Steel and Composite Structures

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Buckling and stability analysis of sandwich beams subjected to varying axial loads

  • Eltaher, Mohamed A. (Department of Mechanical Engineering, Faculty of Engineering, King Abdulaziz University) ;
  • Mohamed, Salwa A (Department of Engineering Mathematics, Faculty of Engineering, Zagazig University)
  • Received : 2019.09.24
  • Accepted : 2019.12.12
  • Published : 2020.01.25
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Abstract

This article presented a comprehensive model to study static buckling stability and associated mode-shapes of higher shear deformation theories of sandwich laminated composite beam under the compression of varying axial load function. Four higher order shear deformation beam theories are considered in formulation and analysis. So, the model can consider the influence of both thick and thin beams without needing to shear correction factor. The compression force can be described through axial direction by uniform constant, linear and parabolic distribution functions. The Hamilton's principle is exploited to derive equilibrium governing equations of unified sandwich laminated beams. The governing equilibrium differential equations are transformed to algebraic system of equations by using numerical differential quadrature method (DQM). The system of equations is solved as an eigenvalue problem to get critical buckling loads and their corresponding mode-shapes. The stability of DQM in determining of buckling loads of sandwich structure is performed. The validation studies are achieved and the obtained results are matched with those. Parametric studies are presented to figure out effects of in-plane load type, sandwich thickness, fiber orientation and boundary conditions on buckling loads and mode-shapes. The present model is important in designing process of aircraft, naval structural components, and naval structural when non-uniform in-plane compressive loading is dominated.

Keywords

Acknowledgement

Supported by : King Abdulaziz University

This work was funded by the Deanship of Scientific Research (DSR), King Abdulaziz University, Jeddah, under grant No. (DF-062-135-1441). The authors, therefore, acknowledge with thanks DSR technical and financial support.

