×

On the nonlinear bending and post-buckling behavior of laminated sandwich cylindrical shells with FG or isogrid lattice cores. (English) Zbl 1428.74147

Summary: 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 [Al; ZrO\(_2\)], [Al; FG core; ZrO\(_2\)], [Al; Gr; ZrO\(_2\)], [Al; Gr; FG core; ZrO\(_2\)], [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.

MSC:

74K25 Shells
74G60 Bifurcation and buckling

Software:

ABAQUS
PDFBibTeX XMLCite
Full Text: DOI

References:

[1] Reddy, J.N.: Mechanics of Laminated Composite Plates and Shells: Theory and Analysis. CRC Press, Boca Raton (2004) · Zbl 1075.74001 · doi:10.1201/b12409
[2] Shiota, I., Miyamoto, Y. (eds.): Functionally Graded Materials 1996. Elsevier, Amsterdam (1997)
[3] Witvrouw, A., Mehta, A.: The use of functionally graded poly-SiGe layers for MEMS applications. Mater. Sci. Forum 492, 255-260 (2005) · doi:10.4028/www.scientific.net/MSF.492-493.255
[4] Ghayesh, M.H., Farokhi, H., Gholipour, A., Tavallaeinejad, M.: Nonlinear oscillations of functionally graded microplates. Int. J. Eng. Sci. 122, 56-72 (2018) · Zbl 06985843 · doi:10.1016/j.ijengsci.2017.03.014
[5] Ghayesh, M.H.: Nonlinear vibration analysis of axially functionally graded shear-deformable tapered beams. Appl. Math. Modell. 59, 583-596 (2018) · Zbl 1480.74107 · doi:10.1016/j.apm.2018.02.017
[6] Ghayesh, M.H.: Dynamics of functionally graded viscoelastic microbeams. Int. J. Eng. Sci. 124, 115-131 (2018) · Zbl 1423.74186 · doi:10.1016/j.ijengsci.2017.11.004
[7] Ghayesh, M.H.: Functionally graded microbeams: simultaneous presence of imperfection and viscoelasticity. Int. J. Mech. Sci. 140, 339-350 (2018) · doi:10.1016/j.ijmecsci.2018.02.037
[8] Ghayesh, M.H., Farokhi, H., Gholipour, A.: Oscillations of functionally graded microbeams. Int. J. Eng. Sci. 110, 35-53 (2017) · Zbl 1423.74483 · doi:10.1016/j.ijengsci.2016.09.011
[9] Vasiliev, V., Morozov, E.V.: Advanced mechanics of composite materials and structural elements, 3rd edn. Elsevier, Newnes (2013)
[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)
[11] Bisagni, C.: Experimental buckling of thin composite cylinders in compression. AIAA J. 37, 276-278 (1999) · doi:10.2514/2.704
[12] Teng, J.G., Rotter, J.M. (eds.): Buckling of Thin Metal Shells. CRC Press, Boca Raton (2006)
[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)
[14] Sanders, L.J.: Nonlinear theories for thin shells. Q. Appl. Math. 21, 21-36 (1963) · doi:10.1090/qam/147023
[15] Koiter, W.T.: On the nonlinear theory of thin elastic shells. In: Proceedings Koniklijke Nederlands Akademie van Wetenschappen, pp. 1-54 (1966)
[16] Yiotis, A.J., Katsikadelis, J.T.: Buckling of cylindrical shell panels: a MAEM solution. Arch. Appl. Mech. 85(9-10), 1545-1557 (2015) · Zbl 1341.74071 · doi:10.1007/s00419-014-0944-9
[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) · Zbl 1356.74075 · doi:10.1007/s00707-012-0705-1
[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) · doi:10.1016/j.ast.2016.05.018
[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) · Zbl 1369.74060 · doi:10.1007/s00707-017-1825-4
[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) · Zbl 1271.74375 · doi:10.1007/s00419-011-0507-2
[21] Ghayesh, M.H., Farokhi, H.: Chaotic motion of a parametrically excited microbeam. Int. J. Eng. Sci. 96, 34-45 (2015) · Zbl 1423.74480 · doi:10.1016/j.ijengsci.2015.07.004
[22] Ghayesh, M.H., Farokhi, H., Hussain, S.: Viscoelastically coupled size-dependent dynamics of microbeams. Int. J. Eng. Sci. 109, 243-255 (2016) · Zbl 1423.74188 · doi:10.1016/j.ijengsci.2016.09.004
[23] Ghayesh, M.H., Farokhi, H.: Nonlinear dynamics of microplates. Int. J. Eng. Sci. 86, 60-73 (2015) · Zbl 1423.74543 · doi:10.1016/j.ijengsci.2014.10.004
[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) · Zbl 1423.74392 · doi:10.1016/j.ijengsci.2012.12.001
[25] Farokhi, H., Ghayesh, M.H.: Supercritical nonlinear parametric dynamics of Timoshenko microbeams. Commun. Nonlinear Sci. Numer. Simul. 59, 592-605 (2018) · Zbl 1510.74071 · doi:10.1016/j.cnsns.2017.11.033
