Skip to main content
Log in

Postbuckling analysis of functionally graded graphene platelet-reinforced polymer composite cylindrical shells using an analytical solution approach

  • Published:
Applied Mathematics and Mechanics Aims and scope Submit manuscript

Abstract

An analytical approach is proposed to study the postbuckling of circular cylindrical shells subject to axial compression and lateral pressure made of functionally graded graphene platelet-reinforced polymer composite (FG-GPL-RPC). The governing equations are obtained in the context of the classical Donnell shell theory by the von Kármán nonlinear relations. Then, based on the Ritz energy method, an analytical solution approach is used to trace the nonlinear postbuckling path of the shell. The effects of several parameters such as the weight fraction of the graphene platelet (GPL), the geometrical properties, and distribution patterns of the GPL on the postbuckling characteristics of the FG-GPL-RPC shell are analyzed.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Similar content being viewed by others

References

  1. ZHU, Y., DAI, Y., MA, Q., and TANG, W. Buckling of externally pressurized cylindrical shell: a comparison of theoretical and experimental data. Thin-Walled Structures, 129, 309–316 (2018)

    Article  Google Scholar 

  2. LI, Z. M., LIU, T., and YANG, D. Q. Postbuckling behavior of shear deformable anisotropic laminated cylindrical shell under combined external pressure and axial compression. Composite Structures, 198, 84–108 (2018)

    Article  Google Scholar 

  3. LI, Z. M. and QIAO, P. Buckling and postbuckling of anisotropic laminated cylindrical shells under combined external pressure and axial compression in thermal environments. Composite Structures, 119, 709–726 (2015)

    Article  Google Scholar 

  4. HUANG, H. and HAN, Q. Nonlinear buckling and postbuckling of heated functionally graded cylindrical shells under combined axial compression and radial pressure. International Journal of Non-Linear Mechanics, 44(2), 209–218 (2009)

    Article  MATH  Google Scholar 

  5. SHAKOURI, M., SHARGHI, H., and KOUCHAKZADEH, M. Torsional buckling of generally laminated conical shell. Meccanica, 52(4/5), 1051–1061 (2017)

    Article  MathSciNet  MATH  Google Scholar 

  6. SOFIYEV, A. Application of the FOSDT to the solution of buckling problem of FGM sandwich conical shells under hydrostatic pressure. Composites Part B: Engineering, 144, 88–98 (2018)

    Article  Google Scholar 

  7. GUO, J., CHEN, J., and PAN, E. Analytical three-dimensional solutions of anisotropic multilayered composite plates with modified couple-stress effect. Composite Structures, 153, 321–331 (2016)

    Article  Google Scholar 

  8. GUO, J., CHEN, J., and PAN, E. Size-dependent behavior of functionally graded anisotropic composite plates. International Journal of Engineering Science, 106, 110–124 (2016)

    Article  MathSciNet  MATH  Google Scholar 

  9. SHOKRIEH, M. and RAFIEE, R. A review of the mechanical properties of isolated carbon nanotubes and carbon nanotube composites. Mechanics of Composite Materials, 46(2), 155–172 (2010)

    Article  Google Scholar 

  10. ASHRAFI, B., HUBERT, P., and VENGALLATORE, S. Carbon nanotube-reinforced composites as structural materials for microactuators in microelectromechanical systems. Nanotechnology, 17(19), 4895–4903 (2006)

    Article  Google Scholar 

  11. ESAWI, A. M. and FARAG, M. M. Carbon nanotube reinforced composites: potential and current challenges. Materials and Design, 28(9), 2394–2401 (2007)

    Article  Google Scholar 

  12. TJONG, S. C. Carbon Nanotube Reinforced Composites: Metal and Ceramic Matrices, John Wiley & Sons, Weinheim (2009)

    Book  Google Scholar 

  13. BAKSHI, S., LAHIRI, D., and AGARWAL, A. Carbon nanotube reinforced metal matrix composites: a review. International Materials Reviews, 55(1), 41–64 (2010)

