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Analytical modelling of multilayer beams with compliant interfaces

  • Skec, L. (University of Rijeka, Faculty of Civil Engineering) ;
  • Schnabl, S. (University of Ljubljana, Faculty of Civil and Geodetic Engineering) ;
  • Planinc, I. (University of Ljubljana, Faculty of Civil and Geodetic Engineering) ;
  • Jelenic, G. (University of Rijeka, Faculty of Civil Engineering)
  • Received : 2012.03.21
  • Accepted : 2012.10.24
  • Published : 2012.11.25

Abstract

Different mathematical models are proposed and their analytical solutions derived for the analysis of linear elastic Reissner's multilayer beams. The models take into account different combinations of contact plane conditions, different material properties of individual layers, different transverse shear deformations of each layer, and different boundary conditions of the layers. The analytical studies are carried out to evaluate the influence of different contact conditions on the static and kinematic quantities. A considerable difference of the results between the models is obtained.

Keywords

References

  1. Adekola, A. (1968), "Partial interaction between elastically connected elements of a composite beam", Int. J. Solids Struct., 4(11), 1125-1135. https://doi.org/10.1016/0020-7683(68)90027-9
  2. Alfano, G. and Crisfield, M.A. (2001), "Finite element interface models for the delamination analysis of laminated composites: mechanical and computational issues", Int. J. Numer. Meth. Eng., 50, 1701-1736. https://doi.org/10.1002/nme.93
  3. Attard, M.M. and Hunt, G.W. (2008), "Sandwich column buckling -A hyperelastic formulation", Int. J. Solids Struct., 45(21), 5540-5555. https://doi.org/10.1016/j.ijsolstr.2008.05.022
  4. Bareisis, J. (2006), "Stiffness and strength of multilayer beams", J. Compos. Mater., 40(6), 515-531. https://doi.org/10.1177/0021998305055267
  5. Challamel, N. and Girhammar, U.A. (2011), "Boundary-layer effect in composite beams with inter-layer slip", J. Aerosp. Eng., 24, 199-209. https://doi.org/10.1061/(ASCE)AS.1943-5525.0000027
  6. Cowper, G.R. (1966), "The shear coefficient in Timoshenko's beam theory", J. Appl. Mech., 33(2), 335-340. https://doi.org/10.1115/1.3625046
  7. rostig, Y. (2003), "Classical and high-order computational models in the analysis of modern sandwich panels", Compos. Part B-Eng., 34, 83-100.
  8. Gara, F., Ranzi, P. and Leoni, G. (2006), "Displacement-based formulations for composite beams with longitudinal slip and vertical uplift", Int. J. Numer. Meth. Eng., 65, 1197-1220. https://doi.org/10.1002/nme.1484
  9. Girhammar, U.A. and Pan, D.H. (2007), "Exact static analysis of partially composite beams and beam-columns", Int. J. Mech. Sci., 49(2), 239-255. https://doi.org/10.1016/j.ijmecsci.2006.07.005
  10. Hjelmstad, K.D. (2005), Fundamentals of Structural Mechanics, Second Edition, Springer-Verlag, New York.
  11. Hozjan, T., Saje, M., Srpcic, S. and Planinc, I. (2013), "Geometrically and materially non-linear analysis of planar structures with an interlayer slip", Comput. Struct., 114-115, 1-17. https://doi.org/10.1016/j.compstruc.2012.09.012
  12. Kryzanowski, A., Schnabl, S., Turk, G. and Planinc, I. (2009), "Exact slip-buckling analysis of two-layer composite columns", Int. J. Solids Struct., 46, 2929-2938. https://doi.org/10.1016/j.ijsolstr.2009.03.020
  13. Kroflic, A., Planinc, I., Saje, M. and Cas, B. (2010a), "Analytical solution of two-layer beam including interlayer slip and uplift", Struct. Eng. Mech., 34(6), 667-683. https://doi.org/10.12989/sem.2010.34.6.667