References

  1. 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.
  2. Akbas, S.D. (2018a), "Thermal post-buckling analysis of a laminated composite beam", Struct. Eng. Mech., 67(4), 337-346. https://doi.org/10.12989/sem.2018.67.4.337.
  3. 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.
  4. Akbas, S.D. (2019), "Hygrothermal post-buckling analysis of laminated composite beams", Int. J. Appl. Mech., 11(01), 1950009. https://doi.org/10.1142/S1758825119500091.
  5. 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.
  6. Ascione, A. and Gherlone, M. (2018), "Nonlinear static response analysis of sandwich beams using the Refined Zigzag Theory", J. Sandw. Struct. Mater., https://doi.org/10.1177/1099636218795381.
  7. Assie, A.E., Eltaher, M.A. and Mahmoud, F.F. (2011), "Behavior of a viscoelastic composite plates under transient load", J. Mecha, Sci. Technol., 25(5), 1129. https://doi.org/10.1007/s12206-011-0302-6.
  8. Basaglia, C., Camotim, D. and Silvestre, N. (2013), "Post-buckling analysis of thin-walled steel frames using generalised beam theory (GBT)", Thin-Wall. Struct., 62, 229-242. https://doi.org/10.1016/j.tws.2012.07.003.
  9. Chen, Z., Li, J., Sun, L. and Li, L.Y. (2019), "Flexural buckling of sandwich beams with thermal-induced non-uniform sectional properties", J. Build.Eng., 25, 100782. https://doi.org/10.1016/j.jobe.2019.100782.
  10. Chowdhury, S.R. and Reddy, J.N. (2019), "Geometrically exact micropolar Timoshenko beam and its application in modelling sandwich beams made of architected lattice core", Compos. Struct., 226, 111228. https://doi.org/10.1016/j.compstruct.2019.111228.
  11. Dabbagh, A., Rastgoo, A. and Ebrahimi, F. (2019), "Finite element vibration analysis of multi-scale hybrid nanocomposite beams via a refined beam theory", Thin-Wall. Struct., 140, 304-317. https://doi.org/10.1016/j.tws.2019.03.031.
  12. Ebrahimi, F. and Farazmandnia, N. (2018), "Thermal buckling analysis of functionally graded carbon nanotube-reinforced composite sandwich beams", Steel Compos. Struct., 27(2), 149-159. https://doi.org/10.12989/scs.2018.27.2.149.
  13. 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.
  14. 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.
  15. 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. https://doi.org/10.1016/j.compstruct.2012.11.039.
  16. 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.
  17. 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.
  18. 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.
  19. 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. https://doi.org/10.1016/j.apm.2019.05.026
  20. Eltaher, M.A. and Mohamed, S.A. (2020), "Buckling and stability analysis of sandwich beams subjected to varying axial loads" Steel Compos. Struct.
  21. Eltaher, M.A., Mohamed, S.A. and Melaibari, M. (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.
  22. Emam, S.A. (2011), "Analysis of shear-deformable composite beams in postbuckling", Compos. Struct., 94(1), 24-30. https://doi.org/10.1016/j.compstruct.2011.07.024.
  23. 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.
  24. Emam, S., Eltaher, M., Khater, M. and Abdalla, W. (2018), "Postbuckling and free vibration of multilayer imperfect nanobeams under a pre-stress load", Appl. Scie., 8(11), 2238. https://doi.org/10.3390/app8112238
  25. Garg, A. and Chalak, H.D. (2019), "A review on analysis of laminated composite and sandwich structures under hygrothermal conditions", Thin-Wall. Struct., 142, 205-226. https://doi.org/10.1016/j.tws.2019.05.005.
  26. Hamed, M.A., 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.
  27. Jun, L., Xiang, H. & 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.
  28. 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.
  29. Kang, J.H. and Leissa, A.W. (2005), "Exact solutions for the buckling of rectangular plates having linearly varying in-plane loading on two opposite simply supported edges", Int. J. Solids Struct., 42(14), 4220-4238. https://doi.org/10.1016/j.ijsolstr.2004.12.011.
  30. 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.
  31. Kahya, V. and Turan, M. (2018), "Vibration and stability analysis of functionally graded sandwich beams by a multi-layer finite element", Compos. Part B: Eng., 146, 198-212. https://doi.org/10.1016/j.compositesb.2018.04.011.
  32. Li, C., Shen, H.S. and Wang, H. (2019), "Nonlinear bending of sandwich beams with functionally graded negative Poisson's ratio honeycomb core", Compos. Struct., 212, 317-325. https://doi.org/10.1016/j.compstruct.2019.01.020
  33. Li, W., Ma, H. and Gao, W. (2019), "A higher-order shear deformable mixed beam element model for accurate analysis of functionally graded sandwich beams", Compos. Struct., 221, 110830. https://doi.org/10.1016/j.compstruct.2019.04.002.
