Structural Engineering and Mechanics

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Transverse stress determination of composite plates

  • Phoenix, S.S. (Department of Ocean Engineering and Naval Architecture, Indian Institute of Technology) ;
  • Sharma, M. (Department of Ocean Engineering and Naval Architecture, Indian Institute of Technology) ;
  • Satsangi, S.K. (Department of Ocean Engineering and Naval Architecture, Indian Institute of Technology)
  • Received : 2006.07.03
  • Accepted : 2007.06.05
  • Published : 2007.11.10
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Abstract

Analysis of transverse stresses at layer interfaces in a composite laminate has always been a challenging task. Composite structures possess highly irregular material properties at layer interfaces, which cause high shear stresses. Classical Plate Theory and First Order Shear Deformation Theory (FSDT) use post computing to calculate transverse stresses. This paper presents Reissner Mixed Variational Theorem (RMVT) based finite element model to carry out layer-wise analysis of composite laminates. Selective integration scheme has been used. The formulation has been validated by solving numerical examples and comparing the results with those published in the literature.

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References

  1. Aitharaju, V.R. (1999), '$C_{z}^{0}$ zig-zag finite element for analysis of laminated composite beams', J. Eng. Mech., 125, 323-330 https://doi.org/10.1061/(ASCE)0733-9399(1999)125:3(323)
  2. Averill, R.C. and Yip, Y.C. (1996), 'Development of simple, robust finite elements based on refined theories for thick laminated beams', Comput. Struct, 59, 529-546 https://doi.org/10.1016/0045-7949(95)00269-3
  3. Bhaskar, K. and Varadan, T.K. (1989), 'Refinement of higher-order laminated plate theories', AIAA J., 27, 1830-1831 https://doi.org/10.2514/3.10345
  4. Briassoulis, D. (1989), 'On the basics of the shear locking problem of $C^{0}$ isoparametric plate elements', Comput. Struct., 33, 169-185 https://doi.org/10.1016/0045-7949(89)90139-9
  5. Carrera, E. (1996), '$C^{0}$ Reissner - Mindlin multilayered plate elements including zig-zag and inter laminar stress continuity', Int. J. Numer. Meth. Eng., 39, 1797-1820 https://doi.org/10.1002/(SICI)1097-0207(19960615)39:11<1797::AID-NME928>3.0.CO;2-W
  6. Carrera, E. (1997), '$C_{z}^{0}$ Requirements - Models for the two dimensional analysis of multilayered structures', Comput. Struct., 37, 373-383 https://doi.org/10.1016/S0263-8223(98)80005-6
  7. Carrera, E. (1998), 'Evaluation of layer-wise mixed theories for laminated plates analysis', AIAA J., 36, 830-839 https://doi.org/10.2514/2.444
  8. Carrera, E. (2000), 'A priori vs. a posteriori evaluation of transverse stresses in multilayered orthotropic plates', Compos. Struct., 48, 245-260 https://doi.org/10.1016/S0263-8223(99)00112-9
  9. Carrera, E. (2003), 'Historical review of zig-zag theories for multilayered plates and shells', Appl. Mech. Rev., 56, 287-308 https://doi.org/10.1115/1.1557614
  10. Carrera, E. (2004), 'On the use of Murukami's zig-zag function in the modeling of layered plates and shells', Comput. Struct., 82, 541-554 https://doi.org/10.1016/j.compstruc.2004.02.006
  11. Carrera, E. (2005), 'A unified formulation to assess theories of multilayered plates for various bending problems', Compos. Struct., 69, 271-293 https://doi.org/10.1016/j.compstruct.2004.07.003
  12. Carrera, E. and Ciuffieda, A. (2005), 'Bending of composites and sandwich plates subjected to localized lateral loadings: A comparison of various theories', Compos. Struct., 68, 185-202 https://doi.org/10.1016/j.compstruct.2004.03.013
