Steel and Composite Structures

  • 제16권3호
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  • Pages.325-337
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  • 2014
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  • 1229-9367(pISSN)
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  • 1598-6233(eISSN)
테크노프레스 (Techno-Press)
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Strength and buckling of a sandwich beam with thin binding layers between faces and a metal foam core

  • Magnucki, Krzysztof (Institute of Applied Mechanics, Poznan University of Technology) ;
  • Jasion, Pawel (Institute of Applied Mechanics, Poznan University of Technology) ;
  • Szyc, Waclaw (Institute of Applied Mechanics, Poznan University of Technology) ;
  • Smyczynski, Mikolaj Jan (Institute of Applied Mechanics, Poznan University of Technology)
  • 투고 : 2011.10.17
  • 심사 : 2013.11.09
  • 발행 : 2014.03.25
⟨ 이전 논문 다음 논문 ⟩

초록

The strength and buckling problem of a five layer sandwich beam under axial compression or bending is presented. Two faces of the beam are thin aluminium sheets and the core is made of aluminium foam. Between the faces and the core there are two thin binding glue layers. In the paper a mathematical model of the field of displacements, which includes a share effect and a bending moment, is presented. The system of partial differential equations of equilibrium for the five layer sandwich beam is derived on the basis of the principle of stationary total potential energy. The equations are analytically solved and the critical load is obtained. For comparison reasons a finite element model of the beam is formulated. For the case of bended beam the static analysis has been performed to obtain the stress distribution across the height of the beam. For the axially compressed beam the buckling analysis was carried out to determine the buckling load and buckling shape. Moreover, experimental investigations are carried out for two beams. The comparison of the results obtained in the analytical and numerical (FEM) analysis is shown in graphs and figures. The main aim of the paper is to present an analytical model of the five layer beam and to compare the results of the theoretical, numerical and experimental analyses.