  34. MalekzadehFard, K., Gholami, M., Reshadi, F. and Livani, M. (2017), "Free vibration and buckling analyses of cylindrical sandwich panel with magneto rheological fluid layer", J. Sandw. Struct. Mater., 19(4), 397-423. https://doi.org/10.1177/1099636215603034.
  35. Martins, A.D. and Silvestre, N. (2019), "Modal analysis of the post-buckling behaviour of cylindrical steel panels under compression: Imperfection sensitivity and local2 interaction", Thin-Wall. Struct., 144, 106345. https://doi.org/10.1016/j.tws.2019.106345.
  36. Meirovitch, L. (2010), Methods of analytical dynamics, Courier Corporation
  37. Meyer-Piening, H. R. (2006), "Sandwich plates: Stresses, deflection, buckling and wrinkling loads-A case study", J. Sandw. Struct. Mater., 8(5), 381-394. https://doi.org/10.1177/1099636206064825
  38. 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.2018.02.014.
  39. 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.
  40. Meradjah, M., Kaci, A., Houari, M.S.A., Tounsi, A. and Mahmoud, S.R. (2015), "A new higher order shear and normal deformation theory for functionally graded beams", Steel Compos. Struct., 18(3), 793-809. https://doi.org/10.12989/scs.2015.18.3.793.
  41. Nasrekani, F.M. and Eipakchi, H. (2019), "Analytical solution for buckling analysis of cylinders with varying thickness subjected to combined axial and radial loads", Int. J. Pressure Vessels Piping, 172, 220-226. https://doi.org/10.1016/j.ijpvp.2019.03.036.
  42. Nguyen, T.K. and Nguyen, B.D. (2015), "A new higher-order shear deformation theory for static, buckling and free vibration analysis of functionally graded sandwich beams", J. Sandw. Struct. Mater., 17(6), 613-631. https://doi.org/10.1177/1099636215589237.
  43. Nguyen, T.K., Vo, T.P., Nguyen, B.D. and Lee, J. (2016), "An analytical solution for buckling and vibration analysis of functionally graded sandwich beams using a quasi-3D shear deformation theory", Compos. Struct., 156, 238-252. https://doi.org/10.1016/j.compstruct.2015.11.074.
  44. Osmani, A. and Meftah, S.A. (2018), "Lateral buckling of tapered thin walled bi-symmetric beams under combined axial and bending loads with shear deformations allowed", Eng. Struct., 165, 76-87. https://doi.org/10.1016/j.engstruct.2018.03.009.
  45. Panda, S.K. and Ramachandra, L.S. (2010), "Buckling of rectangular plates with various boundary conditions loaded by non-uniform inplane loads", Int. J. Mech. Sci., 52(6), 819-828. https://doi.org/10.1016/j.ijmecsci.2010.01.009.
  46. Salami, S.J. and Dariushi, S. (2018), "Geometrically nonlinear analysis of sandwich beams under low velocity impact: analytical and experimental investigation", Steel Compos. Struct., 27(3), 273-283. https://doi.org/10.12989/scs.2018.27.3.273.
  47. Sayyad, A.S. and Ghugal, Y.M. (2017), "A unified shear deformation theory for the bending of isotropic, functionally graded, laminated and sandwich beams and plates", Int. J. Appl. Mech., 9(1), 1750007. https://doi.org/10.1142/S1758825117500077.
  48. Sayyad, A.S. and Ghugal, Y.M. (2019a), "A unified five-degree-of-freedom theory for the bending analysis of softcore and hardcore functionally graded sandwich beams and plates", J. Sandw. Struct. Mater., https://doi.org/10.1177/1099636219840980.
  49. Sayyad, A.S. and Ghugal, Y.M. (2019), "A sinusoidal beam theory for functionally graded sandwich curved beams", Compos. Struct., 226, 111246. https://doi.org/10.1016/j.compstruct.2019.111246.
  50. Shen, Q., Wang, J., Wang, Y. and Wang, F. (2019), "Analytical modelling and design of partially CFRP-wrapped thin-walled circular NCFST stub columns under axial compression", Thin-Wall. Struct., 144, 106276. https://doi.org/10.1016/j.tws.2019.106276.
  51. Silvestre, N. and Camotim, D. (2002a), "First-order generalised beam theory for arbitrary orthotropic materials", Thin-Wall. Struct., 40(9), 755-789. https://doi.org/10.1016/S0263-8231(02)00025-3.
  52. Silvestre, N. and Camotim, D. (2002b), "Second-order generalised beam theory for arbitrary orthotropic materials", Thin-Wall. Struct., 40(9), 791-820. https://doi.org/10.1016/S0263-8231(02)00026-5.
  53. Silvestre, N. (2007), "Generalised beam theory to analyse the buckling behaviour of circular cylindrical shells and tubes", Thin-Wall. Struct., 45(2), 185-198. https://doi.org/10.1016/j.tws.2007.02.001.
  54. 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.
  55. Singh, S.J. and Harsha, S.P. (2019), "Buckling analysis of FGM plates under uniform, linear and non-linear in-plane loading", J. Mech. Sci. Technol., 33(4), 1761-1767. https://doi.org/10.1007/s12206-019-0328-8.
  56. Wang, W. and Shenoi, R.A. (2004), "Analytical solutions to predict flexural behavior of curved sandwich beams", J. Sandw. Struct. Mater., 6(3), 199-216. https://doi.org/10.1177/1099636204032855.

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