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http://dx.doi.org/10.12989/scs.2020.34.1.075

Buckling analysis of sandwich beam rested on elastic foundation and subjected to varying axial in-plane loads  

Hamed, Mostafa A. (Mechanical Engineering Department, Faculty of Engineering, King Abdulaziz University)
Mohamed, Salwa A (Department of Engineering Mathematics, Faculty of Engineering, Zagazig University)
Eltaher, Mohamed A. (Mechanical Engineering Department, Faculty of Engineering, King Abdulaziz University)
Publication Information
Steel and Composite Structures / v.34, no.1, 2020 , pp. 75-89 More about this Journal
Abstract
The current paper illustrates the effect of in-plane varying compressive force on critical buckling loads and buckling modes of sandwich composite laminated beam rested on elastic foundation. To generalize a proposed model, unified higher order shear deformation beam theories are exploited through analysis; those satisfy the parabolic variation of shear across the thickness. Therefore, there is no need for shear correction factor. Winkler and Pasternak elastic foundations are presented to consider the effect of any elastic medium surrounding beam structure. The Hamilton's principle is proposed to derive the equilibrium equations of unified sandwich composite laminated beams. Differential quadrature numerical method (DQNM) is used to discretize the differential equilibrium equations in spatial direction. After that, eigenvalue problem is solved to obtain the buckling loads and associated mode shapes. The proposed model is validated with previous published works and good matching is observed. The numerical results are carried out to show effects of axial load functions, lamination thicknesses, orthotropy and elastic foundation constants on the buckling loads and mode shapes of sandwich composite beam. This model is important in designing of aircrafts and ships when non-uniform compressive load and shear loading is dominated.
Keywords
buckling stability; in-plane load function; sandwich beams; unified beam theories; elastic foundations; Differential Quadrature Method (DQM);
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Times Cited By KSCI : 18  (Citation Analysis)
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1 Panda, S.K. and Ramachandra, L.S. (2010), "Buckling of rectangular plates with various boundary conditions loaded by non-uniform in-plane loads", Int. J. Mech. Sci., 52(6), 819-828. https://doi.org/10.1016/j.ijmecsci.2010.01.009.   DOI
2 Reddy, J.N. (2003), Mechanics of laminated composite plates and shells: theory and analysis. CRC press.
3 Sedighi, H.M., Shirazi, K.H. and Zare, J. (2012a), "An analytic solution of transversal oscillation of quintic non-linear beam with homotopy analysis method", Int. J. Non-Linear Mech., 47(7), 777-784. https://doi.org/10.1016/j.ijnonlinmec.2012.04.008.   DOI
4 Sedighi, H.M., Shirazi, K.H., Noghrehabadi, A.R. and Yildirim, A. (2012b), "Asymptotic investigation of buckled beam nonlinear vibration. Iranian Journal of Science and Technology", T. Mech. Eng., 36(M2), 107-116.
5 Abdalrahmaan, A.A., Eltaher, M.A., Kabeel, A.M., Abdraboh, A.M. and Hendi, A.A. (2019), "Free and forced analysis of perforated beams", Steel Compos. Struct., 31(5), 489-502. https://doi.org/10.12989/scs.2019.31.5.489.   DOI
6 She, G.L., Yan, K.M., Zhang, Y.L., Liu, H.B. and Ren, Y.R. (2018b), "Wave propagation of functionally graded porous nanobeams based on non-local strain gradient theory", Eur. Phys. J. Plus, 133(9), 368.   DOI
7 Sedighi, H.M. and Daneshmand, F. (2014), "Nonlinear transversely vibrating beams by the homotopy perturbation method with an auxiliary term", J. Appl. Comput. Mech., 1(1), 1-9.
