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Analytical Solution for Large Deflection of Multilayered Composite Cantilever Beams with Interlayer Slip

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The solution methodologies for nonlinear differential equations play a significant role in the area of theoretical mechanics, in particular large deflection of beams. In this paper, Euler–Bernoulli’s equation is adapted along with R. Da Silva method for solving the problem of large deflection on multilayered cantilever beams with interlayer slip analytically. Interlayer slip, horizontal displacement and large deflection nonlinear differential equations of multilayered Euler–Bernoulli cantilever beams were derived. The equations are applied to the typical partially interacted multilayered cantilever beam problem with point and uniformly distributed load. Solutions of the geometrically linear theory and geometrically nonlinear theory are compared.

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  1. Barten HJ (1944) On the deflection of cantilever beam. Q Appl Math 2, 16&171 and ibid. 3, 275–276 (1945) (The second article corrects a mistake in the first one)

  2. Battini JM, Nguyen QH, Hjiaj M (2009) Non-linear finite element analysis of composite beams with interlayer slip. Comput Struct 87:904–912

  3. Bisshopp KE, Drucker DC (1945) Large deflections of cantilever beams. Q Appl Math 3:272–275

  4. Brojan M, Videnič T, Kosel F (2009) Large deflections of non-linearly elastic non-prismatic cantilever beams made from materials obeying the generalized Ludwick constitutive law. Meccanica 44:733–739

  5. Campi F, Monetto I (2013) Analytical solutions of two-layer beams with interlayer slip and bi-linear interface law. Int J Solids Struct 50:687–698

  6. Čas B, Saje M, Planinc I (2004) Non-linear finite element analysis of composite planar frames with an interlayer slip. Comput Struct 82:1901–1912

  7. Da Silva AR, Sousa JBM Jr (2009) A family of interface elements for the analysis of composite beams with interlayer slip. Finite Elem Anal Des 45:305–314

  8. Fertis DG (2006) Non-linear structural engineering with unique theories and methods to solve effectively complex non-linear problems. Springer, New York. ISBN 978-3-540-32975-6

  9. Frisch-Fay R (1962) Flexible bars. Butterworths & Co limited, London

  10. Girhammar UA (2009) A simplified analysis method for composite beams with interlayer slip. Int J Mech Sci 51:515–530

  11. Girhammar UA, Pan DH (2007) Exact static analysis of partially composite beams and beam-columns. Int J Mech Sci 49:239–255

  12. Hjiaj M, Battini JM, Nguyen QH (2012) Large displacement analysis of shear deformable composite beams with interlayer slips. Int J Non-linear Mech 47:895–904

  13. Iyengar KTSR, Naqvi MM (1966) Large deflections of rectangular plates. Int J Non-linear Mech 1:109–122

  14. Lee K (2002) Large deflections of cantilever beams of non-linear elastic material under a combined loading. Int J Non-linear Mech 37:439–443

  15. Lewis G, Monasa F (1981) Large deflections of cantilever beams of non-linear materials. Comput Struct 14:357–360

  16. Lewis G, Monasa F (1982) Large deflections of cantilever beams of non-linear materials of the Ludwick type subjected to an end moment. Int J Non-linear Mech 17:1–6

  17. Newmark NM, Siess CP, Viest IM (1951) Tests and analysis of composite beams with incomplete interaction. Proc Soc Exp Stress Anal 9(1):75–92

  18. Ranzi G (2008) Locking problems in the partial interaction analysis of multi-layered composite beams. Eng Struct 30:2900–2911

  19. Ranzi G, Dall’Asta A, Ragni L, Zona A (2010) A geometric non-linear model for composite beams with partial interaction. Eng Struct 32:1384–1396

  20. Sousa JBM Jr, Da Silva AR (2010) Analytical and numerical analysis of multilayered beams with inter-layer slip. Eng Struct 32:1671–1680

  21. Zhang Y, Wang S, Petersson B (2003) Large deflection analysis of composite laminates. J Mater Process Technol 138:34–40

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“Large deflection of multilayered composite cantilever beams with interlayer slip” study was funded by VIT University, Vellore, India—632014.

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Correspondence to Loganathan Rajendran.

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Conflict of interest

R. Loganathan has received research grants as Research scholar from VIT University. Dr. Arun Tom Mathew is working as the Professor in VIT university (School of Mechanical Engineering). The authors declare that they have no conflict of interest.

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Rajendran, L., Mathew, A.T. Analytical Solution for Large Deflection of Multilayered Composite Cantilever Beams with Interlayer Slip. Iran J Sci Technol Trans Mech Eng 44, 23–33 (2020). https://doi.org/10.1007/s40997-018-0246-x

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  • Multilayered beams
  • Interlayer slip
  • Large deflection
  • Nonlinear
  • Partial interaction