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.
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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)
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)
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)
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)
SHAKOURI, M., SHARGHI, H., and KOUCHAKZADEH, M. Torsional buckling of generally laminated conical shell. Meccanica, 52(4/5), 1051–1061 (2017)
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)
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)
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)
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)
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)
ESAWI, A. M. and FARAG, M. M. Carbon nanotube reinforced composites: potential and current challenges. Materials and Design, 28(9), 2394–2401 (2007)
TJONG, S. C. Carbon Nanotube Reinforced Composites: Metal and Ceramic Matrices, John Wiley & Sons, Weinheim (2009)
BAKSHI, S., LAHIRI, D., and AGARWAL, A. Carbon nanotube reinforced metal matrix composites: a review. International Materials Reviews, 55(1), 41–64 (2010)
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)
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)
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)
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)
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)
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)
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)
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
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)
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)
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)
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)
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)
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)
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
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)
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)
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)
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)
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)
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)
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)
VOL’MIR, A. D. S. Stability of Elastic Systems, Foreign Technology Division, Wright-Patterson Air Force Base, Ohio (1965)
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)
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)
YASMIN, A. and DANIEL, I. M. Mechanical and thermal properties of graphite platelet/epoxy composites. Polymer, 45(24), 8211–8219 (2004)
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)
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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
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DOI: https://doi.org/10.1007/s10483-019-2498-8