Application of the Laplace transformation for the analysis of viscoelastic composite laminates based on equivalent single-layer theories

Sy, Ngoc Nguyen;Lee, Jaehun;Cho, Maenghyo

  • Received : 2012.10.30
  • Accepted : 2012.11.26
  • Published : 2012.12.30


In this study, the linear viscoelastic response of a rectangular laminated plate is investigated. The viscoelastic properties, expressed by two basic spring-dashpot models, that is Kelvin and Maxwell models, is assumed in the range to investigate the influence of viscoelastic coefficients to mechanical behavior. In the present study, viscoelastic responses are performed for two popular equivalent single-layered theories, such as the first-order shear deformation theory (FSDT) and third-order shear deformation theory (TSDT). Compliance and relaxation modulus of time-dependent viscoelastic behavior are approximately determined by Prony series. The constitutive equation for linear viscoelastic material as the Boltzmann superposition integral equation is simplified by the convolution theorem of Laplace transformation to avoid direct time integration as well as to improve both accuracy and computational efficiency. The viscoelastic responses of composite laminates in the real time domain are obtained by applying the inverse Laplace transformation. The numerical results of viscoelastic phenomena such as creep, cyclic creep and recovery creep are presented.


Composite Laminates;Viscoelastic;Equivalent Single-layered Theories;Laplace Transformation;Maxwell Model;Kelvin Model


  1. Aboudi, J. and Cederbaum, G., "Analysis of viscoelastic laminated composite plates", Composite Structures, Vol. 12, 1989, pp. 243-256.
  2. Cederbaum, G. and Aboudi, J., "Dynamic response of viscoelastic laminated plates", Journal of Sound and Vibration, Vol. 133, No. 2, 1989, pp. 225-238.
  3. Chen, T. M., "The hybrid Laplace transform/finite element method applied to the quasi-static and dynamic analysis of viscoelastic Timoshenko beams", International Journal for Numerical Methods in Engineering, Vol. 38, 1995, pp. 509-522.
  4. Cho, M. and Kim, J. S., "Improved Mindlin plate stress analysis for laminated composites in finite element method", AIAA Journal, Vol. 35, No. 3, 1997, pp. 587-590.
  5. Cho, M. and Oh, J., "Higher order zig-zag plate theory under thermo-electric-mechanical loads combined", Composites: Part B, Vol. 34, 2003, pp. 67-82.
  6. Cho, M. and Parmerter, R. R., "Higher order composite plate theory for general lamination configurations", AIAA Journal, Vol. 31, No. 7, 1993, pp. 1299-1306.
  7. Eshmatov, B. K., "Nonlinear vibrations and dynamic stability of viscoelastic orthotropic rectangular plates", Journal of Sound and Vibration, Vol. 300, 2007, pp.709-726.
  8. Flaggs, D. L. and Crossman, F. W., "Analysis of the viscoelastic response of composite laminates during hygrothermal exposure", Journal of Composite Materials, Vol. 15, 1981, pp. 21-40.
  9. Flugge, W., Viscoelasticity, Springer, Berlin, Heidelberg,1975.
  10. Hilton, H. H. and Yi, S., "Anisotropic viscoelastic finite element analysis of mechanically and hygrothermally loaded composites", Composite Engineering, Vol. 3, No. 2,1993, pp. 123-135.
  11. Jones, R. M., Mechanics of Composite Materials, McGraw-Hill, Inc, City, 1975.
  12. Kim, J. S. and Cho, M., "Enhanced first-order theory based on mixed formulation and transverse normal effect", International Journal of Solids and Structures, Vol. 44, 2007, pp. 1256-1276.
  13. Lakes, R., Viscoelastic materials, Cambridge University Press, New York, 2009.
  14. Li, J. and Weng, G. J., "Effect of a viscoelastic interphase on the creep and stress/strain behavior of fiber-reinforced polymer matrix composite" Composite part B, Vol. 27B, 1996, pp. 589-598.
  15. Lo, K. H. and Christensen, R. M., "A higher-order theory of plate deformation, part 2: laminated plates", Journal of Applied Mechanics, Vol. 44, 1977, pp. 669-676.
  16. Narayanan, G. V. and Beskos, D. E., "Numerical operational methods for time-dependent linear problems", International Journal for Numerical Methods in Engineering, Vol. 18, 1982, pp.1829-1854.
  17. Pagano, N. J., "Exact solutions for composite laminates in cylindrical bending", Journal of Composite Materials, Vol. 3, 1969, pp. 398.
  18. Pagano, N. J., "Exact solutions for rectangular bidirectional composites and sandwich plates", Journal of Composite Materials, Vol. 4, 1970, pp. 20.
  19. Pandya, B. N. and Kant, T., "Finite element stress analysis of laminated composite plates using higher order displacement model", Composites Science and Technology, Vol. 32, 1988, pp. 137-155.
  20. Reddy, J. N., "A simple higher-order theory for laminated composite plates", Journal of Applied Mechanics, Vol. 51, 1984, pp. 745-752.
  21. Reddy, J. N., Mechanics of Laminated Composite Plates and Shells: Theory and Analysis, CRC Press, City, 2004.
  22. Srinatha, H. R. and Lewis, R. W., "A finite element method for thermoviscoelastic analysis of plane problems", Computer Methods in Applied Mechanics and Engineering, Vol. 25, 1981, pp. 21-33.
  23. Whitney, J. M. and Pagano, N. J., "Shear deformation in heterogeneous anisotropic plates", Journal of Applied Mechanics, Vol. 37, 1970, pp. 1031-1036.
  24. Yi, S., Pollock, G. D., Ahmad, M. F. and Hilton, H. H., "Effective transverse Young's modulus of composite with viscoelastic interphase", AIAA Journal, Vol. 33, No. 8, 1994, pp. 1548-1550.

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Supported by : Ministry of Education, Science and Technology