8 She, G.L., Yuan, F.G. and Ren, Y.R. (2017), "Thermal buckling and post-buckling analysis of functionally graded beams based on a general higher-order shear deformation theory", Appl. Math. Model., 47, 340-357. https://doi.org/10.1016/j.apm.2017.03.014.   DOI
9 She, G.L., Ren, Y.R., Xiao, W.S. and Liu, H. (2018a), "Study on thermal buckling and post-buckling behaviors of FGM tubes resting on elastic foundations", Struct. Eng. Mech., 66(6), 729-736. https://doi.org/10.12989/sem.2018.66.6.729.   DOI
10 She, G.L., Jiang, X.Y. and Karami, B. (2019a), "On thermal snapbuckling of FG curved nanobeams", Mater. Res. Express, 6(11), 115008.   DOI
11 Akbas, S.D. (2019a), "Hygrothermal post-buckling analysis of laminated composite beams", Int. J. Appl. Mech., 11(1), 1950009. https://doi.org/10.1142/S1758825119500091.   DOI
12 Akbas, S.D. (2018a), "Geometrically nonlinear analysis of a laminated composite beam", Struct. Eng. Mech., 66(1), 27-36. https://doi.org/10.12989/sem.2018.66.1.27.   DOI
13 Akbas, S.D. (2018b), "Post-buckling responses of a laminated composite beam", Steel Compos. Struct., 26(6), 733-743. https://doi.org/10.12989/scs.2018.26.6.733.   DOI
14 Akbas, S.D. (2018c), "Nonlinear thermal displacements of laminated composite beams", Coupled Syst. Mech., 7(6), 691-705. https://doi.org/10.12989/csm.2018.7.6.691.   DOI
15 Akbas, S.D. (2019b), "Hygro-thermal post-buckling analysis of a functionally graded beam", Coupled Syst. Mech., 8(5), 459-471. https://doi.org/10.12989/csm.2019.8.5.459.   DOI
16 Almitani, K.H., Abdalrahmaan, A.A. and Eltaher, M.A. (2019), "On forced and free vibrations of cutout squared beams", Steel Compos. Struct., 32(5), 643-655. https://doi.org/10.12989/scs.2019.32.5.643.   DOI
17 Assie, A.E., Eltaher, M.A. and Mahmoud, F.F. (2011), "Behavior of a viscoelastic composite plates under transient load", J. Mech. Sci. Technol., 25(5), 1129. https://doi.org/10.1007/s12206-011-0302-6.   DOI
18 Shimpi, R.P., Guruprasad, P.J. and Pakhare, K.S. (2019), "Simple two variable refined theory for shear deformable isotropic rectangular beams", J. Appl. Comput. Mech.. 10.22055/JACM.2019.29555.1615.
19 Bessaim, A., Ahmed Houari, M.S., Abdelmoumen Anis, B., Kaci, A., Tounsi, A., Bedia, A. and Abbes, E. (2018), "Buckling analysis of embedded nanosize FG beams based on a refined hyperbolic shear deformation theory", J. Appl. Comput. Mech., 4(3), 140-146.
20 She, G.L., Ren, Y.R. and Yan, K.M. (2019b), "On snap-buckling of porous FG curved nanobeams", Acta Astronautica, 161, 475-484. https://doi.org/10.1016/j.actaastro.2019.04.010.   DOI
21 Eltaher, M.A., Alshorbagy, A.E. and Mahmoud, F.F. (2013b), "Determination of neutral axis position and its effect on natural frequencies of functionally graded macro/nanobeams", Compos. Struct., 99, 193-201.   DOI
22 Dehrouyeh-Semnani, A.M. (2018), "On the thermally induced non-linear response of functionally graded beams", Int. J. Eng. Sci., 125, 53-74. https://doi.org/10.1016/j.ijengsci.2017.12.001.   DOI
23 Eltaher, M.A., Emam, S.A. and Mahmoud, F.F. (2012), "Free vibration analysis of functionally graded size-dependent nanobeams", Appl. Math. Comput., 218(14), 7406-7420. https://doi.org/10.1016/j.amc.2011.12.090.   DOI
24 Eltaher, M.A., Emam, S.A. and Mahmoud, F.F. (2013a), "Static and stability analysis of nonlocal functionally graded nanobeams", Compos. Struct., 96, 82-88. https://doi.org/10.1016/j.compstruct.2012.09.030.   DOI
25 Eltaher, M.A., Khairy, A., Sadoun, A.M. and Omar, F.A. (2014a), "Static and buckling analysis of functionally graded Timoshenko nanobeams", Appl. Math. Comput., 229, 283-295. https://doi.org/10.1016/j.amc.2013.12.072.   DOI
26 Eltaher, M.A., Abdelrahman, A.A., Al-Nabawy, A., Khater, M. and Mansour, A. (2014b), "Vibration of nonlinear graduation of nano-Timoshenko beam considering the neutral axis position", Appl. Math. Comput., 235, 512-529. https://doi.org/10.1016/j.amc.2014.03.028.   DOI
27 Eltaher, M.A., Mohamed, N., Mohamed, S. and Seddek, L.F. (2019a), "Postbuckling of curved carbon nanotubes using energy equivalent model", J. Nano Res., 57, 136-157. https://doi.org/10.4028/www.scientific.net/JNanoR.57.136.   DOI
28 Soldatos, K.P. and Timarci, T. (1993), "A unified formulation of laminated composite, shear deformable, five-degrees-offreedom cylindrical shell theories", Compos. Struct., 25(1-4), 165-171. https://doi.org/10.1016/0263-8223(93)90162-J.   DOI
