DOI QR코드

DOI QR Code

Mixed finite element model for laminated composite beams

  • Desai, Y.M. (Department of Civil Engineering, Indian Institute of Technology Bombay) ;
  • Ramtekkar, G.S. (Department of Civil Engineering, Indian Institute of Technology Bombay)
  • 발행 : 2002.03.25

초록

A novel, 6-node, two-dimensional mixed finite element (FE) model has been developed to analyze laminated composite beams by using the minimum potential energy principle. The model has been formulated by considering four degrees of freedom (two displacement components u, w and two transverse stress components ${\sigma}_z$, $\tau_{xz}$) per node. The transverse stress components have been invoked as nodal degrees of freedom by using the fundamental elasticity equations. Thus, the present mixed finite element model not only ensures the continuity of transverse stress and displacement fields through the thickness of the laminated beams but also maintains the fundamental elasticity relationship between the components of stress, strain and displacement fields throughout the elastic continuum. This is an important feature of the present formulation, which has not been observed in various mixed formulations available in the literature. Results obtained from the model have been shown to be in excellent agreement with the elasticity solutions for thin as well as thick laminated composite beams. A few results for a cross-ply beam under fixed support conditions are also presented.

키워드

참고문헌

  1. Carrera, E. (1996), "$C^0$ Reissner-Mindlin multilayered plate elements including zig-zag and interlaminar stress continuity", Int. J. Numer. Meth. Engng., 39, 1797-1820. https://doi.org/10.1002/(SICI)1097-0207(19960615)39:11<1797::AID-NME928>3.0.CO;2-W
  2. Carrera, E. (1998), "Mixed layer-wise models for multilayered plates analysis", Compos. Struct., 43, 57-70. https://doi.org/10.1016/S0263-8223(98)00097-X
  3. Carrera, E. (1999), "Transverse normal stress effects in multilayered plates", J. Appl. Mech., ASME 66, 1004- 1011. https://doi.org/10.1115/1.2791769
  4. Engblom, J.J., and Ochoa, O.O. (1985), "Through the thickness stress predictions for laminated plates of advanced composite materials", Int. J. Numer. Meth. Engng., 21, 1759-1776. https://doi.org/10.1002/nme.1620211003
  5. Jones, R.M. (1975), Mechanics of composite materials, int. student ed., Hemisphere, New York. 210-223.
  6. Lo, K.H., Christensen, R.M., and Wu, E.M. (1978), "Stress solution determination for high order plat theory", Int J. Solids Struct., 14, 655-662. https://doi.org/10.1016/0020-7683(78)90004-5
  7. Lu, X., and Lin, D. (1992), "An interlaminar shear stress continuity theory for both thin and thick composite laminates", J. Appl. Mech., ASME 59, 502-509. https://doi.org/10.1115/1.2893752
  8. Manjunatha, B.S., and Kant, T. (1993a), "New theories for symmetric/unsymmetric composite and sandwich beams with $C^0$ finite elements", Compos. Struct., 23, 61-73. https://doi.org/10.1016/0263-8223(93)90075-2
  9. Manjunatha, B.S., and Kant, T. (1993b), "Different numerical techniques for the estimation of multiaxial stresses in symmetric/unsymmetric composite and sandwich beams with refined theories", J. Reinf. Plast. Compos., 12, 2-37. https://doi.org/10.1177/073168449301200101
  10. Pagano, N.J. (1969), "Exact solutions for composite laminates in cylindrical bending", J. Compos. Mater., 3, 398-411. https://doi.org/10.1177/002199836900300304
  11. Pagano, N.J. (1970), "Exact solutions for rectangular bi-directional composites and sandwich plates", J. Compos. Mater., 4, 20-35.
  12. Pagano, N.J., and Hatfield, S.J. (1972), "Elastic behavior of multilayered bi-directional composites", AIAA J., 10, 931-933. https://doi.org/10.2514/3.50249
  13. Pipes, R.B., and Pagano, N.J. (1970), "Interlaminar stresses in composite laminates under uniform axial loading", J. Compos. Mater., 4, 538-548. https://doi.org/10.1177/002199837000400409
  14. Reddy, J.N. (1987), "A generalization of two-dimensional theories of laminated composite plates", Commun. Appl. Numer. Meth., 3, 173-180. https://doi.org/10.1002/cnm.1630030303
  15. Rybicki, E.F. (1971), "Approximate three-dimensional solutions for symmetric laminates under in-plane loading", J. Compos. Mater., 5, 354-360. https://doi.org/10.1177/002199837100500305
  16. Shi, Y.B., and Chen, H.R. (1992), "A mixed finite element for interlaminar stress computation", Compos. Struct., 20, 127-136. https://doi.org/10.1016/0263-8223(92)90019-9
  17. Shimpi, R.P., and Ghugal, Y.M. (1999), "A layerwise trigonometric shear deformation theory for two layered cross-ply laminated beams", J. Reinf. Plast. Compos., 18, 1516-1543. https://doi.org/10.1177/073168449901801605
  18. Soldatos, K.P.A. (1992), "A general laminated plate theory accounting for continuity of displacements and transverse shear stresses at material interfaces", Compos. Struct., 20, 195-211. https://doi.org/10.1016/0263-8223(92)90026-9
  19. Spilker, R.L. (1982), "Hybrid stress eight node elements for thin and thick multilayer laminated plates", Int. J. Numer. Meth. Engng., 18, 801-828. https://doi.org/10.1002/nme.1620180602
  20. Srinivas, S., and Rao, A.K. (1970), "Bending vibration and buckling of simply supported thick orthotropic rectangular plates and laminates", Int. J. Solids Struct., 6, 1463-1481. https://doi.org/10.1016/0020-7683(70)90076-4
  21. Toledano, A., and Murakami, H. (1987), "A higher order laminated plate theory with improved inplane responses", Int. J. Solids Struct., 23(1), 111-131. https://doi.org/10.1016/0020-7683(87)90034-5
  22. Wen-Jinn, L., and Sun, C.T. (1987), "A three-dimensional hybrid stress isoparametric element for the analysis of laminated composite plates", Comput. Struct., 25(2), 241-249. https://doi.org/10.1016/0045-7949(87)90147-7
  23. Wu, C.P., and Kuo, H.C. (1993), "An interlaminar stress mixed finite element method for the analysis of thick laminated composite plates", Compos. Struct., 24, 29-42. https://doi.org/10.1016/0263-8223(93)90052-R
  24. Wu, C.P., and Hsu, C.S. (1993), "A new local high-order laminate theory", Compos. Struct., 25, 439-448. https://doi.org/10.1016/0263-8223(93)90191-R
  25. Wu, C.P., and Lin, C.C. (1993), "Analysis of sandwich plates using mixed finite element", Compos. Struct., 25, 397-405. https://doi.org/10.1016/0263-8223(93)90187-U

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