    Article  Google Scholar 

  14. EBRAHIMI, F. and FARAZMANDNIA, N. Thermo-mechanical vibration analysis of sandwich beams with functionally graded carbon nanotube-reinforced composite face sheets based on a higher-order shear deformation beam theory. Mechanics of Advanced Materials and Structures, 24(10), 820–829 (2017)

    Article  Google Scholar 

  15. FU, Y., ZHONG, J., SHAO, X., and TAO, C. Analysis of nonlinear dynamic stability for carbon nanotube-reinforced composite plates resting on elastic foundations. Mechanics of Advanced Materials and Structures, 23(11), 1284–1289 (2016)

    Article  Google Scholar 

  16. THOSTENSON, E. T., REN, Z., and CHOU, T. W. Advances in the science and technology of carbon nanotubes and their composites: a review. Composites Science and Technology, 61(13), 1899–1912 (2001)

    Article  Google Scholar 

  17. LAU, K. T., GU, C., GAO, G. H., LING, H. Y., and REID, S. R. Stretching process of single-and multi-walled carbon nanotubes for nanocomposite applications. Carbon, 42(2), 426–428 (2004)

    Article  Google Scholar 

  18. VEEDU, V. P., CAO, A., LI, X., MA, K., SOLDANO, C., KAR, S., AJAYAN, P. M., and GHASEMI-NEJHAD, M. N. Multifunctional composites using reinforced laminae with carbon-nanotube forests. Nature Materials, 5(6), 457–462 (2006)

    Article  Google Scholar 

  19. KIM, M., PARK, Y. B., OKOLI, O. I., and ZHANG, C. Processing, characterization, and modeling of carbon nanotube-reinforced multiscale composites. Composites Science and Technology, 69(3), 335–342 (2009)

    Article  Google Scholar 

  20. SUN, K., YU, J., ZHANG, C., and ZHOU, X. In situ growth carbon nanotube reinforced SiCf/SiC composite. Materials Letters, 66(1), 92–95 (2012)

    Article  Google Scholar 

  21. AHMADI, M., ANSARI, R., and HASSANZADEH-AGHDAM, M. Low velocity impact analysis of beams made of short carbon fiber/carbon nanotube-polymer composite: a hier-archical finite element approach. Mechanics of Advanced Materials and Structures (2018) https://doi.org/10.1080/15376494.2018.1430276

  22. JI, X. Y., CAO, Y. P., and FENG, X. Q. Micromechanics prediction of the effective elastic moduli of graphene sheet-reinforced polymer nanocomposites. Modelling and Simulation in Materials Science and Engineering, 18(4), 045005 (2010)

    Article  Google Scholar 

  23. TERRONES, M. and TERRONES, H. The carbon nanocosmos: novel materials for the twenty-first century. Philosophical Transactions of the Royal Society of London A: Mathematical, Physical and Engineering Sciences, 361(1813), 2789–2806 (2003)

    Article  Google Scholar 

  24. SHI, G., ARABY, S., GIBSON, C. T., MENG, Q., ZHU, S., and MA, J. Graphene platelets and their polymer composites: fabrication, structure, properties, and applications. Advanced Functional Materials, 28(19), 1706705 (2018)

    Article  Google Scholar 

  25. GHOLAMI, R. and ANSARI, R. Nonlinear harmonically excited vibration of third-order shear deformable functionally graded graphene platelet-reinforced composite rectangular plates. Engineering Structures, 156, 197–209 (2018)

    Article  Google Scholar 

  26. RAFIEE, M., NITZSCHE, F., and LABROSSE, M. Modeling and mechanical analysis of multiscale fiber-reinforced graphene composites: nonlinear bending, thermal post-buckling and large amplitude vibration. International Journal of Non-Linear Mechanics, 103, 104–112 (2018)