29 Shu, C. (2012), "Differential quadrature and its application in engineering", Springer Science & Business Media.
30 Simsek, M. and Reddy, J.N. (2013), "A unified higher order beam theory for buckling of a functionally graded microbeam embedded in elastic medium using modified couple stress theory", Compos. Struct., 101, 47-58. https://doi.org/10.1016/j.compstruct.2013.01.017.   DOI
31 Hamed, M., Sadoun A.M. and Eltaher, M.A., (2019), "Effects of porosity models on static behavior of size dependent functionally graded beam", Struct. Eng. Mech., 71(1), 89-98. https://doi.org/10.12989/sem.2019.71.1.089.   DOI
32 Eltaher, M.A., Mohamed, N., Mohamed, S.A. and Seddek, L.F. (2019b), "Periodic and nonperiodic modes on postbuckling and nonlinear vibration of beams attached with nonlinear foundations", Appl. Math. Model., 75, 414-445.   DOI
33 Eltaher, M.A., Mohamed, S.A. and Melaibari, A. (2020), "Static stability of a unified composite beams under varying axial loads", Thin Wall. Struct., 147, 106488. https://doi.org/10.1016/j.tws.2019.106488.   DOI
34 Emam, S. and Eltaher, M.A. (2016), "Buckling and postbuckling of composite beams in hygrothermal environments", Compos. Struct., 152, 665-675. https://doi.org/10.1016/j.compstruct.2016.05.029.   DOI
35 Emam, S., Eltaher, M., Khater, M. and Abdalla, W. (2018), "Postbuckling and free vibration of multilayer imperfect nanobeams under a pre-stress load", Appl. Sci., 8(11), 2238. https://doi.org/10.3390/app8112238.   DOI
36 Farajpour, A., Shahidi, A.R., Mohammadi, M. and Mahzoon, M. (2012), "Buckling of orthotropic micro/nanoscale plates under linearly varying in-plane load via nonlocal continuum mechanics", Compos. Struct., 94(5), 1605-1615. https://doi.org/10.1016/j.compstruct.2011.12.032Get rights and content.   DOI
37 Hu, H., Badir, A. and Abatan, A. (2003), "Buckling behavior of a graphite/epoxy composite plate under parabolic variation of axial loads", Int. J. Mech. Sci., 45(6-7), 1135-1147. https://doi.org/10.1016/j.ijmecsci.2003.08.003.   DOI
38 Jun, L., Xiang, H. and Xiaobin, L. (2016), "Free vibration analyses of axially loaded laminated composite beams using a unified higher-order shear deformation theory and dynamic stiffness method", Compos. Struct., 158, 308-322. https://doi.org/10.1016/j.compstruct.2016.09.012.   DOI
39 Karamanli, A. and Aydogdu, M. (2019), "Buckling of laminated composite and sandwich beams due to axially varying in-plane loads", Compos. Struct., 210, 391-408. https://doi.org/10.1016/j.compstruct.2018.11.067.   DOI
40 Jun, L., Li, J. and Xiaobin, L. (2017), "A spectral element model for thermal effect on vibration and buckling of laminated beams based on trigonometric shear deformation theory", Int. J. Mech. Sci., 133, 100-111. https://doi.org/10.1016/j.ijmecsci.2017.07.059.   DOI
41 Khater, M.E., Eltaher, M.A., Abdel-Rahman, E. and Yavuz, M. (2014), "Surface and thermal load effects on the buckling of curved nanowires", Eng. Sci. Technol. Int. J., 17(4), 279-283. https://doi.org/10.1016/j.jestch.2014.07.003.   DOI
42 Kim, N.I., Shin, D.K. and Park, Y.S. (2010), "Coupled stability analysis of thin-walled composite beams with closed crosssection", Thin Wall. Struct., 48(8), 581-596. https://doi.org/10.1016/j.tws.2010.03.006.   DOI
43 Mohamed, N., Eltaher, M.A., Mohamed, S.A. and Seddek, L.F. (2019), "Energy equivalent model in analysis of postbuckling of imperfect carbon nanotubes resting on nonlinear elastic foundation", Struct. Eng. Mech., 70(6), 737-750. https://doi.org/10.12989/sem.2019.70.6.737.   DOI
44 Li, C., Shen, H.S. and Wang, H. (2019), "Thermal post-buckling of sandwich beams with functionally graded negative Poisson's ratio honeycomb core", Int. J. Mech. Sci., 152, 289-297. https://doi.org/10.1016/j.ijmecsci.2019.01.002.   DOI
45 Mijuskovis, O., Soris, B. and Ssepanovis, B. (2014), "Exact stress functions implementation in stability analysis of plates with different boundary conditions under uniaxial and biaxial compression", Thin Wall. Struct., 80, 192-206. https://doi.org/10.1016/j.tws.2014.03.006.   DOI
46 Mohamed, N., Eltaher, M.A., Mohamed, S.A. and Seddek, L.F. (2018), "Numerical analysis of nonlinear free and forced vibrations of buckled curved beams resting on nonlinear elastic foundations", Int. J. Non-Linear Mech., 101, 157-173. https://doi.org/10.1016/j.ijnonlinmec.2018.02.014Get rights and content.   DOI