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참고문헌

  1. Allen, H.G. (1969), Analysis and Design of Structural Sandwich Panels, Pergamon Press, Oxford, London, Edinburgh, New York, Toronto, Sydney, Paris, Braunschweig.
  2. Burlayenko, V.N. and Sadowski, T. (2009), "Dynamic behaviour of sandwich plates containing single/multiple debonding", Computat. Mater. Sci., 50(4), 1263-1268.
  3. Burlayenko, V.N. and Sadowski, T. (2010), "Influence of skin/core debonding on free vibration behavior of foam and honeycomb cored sandwich plates", Int. J. Non-Linear Mech., 45(10), 959-968. https://doi.org/10.1016/j.ijnonlinmec.2009.07.002
  4. Carrera, E. (2000), "An assessment of mixed and classical theories on global and local response of multilayered orthotropic plates", Compos. Struct., 50(2), 183-198. https://doi.org/10.1016/S0263-8223(00)00099-4
  5. Chakrabarti, A., Chalak, H.D., Iqbal, M.A. and Sheikh, A.H. (2011), "A new FE model based on higher order zigzag theory for the analysis of laminated sandwich beam with soft core", Composite Structures, 93(2), 271-279. https://doi.org/10.1016/j.compstruct.2010.08.031
  6. Chen, X.W. and Yu, T.X. (2000), "Elastic-plastic beam-on-foundation under quasi-static loading", Int. J. Mech. Sci., 42(12), 2261-2281. https://doi.org/10.1016/S0020-7403(99)00103-4
  7. Grigolyuk, E.I. and Chulkov, P.P. (1973), Stability and Vibrations of Three Layers Shells, Mashinostroene, Moscow, Russia.
  8. Jakobsen, J., Andreasen, J.H. and Bozhevolnaya, E. (2008), "Crack kinking of a delamination at an inclined core junction interface in a sandwich beam", Eng. Fracture Mech., 75(16), 4759-4773. https://doi.org/10.1016/j.engfracmech.2008.06.034
  9. Jasion, P., Magnucka-Blandzi, E., Szyc, W. and Magnucki, K. (2012), "Global and local buckling of sandwich circular and beam-rectangular plates with metal foam core", Thin-Wall. Struct., 61, 154-161. https://doi.org/10.1016/j.tws.2012.04.013
  10. Jasion, P. and Magnucki, K. (2012), "Face wrinkling of sandwich beams under pure bending", J. Theor. Appl. Mech., 50(4), 933-941.
  11. Jasion, P. and Magnucki, K. (2013), "Global buckling of a sandwich column with metal foam core", J. Sandwich Struct. Mater., 15(6), 718-732. https://doi.org/10.1177/1099636213499339
  12. Kasprzak, J. and Ostwald, M. (2006), "A generalized approach to modelling displacements in plates made of non-homogeneous materials", XLV Sympozjon, "Modelling in Mechanics", Wisla, Poland.
  13. Kesler, O. and Gibson, L.J. (2002), "Size effects in metallic foam core sandwich beams", Mater. Sci. Eng. A, 326(2), 228-234. https://doi.org/10.1016/S0921-5093(01)01487-3
  14. Magnucka-Blandzi, E. (2008), "Axi-symmetrical deflection and buckling of circular porous-cellular plate", Thin-Wall. Struct., 46(3), 333-337.
  15. Magnucka-Blandzi, E. (2009), "Dynamic stability of a metal foam circular plate", J. Theor. Appl. Mech., 47(2), 421-433.
  16. Magnucka-Blandzi, E. (2011), "Dynamic stability and static stress state of a sandwich beam with a metal foam core using three modified Timoshenko Hypotheses", Mech. Adv. Mater. Struct., 18(2), 147-158 https://doi.org/10.1080/15376494.2010.496065
  17. Magnucka-Blandzi, E. and Magnucki, K. (2007), "Effective design of a sandwich beam with a metal foam core", Thin-Wall. Struct., 45(4), 432-438. https://doi.org/10.1016/j.tws.2007.03.005
  18. Magnucki, K., Jasion, P., Krus, M., Kuligowski, P. and Wittenbeck, L. (2013a), "Strength and buckling of sandwich beams with corrugated core", J. Theor. Appl. Mech., 51(1), 15-24.
  19. Magnucki, K., Malinowski, M. and Kasprzak, J. (2006), "Bending and buckling of a rectangular porous plate", Steel Compos. Struct., Int. J., 6(4), 319-333. https://doi.org/10.12989/scs.2006.6.4.319
  20. Magnucki, K., Jasion, P., Szyc, W. and Smyczynski, M. (2011), "Strength and buckling of a sandwich beam with thin binding layers between faces and a metal foam core", The 2011 World Congress on Advances in Structural Engineering and Mechanics (ASEM'11), Seoul, Korea, September, pp. 826-835.
  21. Magnucki, K., Smyczynski, M. and Jasion, P. (2013b), "Deflection and strength of a sandwich beam with thin binding layers between faces and a core", Arch. Mech., 65(4), 301-311.
  22. Magnucki, K. and Szyc, W. (2012), "Strength and stability of sandwich beams and plates with aluminium foam core", Wydawnictwo Politechniki Poznanskiej, Poznan. [In Polish]
  23. Noor, A.K., Burton W.S. and Bert C.W. (1996), "Computational models for sandwich panels and shells", Appl. Mech. Reviews, ASME, 49(3), 155-199. https://doi.org/10.1115/1.3101923
  24. Plantema, F.J. (1966), Sandwich Construction, John Wiley & Sons, New York, London, Sydney.
  25. Qin, Q.H. and Wang, T.J. (2009), "An analytical solution for the large deflections of a slender sandwich beam with a metallic foam core under transverse loading by a flat punch", Compos. Struct., 88(4), 509-518. https://doi.org/10.1016/j.compstruct.2008.05.012
  26. Rakow, J.F. and Waas, A.M. (2005), "Size effects and the shear response of aluminium foam", Mech. Mater., 37(1), 69-82. https://doi.org/10.1016/j.mechmat.2003.12.002
  27. Steeves, C.A. and Fleck, N.A. (2004), "Collapse mechanisms of sandwich beams with composite faces and a foam core, loaded in three-point bending. Part I: analytical models and minimum weight design", Int. J. Mech. Sci., 46(4), 561-583. https://doi.org/10.1016/j.ijmecsci.2004.04.003
  28. Vinson, J.R. (2001), "Sandwich structures", Appl. Mech. Reviews, ASME, 54(3), 201-214. https://doi.org/10.1115/1.3097295
  29. Vlasov, V.Z. and Leont'ev, N.N. (1960), Beams, Plates and Shells on Elastic Foundation, Gosud. Izd. Fiz-Mat-Lit, Moscow, Russia.
  30. Wang, C.M., Reddy, J.N. and Lee, K.H. (2000), Shear Deformable Beams and Plates, Elsevier, Amsterdam, Laussane, New York, Oxford, Shannon, Singapore, Tokyo.
  31. Zenkert, D. (1991), "Strength of sandwich beams with interface debondings", Compos. Struct., 17(4), 331-350. https://doi.org/10.1016/0263-8223(91)90025-T
  32. Zhang, C. and Wang, J. (2011), "Delamination of layered structures on elastic foundation", Eng. Fracture Mech., 78(6), 1055-1066. https://doi.org/10.1016/j.engfracmech.2011.01.005

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