  13. Carrera, E. and Demasi, L. (2002), 'Classical and advanced multilayered plate elements based upon PVD and RMVT. Part 2: Numerical implementations', Int. J. Numer. Meth. Eng., 55, 253-291 https://doi.org/10.1002/nme.493
  14. Carrera, E. and Demasi, L. (2003), 'Two benchmarks to assess two-dimensional theories of sandwich, composite plates', AIAA, 41(7), 1356-1362 https://doi.org/10.2514/2.2081
  15. Carrera, E. and Parisch, H. (1998), 'An evaluation of geometrical nonlinear effects of thin and moderately thick multilayered composite shells', Comput. Struct., 40, 11-24
  16. Cho, M. and Parmerter, R. (1993), 'Efficient Higher order composite plate theory for general lamination configurations', AIAA J., 31, 1299-1306 https://doi.org/10.2514/3.11767
  17. Demasi, L. (2005), 'Refined multilayered plate elements based on Murakami zig-zag functions', Compos. Struct., 70, 308-316 https://doi.org/10.1016/j.compstruct.2004.08.036
  18. Demasi, L. (2006) 'Treatment of stress variables in advanced multilayered plate elements based upon Reissner's mixed variational theorem', Comput. Struct., 84, 1215-1221 https://doi.org/10.1016/j.compstruc.2006.01.036
  19. Demasi, L. (2006), 'Quassi-3D analysis of free vibration of anisotropic plates', Compos. Struct., 74, 449-457 https://doi.org/10.1016/j.compstruct.2005.04.025
  20. Di Sciuva, M. (1992), 'Multilayered anisotropic plate models with continuous interlaminar stresses', Compos. Struct., 22, 149-168 https://doi.org/10.1016/0263-8223(92)90003-U
  21. Lee, C.Y. and Liu, D. (1993), 'Nonlinear analysis of composite plates using interlaminar shear stress continuity theory', Compos. Eng., 3, 151-168 https://doi.org/10.1016/0961-9526(93)90039-M
  22. Murakami, H. (1986), 'Laminated composite plate theory with improved in-plane response', J. Appl. Mech., 53, 661-666 https://doi.org/10.1115/1.3171828
  23. Pagano, N.J. (1969), 'Exact solutions for composite laminates in cylindrical bending', J. Compos. Mater., 3, 398-411 https://doi.org/10.1177/002199836900300304
  24. Pagano, N.J. (1970), 'Exact solutions for rectangular bidirectional composites and sandwich plates', J. Compos. Mater., 4, 20-34 https://doi.org/10.1177/002199837000400102
  25. Pagano, N.J. and Hatfield, S.J. (1972), 'Elastic behavior of multilayered bidirectional composites', AIAA J., 10, 931-933 https://doi.org/10.2514/3.50249
  26. Pawsey, S.F. and Clough, R.W. (1971), 'Improved numerical integration ofthick shell finite elements', Int. J. Numer Meth. Eng., 3, 575-586 https://doi.org/10.1002/nme.1620030411
  27. Reddy, J.N. and. Robbins Jr. D.H. (1994), 'Theories and computational models for composite laminates', Appl. Mech. Rev., 47, 147-169 https://doi.org/10.1115/1.3111076
  28. Reissner, E. (1984), 'On a certain mixed variational theory and a proposed applications', Int. J. Numer. Meth. Eng., 20, 1366-1368 https://doi.org/10.1002/nme.1620200714
  29. Reissner, E. (1986), 'On a mixed variational theorem and on a shear deformable plate theory', Int. J. Numer. Meth. Eng., 23, 193-198 https://doi.org/10.1002/nme.1620230203
  30. Setoodeh, A.R. and Karami, G. (2004), 'Static, free vibration and buckling analysis of anisotropic thick laminated composite plates on distributed and point elastic support using a 3D Layerwise FEM', Eng. Struct., 26, 211-220 https://doi.org/10.1016/j.engstruct.2003.09.009
  31. Toledano, A. and Murakami, H. (1987), 'A higher-order laminated plate theory with improved in-plane responses', Int. J. Solids Struct., 23, 111-131 https://doi.org/10.1016/0020-7683(87)90034-5
  32. Zienkiewicz, O.C., Taylor, R.L. and Too, J.M. (1971), 'Reduced integration technique in general analysis of plates and shells', Int. J. Numer Meth. Eng., 3, 275-290 https://doi.org/10.1002/nme.1620030211