[26] Shen, H.S.: Postbuckling analysis of axially-loaded functionally graded cylindrical shells in thermal environments. Compos. Sci. Technol. 62, 977-987 (2002) · doi:10.1016/S0266-3538(02)00029-5
[27] Shen, H.S.: Postbuckling analysis of pressure-loaded functionally graded cylindrical shells in thermal environments. Eng. Struct. 25, 487-497 (2003) · doi:10.1016/S0141-0296(02)00191-8
[28] Shen, H.S.: Thermal postbuckling behavior of functionally graded cylindrical shells with temperature-dependent properties. Int. J. Solids Struct. 41, 1961-1974 (2004) · Zbl 1106.74352 · doi:10.1016/j.ijsolstr.2003.10.023
[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) · Zbl 1119.74477 · doi:10.1016/j.ijsolstr.2005.02.005
[30] Shen, H.S.: Thermal postbuckling of shear deformable FGM cylindrical shells with temperature-dependent properties. Mech. Adv. Mater. Struct. 14, 439-452 (2007) · doi:10.1080/15376490701298942
[31] Shen, H.S.: Postbuckling of axially loaded FGM hybrid cylindrical shells in thermal environments. Compos. Sci. Technol. 65, 1675-1690 (2005) · doi:10.1016/j.compscitech.2005.02.008
[32] Shen, H.S., Noda, N.: Postbuckling of pressure-loaded FGM hybrid cylindrical shells in thermal environments. Compos. Struct. 77, 546-560 (2007) · doi:10.1016/j.compstruct.2005.08.006
[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) · Zbl 1203.74044 · doi:10.1016/j.ijnonlinmec.2008.11.016
[34] Huang, H., Han, Q.: Research on nonlinear postbuckling of functionally graded cylindrical shells under radial loads. Compos. Struct. 92, 1352-1357 (2010) · doi:10.1016/j.compstruct.2009.11.016
[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) · doi:10.1016/j.compstruct.2017.08.027
[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) · Zbl 1365.74112 · doi:10.1007/s10483-017-2198-9
[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) · doi:10.1177/1099636217704863
[38] Huang, H., Han, Q.: Buckling of imperfect functionally graded cylindrical shells under axial compression. Eur. J. Mech. A/Solids 27, 1026-1036 (2008) · Zbl 1151.74356 · doi:10.1016/j.euromechsol.2008.01.004
[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) · Zbl 1480.74084 · doi:10.1016/j.euromechsol.2009.06.002
[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) · doi:10.1080/15376494.2010.516882
[41] Huang, H., Han, Q., Wei, D.: Buckling of FGM cylindrical shells subjected to pure bending load. Compos. Struct. 93, 2945-2952 (2011) · doi:10.1016/j.compstruct.2011.05.009
[42] Shahsiah, R., Eslami, M.R.: Thermal buckling of functionally graded cylindrical shell. AIAA J. 41(9), 1819-1826 (2003) · doi:10.2514/2.7301
[43] Wu, L., Jiang, Z., Liu, J.: Thermoelastic stability of functionally graded cylindrical shells. Compos. Struct. 70, 60-68 (2005) · doi:10.1016/j.compstruct.2004.08.012
[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) · doi:10.1016/j.ijmecsci.2015.07.025
[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) · Zbl 1279.74024 · doi:10.4208/aamm.2012.m39
[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) · doi:10.1080/15376494.2015.1036181
[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) · doi:10.1016/j.compstruct.2014.11.048
[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) · doi:10.1016/j.compstruct.2013.02.005
[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) · doi:10.1016/j.compositesa.2013.10.008
[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) · doi:10.1016/j.ijsolstr.2018.03.021
[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) · doi:10.1016/j.compositesb.2018.07.051
[52] Shen, H.S.: A Two-Step Perturbation Method in Nonlinear Analysis of Beams, Plates and Shells. Wiley, New York (2013) · Zbl 1292.74001 · doi:10.1002/9781118649893
[53] Kaplan, W.: Operational Methods for Linear Systems. Addison-Wesley Pub. Co, Boston (1962) · Zbl 0143.11204
[54] Timoshenko, S.P., Gere, J.M.: Theory of Elastic Stability. Courier Corporation, Mineola (2009)
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.