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Global-Local Laminate Variational Model

  • N. J. Pagano
  • S. R. Soni
Part of the Solid Mechanics and Its Applications book series (SMIA, volume 34)

Abstract

The absence of a unified, tractable model to predict the elastic response of a multi-layered laminate (say 100 layers) has foiled attempts to understand the failure modes of practical composite structures. Global models, which follow from an assumed displacement field and lead to the definition of effective (or smeared) laminate moduli, are not sufficiently accurate for stress field computation. On the other hand, local models, in which each layer is represented as a homogeneous anisotropie continuum, become intractable as the number of layers becomes even moderately large (approx. l0). In this work, we blend these concepts into a self-consistent model which can define detailed response functions in a region of interest (local), while representing the remainder of the domain by effective properties (global). In this investigation the laminate thickness is divided into two parts. A variational principle has been used to derive the governing equations of equilibrium. For the global region of the laminate, potential energy has been utilized, while the Reissner functional has been used for the local region. The field equations are based upon an assumed thickness distribution of stress components within each layer of the local region and displacement components in the global region. The derived boundary conditions imply that the computed stress field on the surfaces of the global region and the prescribed tractions (point wise in an elasticity sense) satisfy the conditions of vanishing resultant force and moment identically. The same conditions are satisfied in the local region. The stress fields obtained by this formulation compare very well with those obtained by other approaches for laminates with a small number of layers. For large number of layers, internally consistent results are achieved by varying the representation of the global region in the present model.

Keywords

Stress Component Composite Laminate Edge Condition Global Region Local Domain 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

  1. 1.
    N. J. Pagano, Stress fields in composite laminates. AFML.TR-77–114, Wright Patterson Air Force Base, Dayton, Ohio, August 1977. Also, Int. J. Solids Structures 14, 385 (1978).zbMATHCrossRefGoogle Scholar
  2. 2.
    M. E. Gurtin, Continuum theory of Fracture. Mechanics of Composites Review, p. 83. Bergamo Center, Dayton, Ohio (1977).Google Scholar
  3. 3.
    A. S. D. Wang and F. W. Crossman, Some new results on edge effect in symmetric composite laminates. J. Composite Mat. 11, 92 (1977).ADSCrossRefGoogle Scholar
  4. 4.
    E. L. Stanton, L. M. Crain and T. F. Neu, A parametric cubic modelling system for general solids of composite material. Int. J. Nuns. Meth. Engng 11, 653 (1977).zbMATHCrossRefGoogle Scholar
  5. 5.
    N. J. Pagano, Exact moduli of anisotropic laminates. In Composite Materials, Mechanics of Composite Materials (Edited by G. P. Sendecky), Vol. 2, pp. 23–44. Academic Press, New York (1974).Google Scholar
  6. 6.
    J. M. Whitney and C. T. Sun, A higher order theory for extensional motion of laminated composites. I. Sound Vibr. 30, 85 (1973).ADSzbMATHCrossRefGoogle Scholar
  7. 7.
    N. J. Pagano, On the calculation of interlaminar normal stress in composite laminate. J. Composite Mat. 8, 65 (1974).ADSCrossRefGoogle Scholar
  8. 8.
    N. J. Solomon, An assessment of the interlaminar stress problem in laminated composites. J. Composite Mati Supplement 14, 177 (1980).ADSCrossRefGoogle Scholar
  9. 9.
    R. L. Spilker and T. C. T. Ting, Stress analysis of composites. Army Materials and Mechanics Research Center, Watertown, Mass. Techn. Rep. AMMRC-TR-81–5, 1981.Google Scholar
  10. 10.
    I. S. Raju, J. D. Whitcomb and J. G. Goree. A new look at numerical analyses of free edge stresses in composite laminates. NASA Tech. Paper 1751, 1981.Google Scholar
  11. 11.
    N. N. Blumberg and V. P. Tamuzh, Edge effects and stress concentrations in multilaminate composite plates. Mechanics of Composite Materisls, pp. 298–307 (1980). Translated from Russian Il. Mekh Kompositn. Mater. 3, 424 (1980).Google Scholar
  12. 12.
    V. V. Partsevskii, Approximate analysis of mechanisms of fracture of laminated composites at a free edge. Mechanics of Composite Materials, pp. 179–185 (1980). Translation from Russian IL Mekh. Kompositn. Mater. 2, 246 (1980).Google Scholar
  13. 13.
    N. J. Pagano and R. B. Pipes, Some observations on the interlaminar strength of composite laminates. Int. Mech. Sci. 15, 679 (1973).CrossRefGoogle Scholar
  14. 14.
    N. J. Pagano, Free edge stress fields in composite laminates. Int. J. Solids Structures 14, 401 (1978).zbMATHCrossRefGoogle Scholar
  15. 15.
    M. A. Jenkins and J. F. Traub, A three stage variable-shift interation for polynomial zeros and its relation to generalized Rayleigh iteration. Numerische Mathematik 14, 252 (1970).MathSciNetzbMATHCrossRefGoogle Scholar
  16. 16.
    M. Knight and N. J. Pagano, The determination of interlaminar moduli of graphite/epoxy composites. Seventh Annual Mechanics of Composites Review, AFWALINASAINAVYIARMY, Dayton Ohio, 28–30, Oct. 1981.Google Scholar

Copyright information

© Springer Science+Business Media Dordrecht 1994

Authors and Affiliations

  • N. J. Pagano
    • 1
  • S. R. Soni
    • 2
  1. 1.AFWAL/MLBM, Wright-Patterson AFBUSA
  2. 2.University of Dayton Research InstituteDaytonUSA

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