
  32. 32.
    Shen, H.S., Noda, N.: Postbuckling of pressure-loaded FGM hybrid cylindrical shells in thermal environments. Compos. Struct. 77, 546–560 (2007)CrossRefGoogle Scholar
  33. 33.
    Huang, H., Han, Q.: Nonlinear buckling and postbuckling of heated functionally graded cylindrical shells under combined axial compression and radial pressure. Int. J. Non-Linear Mech. 44, 209–218 (2009)CrossRefzbMATHGoogle Scholar
  34. 34.
    Huang, H., Han, Q.: Research on nonlinear postbuckling of functionally graded cylindrical shells under radial loads. Compos. Struct. 92, 1352–1357 (2010)CrossRefGoogle Scholar
  35. 35.
    Soltanieh, G., Kabir, M.Z., Shariyat, M.: Snap instability of shallow laminated cylindrical shells reinforced with functionally graded shape memory alloy wires. Compos. Struct. 180, 581–595 (2017)CrossRefGoogle Scholar
  36. 36.
    Dung, D.V., Nga, N.T., Hoa, L.K.: Nonlinear stability of functionally graded material (FGM) sandwich cylindrical shells reinforced by FGM stiffeners in thermal environment. Appl. Math. Mech. 38(5), 647–670 (2017)MathSciNetCrossRefzbMATHGoogle Scholar
  37. 37.
    Dung, D.V., Nga, N.T., Vuong, P.M.: Nonlinear stability analysis of stiffened functionally graded material sandwich cylindrical shells with general Sigmoid law and power law in thermal environment using third-order shear deformation theory. J. Sandw. Struct. Mater 21, 938–972 (2019)CrossRefGoogle Scholar
  38. 38.
    Huang, H., Han, Q.: Buckling of imperfect functionally graded cylindrical shells under axial compression. Eur. J. Mech. A/Solids 27, 1026–1036 (2008)CrossRefzbMATHGoogle Scholar
  39. 39.
    Huang, H., Han, Q.: Nonlinear buckling of torsion-loaded functionally graded cylindrical shells in thermal environment. Eur. J. Mech. A/Solids 29, 42–48 (2010)MathSciNetCrossRefGoogle Scholar
  40. 40.
    Huang, H., Han, Q., Feng, N., Fan, X.: Buckling of functionally graded cylindrical shells under combined loads. Mech. Adv. Mater. Struct. 18, 337–346 (2011)CrossRefGoogle Scholar
  41. 41.
    Huang, H., Han, Q., Wei, D.: Buckling of FGM cylindrical shells subjected to pure bending load. Compos. Struct. 93, 2945–2952 (2011)CrossRefGoogle Scholar
  42. 42.
    Shahsiah, R., Eslami, M.R.: Thermal buckling of functionally graded cylindrical shell. AIAA J. 41(9), 1819–1826 (2003)CrossRefGoogle Scholar
  43. 43.
    Wu, L., Jiang, Z., Liu, J.: Thermoelastic stability of functionally graded cylindrical shells. Compos. Struct. 70, 60–68 (2005)CrossRefGoogle Scholar
  44. 44.
    Sofiyev, A.H., Kuruoglu, N.: Parametric instability of shear deformable sandwich cylindrical shells containing an FGM core under static and time dependent periodic axial loads. Int. J. Mech. Sci. 101, 114–123 (2015)CrossRefGoogle Scholar
  45. 45.
    Mohammadzadeh, R., Najafizadeh, M.M., Nejati, M.: Buckling of 2D-FG cylindrical shells under combined external pressure and axial compression. Adv. Appl. Math. Mech. 5(3), 391–406 (2013)MathSciNetCrossRefzbMATHGoogle Scholar
  46. 46.
    Allahkarami, F., Satouri, S., Najafizadeh, M.M.: Mechanical buckling of two-dimensional functionally graded cylindrical shells surrounded by Winkler–Pasternak elastic foundation. Mech. Adv. Mater. Struct. 23(8), 873–887 (2016)CrossRefGoogle Scholar
  47. 47.
    Lopatin, A.V., Morozov, E.V.: Buckling of the composite sandwich cylindrical shell with clamped ends under uniform external pressure. Compos. Struct. 122, 209–216 (2015)CrossRefGoogle Scholar
  48. 48.
    Sun, F., Fan, H., Zhou, C., Fang, D.: Equivalent analysis and failure prediction of quasi-isotropic composite sandwich cylinder with lattice core under uniaxial compression. Compos. Struct. 101, 180–190 (2013)CrossRefGoogle Scholar
  49. 49.
    Xiong, J., Ghosh, R., Ma, L., Vaziri, A., Wang, Y., Wu, L.: Sandwich-walled cylindrical shells with lightweight metallic lattice truss cores and carbon fiber-reinforced composite face sheets. Compos. Part A Appl. Sci. Manuf. 56, 226–238 (2014)CrossRefGoogle Scholar
  50. 50.
    Ghahfarokhi, D.S., Rahimi, G.: An analytical approach for global buckling of composite sandwich cylindrical shells with lattice cores. Int. J. Solids Struct. 146, 69–79 (2018)CrossRefGoogle Scholar
  51. 51.
    Fallah, F., Taati, E., Asghari, M.: Decoupled stability equation for buckling analysis of FG and multilayered cylindrical shells based on the first-order shear deformation theory. Compos. Part B Eng. 154, 225–241 (2018)CrossRefGoogle Scholar
  52. 52.
    Shen, H.S.: A Two-Step Perturbation Method in Nonlinear Analysis of Beams, Plates and Shells. Wiley, New York (2013)CrossRefzbMATHGoogle Scholar
  53. 53.
    Kaplan, W.: Operational Methods for Linear Systems. Addison-Wesley Pub. Co, Boston (1962)zbMATHGoogle Scholar
  54. 54.
    Timoshenko, S.P., Gere, J.M.: Theory of Elastic Stability. Courier Corporation, Mineola (2009)Google Scholar

Copyright information

© Springer-Verlag GmbH Austria, part of Springer Nature 2019

Authors and Affiliations

  1. 1.School of Mechanical EngineeringSharif University of TechnologyTehranIran

Personalised recommendations