    Article  Google Scholar 

  27. LIU, D., KITIPORNCHAI, S., CHEN, W., and YANG, J. Three-dimensional buckling and free vibration analyses of initially stressed functionally graded graphene reinforced composite cylindrical shell. Composite Structures, 189, 560–569 (2018)

    Article  Google Scholar 

  28. GHOLAMI, R. and ANSARI, R. On the nonlinear vibrations of polymer nanocomposite rectangular plates reinforced by graphene nanoplatelets: a unified higher-order shear deformable model. Iranian Journal of Science and Technology, Transactions of Mechanical Engineering (2018) https://doi.org/10.1007/s40997-018-0182-9

  29. KITIPORNCHAI, S., CHEN, D., and YANG, J. Free vibration and elastic buckling of functionally graded porous beams reinforced by graphene platelets. Materials and Design, 116, 656–665 (2017)

    Article  Google Scholar 

  30. SONG, M., YANG, J., and KITIPORNCHAI, S. Bending and buckling analyses of functionally graded polymer composite plates reinforced with graphene nanoplatelets. Composites Part B: Engineering, 134, 106–113 (2018)

    Article  Google Scholar 

  31. GHOLAMI, R. and ANSARI, R. Large deflection geometrically nonlinear analysis of functionally graded multilayer graphene platelet-reinforced polymer composite rectangular plates. Composite Structures, 180, 760–771 (2017)

    Article  Google Scholar 

  32. WANG, Y., FENG, C., ZHAO, Z., and YANG, J. Buckling of graphene platelet reinforced composite cylindrical shell with cutout. International Journal of Structural Stability and Dynamics, 18(3), 1850040 (2018)

    Article  Google Scholar 

  33. WANG, Y., FENG, C., ZHAO, Z., LU, F., and YANG, J. Torsional buckling of graphene platelets (GPLs) reinforced functionally graded cylindrical shell with cutout. Composite Structures, 197, 72–79 (2018)

    Article  Google Scholar 

  34. YANG, J., WU, H., and KITIPORNCHAI, S. Buckling and postbuckling of functionally graded multilayer graphene platelet-reinforced composite beams. Composite Structures, 161, 111–118 (2017)

    Article  Google Scholar 

  35. RAFIEE, M. A., RAFIEE, J., WANG, Z., SONG, H., YU, Z. Z., and KORATKAR, N. Enhanced mechanical properties of nanocomposites at low graphene content. ACS Nano, 3(12), 3884–3890 (2009)

    Article  Google Scholar 

  36. VOL’MIR, A. D. S. Stability of Elastic Systems, Foreign Technology Division, Wright-Patterson Air Force Base, Ohio (1965)

    Google Scholar 

  37. BAGHERIZADEH, E., KIANI, Y., and ESLAMI, M. Mechanical buckling of functionally graded material cylindrical shells surrounded by Pasternak elastic foundation. Composite Structures, 93(11), 3063–3071 (2011)

    Article  Google Scholar 

  38. SHEN, H. S. Postbuckling analysis of axially-loaded functionally graded cylindrical shells in thermal environments. Composites Science and Technology, 62(7/8), 977–987 (2002)

    Article  Google Scholar 

  39. YASMIN, A. and DANIEL, I. M. Mechanical and thermal properties of graphite platelet/epoxy composites. Polymer, 45(24), 8211–8219 (2004)

    Article  Google Scholar 

  40. LIU, F., MING, P., and LI, J. Ab initio calculation of ideal strength and phonon instability of graphene under tension. Physical Review B, 76(6), 064120 (2007)

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to R. Gholami.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Blooriyan, S., Ansari, R., Darvizeh, A. et al. Postbuckling analysis of functionally graded graphene platelet-reinforced polymer composite cylindrical shells using an analytical solution approach. Appl. Math. Mech.-Engl. Ed. 40, 1001–1016 (2019). https://doi.org/10.1007/s10483-019-2498-8

Download citation

  • Received:

  • Revised:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10483-019-2498-8

Key words

Chinese Library Classification

2010 Mathematics Subject Classification

Navigation