  14. Kroflic, A., Planinc, I., Saje, M., Turk, G. and Cas, B. (2010b), "Non-linear analysis of two-layer timber beams considering interlayer slip and uplift", Eng. Struct., 32, 1617-1630. https://doi.org/10.1016/j.engstruct.2010.02.009
  15. Kroflic, A., Saje, M. and Planinc, I. (2011), "Non-linear analysis of two-layer beams with interlayer slip and uplift", Comput. Struct., 89(23-24), 2414-2424.
  16. McCutheon, W.J. (1986), "Stiffness of framing members with partial composite action", J. Struct. Eng., ASCE, 112(7), 1623-1637. https://doi.org/10.1061/(ASCE)0733-9445(1986)112:7(1623)
  17. Nguyen, N.T., Oehlers, D.J. and Bradford, M.A. (2001), "An analytical model for reinforced concrete beams with bolted side plates accounting for longitudinal and transverse partial interaction", Int. J. Solids Struct., 38, 6985-6996. https://doi.org/10.1016/S0020-7683(01)00036-1
  18. Perko, L. (2001), Differential Equations and Dynamical Systems, Third Edition, Springer-Verlag, New York.
  19. Ranzi, G., Gara, F. and Ansourian, P. (2006), "General method of analysis for composite beams with longitudinal and transverse partial interaction", Comput. Struct., 84, 2373-2384. https://doi.org/10.1016/j.compstruc.2006.07.002
  20. Ranzi, G., Dall'Asta, A., Ragni, L. and Zona, A. (2010), "A geometric nonlinear model for composite beams with partial interaction", Eng. Struct., 32, 1384-1396. https://doi.org/10.1016/j.engstruct.2010.01.017
  21. Reissner, E. (1972), "On one-dimensional finite-strain beam theory: The plane problem", J. Appl. Mech. Phy. (ZAMP), 23, 795-804. https://doi.org/10.1007/BF01602645
  22. Schnabl, S., Planinc, I., Saje, M., Cas, B. and Turk, G. (2006), "An analytical model of layered continuous beams with partial interaction", J. Struct. Eng. Mech., 22(3), 263-278. https://doi.org/10.12989/sem.2006.22.3.263
  23. Schnabl, S., Saje, M., Turk, G. and Planinc, I. (2007), "Analytical solution of two-layer beam taking into account interlayer slip and shear deformation", J. Struct. Eng. ASCE, 133(6), 886-894. https://doi.org/10.1061/(ASCE)0733-9445(2007)133:6(886)
  24. Schnabl, S. and Planinc, I. (2010), "The influence of boundary conditions and axial deformability on buckling behavior of two-layer composite columns with interlayer slip", Eng. Struct., 32(10), 3103-3111. https://doi.org/10.1016/j.engstruct.2010.05.029
  25. Schnabl, S. and Planinc, I. (2011), "The effect of transverse shear deformation on the buckling of two-layer composite columns with interlayer slip", Int. J. Nonlin. Mech., 46(3), 543-553. https://doi.org/10.1016/j.ijnonlinmec.2011.01.001
  26. Schnabl, S. and Planinc, I. (2013), "Exact buckling loads of two-layer composite Reissner's columns with interlayer slip and uplift", Int. J. Solids Struct., 50(1), 30-37. https://doi.org/10.1016/j.ijsolstr.2012.08.027
  27. Sousa, J.B.M. and da Silva, A.R. (2010), "Analytical and numerical analysis of multilayered beams with interlayer slip", Eng. Struct., 32, 1671-1680. https://doi.org/10.1016/j.engstruct.2010.02.015
  28. Timoshenko, S.P. (1940), Strength of Materials, Part I, Elementary Theory and Problems, 2nd Edition, D. Van Nostrand Company, New York.
  29. Volokh, K.Y. and Needleman, A. (2002), "Buckling of sandwich beams with compliant interfaces", Comput. Struct., 80(14-15), 1329-1335. https://doi.org/10.1016/S0045-7949(02)00076-7
  30. Vu-Quoc, L., Den, H. and Ebcio lu, K. (1996), "Multilayer beams: a geometrically exact formulation", J. Nonlin. Sci., 6, 239-270. https://doi.org/10.1007/BF02439311

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