Acta Mechanica Solida Sinica

, Volume 19, Issue 2, pp 181–188 | Cite as

A three-dimensional solution for laminated orthotropic rectangular plates with viscoelastic interfaces

  • Wei Yan
  • Ji Ying
  • Weiqiu Chen


When a body consists completely or even partly of viscoelastic materials, its response under static loading will be time-dependent. The adhesives used to glue together single plies in laminates usually exhibit a certain viscoelastic characteristic in a high temperature environment. In this paper, a laminated orthotropic rectangular plate with viscoelastic interfaces, described by the Kelvin-Voigt model, is considered. A power series expansion technique is adopted to approximate the time-variation of various field quantities. Results indicate that the response of the laminated plate with viscoelastic interfaces changes remarkably with time, and is much different from that of a plate with spring-like or viscous interfaces.

Key words

laminated orthotropic plate state-space method viscoelastic interfaces Kelvin-Voigt model 


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  1. [1]
    Pagano, N.J., Exact solutions for composite laminates in cylindrical bending, J. Compos. Mater., Vol.3, 1969, 398–411.CrossRefGoogle Scholar
  2. [2]
    Pagano, N.J., Exact solutions for rectangular bi-directional composites and sandwich plates, J. Compos. Mater., Vol.4, 1970, 20–35.CrossRefGoogle Scholar
  3. [3]
    Pagano, N.J., Influence of shear coupling in cylindrical bending of anisotropic laminates, J. Compos. Mater., Vol.4, 1970, 330–343.CrossRefGoogle Scholar
  4. [4]
    Wang, Z.K., and Huang, J.X., The axisymmetrical elastic field of an ellipsoidal inclusion with a slipping interface, Acta Mechanica Solida Sinica, Vol.1, 1988, 383–393.Google Scholar
  5. [5]
    Zhai, J. and Luo, H., The validity of the modified Mori-Tanaka method for composites with slightly weakened interface, Acta Mechanica Solida Sinica, Vol.10, No.2, 1997, 108–117.Google Scholar
  6. [6]
    Zhong, Z. and Meguid, S.A., On the eigenstrain problem of a spherical inclusion with an imperfectly bonded interface, J. Appl. Mech., Vol.63, 1996, 877–883.CrossRefGoogle Scholar
  7. [7]
    Chen, W.Q., Cai, J.B. and Ye, G.R., Exact solution of cross-ply laminates with bonding imperfections, AIAA J., Vol.41, 2003, 2244–2250.CrossRefGoogle Scholar
  8. [8]
    Chen, W.Q., Ying, J., Cai, J.B., and Ye, G.R., Benchmark solution of laminated beams with bonding imperfections, AIAA J., Vol.42, 2004, 426–429.CrossRefGoogle Scholar
  9. [9]
    Chen, W.Q. and Lee, K.Y., Three-dimensional exact analysis of angle-ply laminates in cylindrical bending with interfacial damage via state-space method, Compos. Struct., Vol.64, 2004, 275–283.CrossRefGoogle Scholar
  10. [10]
    Yu, H.Y., A new dislocation-like model for imperfect interfaces and their effect on load transfer, Composites Part A, Vol.29A, 1998, 1057–1062.CrossRefGoogle Scholar
  11. [11]
    Yu, H.Y., Wei, Y.N. and Chiang, F.P., Load transfer at imperfect interfaces — dislocation-like model, Int. J. Eng. Sci., Vol.40, 2002, 1647–1662.CrossRefGoogle Scholar
  12. [12]
    He, L.H., and Jiang, J., Transient mechanical response of laminated elastic strips with viscous interfaces in cylindrical bending, Compos. Sci. Tech., Vol.63, 2003, 821–828.CrossRefGoogle Scholar
  13. [13]
    Chen, W.Q. and Lee, K.Y., Time-dependent behaviors of angle-ply laminates with viscous interfaces in cylindrical bending, Euro. J. Mech. A/Solids, Vol.23, 2004, 235–245.CrossRefGoogle Scholar
  14. [14]
    Hashin, Z., Composite materials with viscoelastic interphase: creep and relaxation, Mech. Mater., Vol.11, 1991, 135–148.CrossRefGoogle Scholar
  15. [15]
    Fan, H. and Wang, G.F., Interaction between a screw dislocation and viscoelastic interfaces, Int. J. Solids Struct., Vol.40, 2003, 763–776.CrossRefGoogle Scholar
  16. [16]
    Yan, W. and Chen, W.Q., Time-dependent response of laminated isotropic strips with viscoelastic interfaces, J. Zhejiang Univ. (SCIENCE), Vol.5, 2004, 1318–1321.CrossRefGoogle Scholar
  17. [17]
    Chen, W.Q. and Ding, H.J., Bending of functionally graded piezoelectric rectangular plates, Acta Mechanica Solida Sinica, Vol.13, No.4, 2000, 312–319.Google Scholar
  18. [18]
    Fan, J.R. and Ye, J.Q., An exact solution for the statics and dynamics of laminated thick plates with orthotopic layer, Int. J. Solids Struct., Vol.26, 1990, 655–662.CrossRefGoogle Scholar
  19. [19]
    Chen, W.Q., Bian, Z.G. and Ding, H.J., Three-dimensional analysis of a thick FGM rectangular plate in thermal environment, J. Zhejiang Univ. (SCIENCE), Vol.4, 2003, 1–7.CrossRefGoogle Scholar

Copyright information

© The Chinese Society of Theoretical and Applied Mechanics and Technology 2006

Authors and Affiliations

  • Wei Yan
    • 1
    • 2
  • Ji Ying
    • 3
  • Weiqiu Chen
    • 1
    • 2
  1. 1.Department of Civil EngineeringZhejiang UniversityHangzhouChina
  2. 2.State Key Lab of CAD & CGZhejiang UniversityHangzhouChina
  3. 3.Department of Mechanical EngineeringZhejiang UniversityHangzhouChina

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