Applied Mathematics and Mechanics

, Volume 34, Issue 5, pp 597–612 | Cite as

Two-dimensional analyses of delamination buckling of symmetrically cross-ply rectangular laminates

  • Jiang-hong Xue (薛江红)
  • Qing-zi Luo (罗庆姿)
  • Feng Han (韩峰)
  • Ren-huai Liu (刘人怀)


The conventional approach to analysis the buckling of rectangular laminates containing an embedded delamination subjected to the in-plane loading is to simplify the laminate as a beam-plate from which the predicted buckling load decreases as the length of the laminate increases. Two-dimensional analyses are employed in this paper by extending the one-dimensional model to take into consideration of the influence of the delamination width on the buckling performance of the laminates. The laminate is simply supported containing a through width delamination. A new parameter β defined as the ratio of delamination length to delamination width is introduced with an emphasis on the influence of the delamination size. It is found that (i) when the ratio β is greater than one snap-through buckling prevails, the buckling load is determined by the delamination size and depth only; (ii) as the ratio β continues to increase, the buckling load will approach to a constant value. Solutions are verified with the well established results and are found in good agreement with the latter.

Key words

two-dimensional analysis rectangular laminate delamination buckling laminate theory 

Chinese Library Classification


2010 Mathematics Subject Classification



Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. [1]
    Chai, H., Babcock, C. D., and Knauss, W. G. One dimensional modelling of failure in laminated plates by delamination buckling. International Journal of Solids and Structures, 17(11), 1069–1083 (1981)zbMATHCrossRefGoogle Scholar
  2. [2]
    Simitses, G. J., Sallam, S., and Yin, W. L. Effect of delamination of axially loaded homogeneous laminated plates. AIAA Journal, 23(9), 1437–1444 (1985)CrossRefGoogle Scholar
  3. [3]
    Yazdi, A. A. and Rezaeepazhand, J. Structural similitude for flutter of delaminated composite beam-plates. Composite Structures, 93, 1918–1922 (2011)CrossRefGoogle Scholar
  4. [4]
    Gu, H. and Chattopadhyay, A. An experimental investigation of delamination buckling and postbuckling of composite laminates. Composites Science and Technology, 59, 903–910 (1999)CrossRefGoogle Scholar
  5. [5]
    Nilsson, K. F., Thesken, J. C., Sindelar, P., Giannqkopoulos, A. E., and Stoåkers, B. A theoretical and experimental investigation of buckling induced delamination growth. Journal of the Mechanics and Physics of Solids, 41(4), 783–807 (1993)MathSciNetCrossRefGoogle Scholar
  6. [6]
    Parlapalli, M. and Shu, D. Buckling analysis of two-layer beams with an asymmetric delamination. Engineering Structures, 26, 651–658 (2004)CrossRefGoogle Scholar
  7. [7]
    Karihaloo, B. L. and Stang, H. Buckling-driven delamination growth in composite laminates: guidelines for assessing the threat posed by interlaminar matrix delamination. Composites: Part B Engineering, 39, 386–395 (2008)CrossRefGoogle Scholar
  8. [8]
    Gilate, R., Williams, T. O., and Aboudi, J. Buckling of composite plates by global-local plate theory. Composites: Part B Engineering, 32, 229–236 (2001)CrossRefGoogle Scholar
  9. [9]
    Bruno, D. and Greco, F. Mixed mode delamination in plates: a refined approach. International Journal of Solids and Structures, 38(50–51), 9149–9177 (2001)zbMATHCrossRefGoogle Scholar
  10. [10]
    Barbero, E. J. and Reddy, J. N. Modeling of delamination in composite laminates using a layerwise plate theory. International Journal of Solids and Structures, 28(3), 373–388 (1991)zbMATHCrossRefGoogle Scholar
  11. [11]
    Robbins, D. H., Reddy, J. N., and Krishna, M. A. V. On the modeling of delamination in thick composites. Enhancing Analysis Techniques for Composite Materials, 10, 133–214 (1991)Google Scholar
  12. [12]
    Lee, J., Gurdal, Z., and Griffin, O. J. Layer-wise approach for the bifurcation problem in laminated composites with delaminations. AIAA Journal, 31(2), 331–338 (1993)zbMATHCrossRefGoogle Scholar
  13. [13]
    Tafreshi, A. and Oswald, T. Global buckling behaviour and local damage propagation in composite plates with embedded delaminations. International Journal of Pressure Vessels and Piping, 80, 9–20 (2003)CrossRefGoogle Scholar
  14. [14]
    Qing, G. H., Liu, Y. H., and Li, D. H. A semi-analytical model for the energy release rate analyses of composite laminates with a delamination. Finite Elements in Analysis and Design, 47, 1017–1024 (2011)CrossRefGoogle Scholar
  15. [15]
    Riccio, A., Scaramuzzino, F., and Perugini, P. Embedded delamination growth in composite panels under compressive load. Composites: Part B Engineering, 32(3), 209–218 (2001)CrossRefGoogle Scholar
  16. [16]
    Aslan, Z. and Sahin, M. Buckling behavior and compressive failure of composite laminates containing multiple large delaminations. Composite Structures, 89, 382–390 (2009)CrossRefGoogle Scholar
  17. [17]
    Kyoung, W. M., Kim, C. G., and Hong, C. S. Buckling and post buckling behavior of composite cross-ply laminates with multiple delaminations. Composite Structures, 43, 257–274 (1999)CrossRefGoogle Scholar
  18. [18]
    Lonetti, P. and Zinno, P. Simulation of multiple delaminations in composite laminates under mixed-mode deformations. Simulation Modelling Practice and Theory, 11, 483–500 (2003)CrossRefGoogle Scholar
  19. [19]
    Park, T., Lee, S. Y., and Voyiadjis, G. Z. Finite element vibration analysis of composite skew laminates containing delaminations around quadrilateral cutouts. Composites: Part B Engineering, 40, 225–236 (2009)CrossRefGoogle Scholar
  20. [20]
    Hu, N., Sekine, H., Fukunaga, H., and Yao, Z. H. Impact analysis of composite laminates with multiple delaminations. International Journal of Impact Engineering, 22, 633–648 (1999)CrossRefGoogle Scholar
  21. [21]
    Wang, X. W., Pont-Lezica, I., Harris, J. M., Guild, F. J., and Pavier, M. J. Compressive failure of composite laminates containing multiple delaminations. Composites Science and Technology, 65, 191–200 (2005)CrossRefGoogle Scholar
  22. [22]
    Suemasu, H., Sasaki, W., Ishikawa, T., and Aoki, Y. A numerical study on compressive behavior of composite plates with multiple circular delaminations considering delamination propagation. Composites Science and Technology, 68, 2562–2567 (2005)CrossRefGoogle Scholar
  23. [23]
    Roy, T. and Chakraborty, D. Delamination in FRP laminates with holes under transverse impact. Materials and Design, 29, 124–132 (2008)CrossRefGoogle Scholar
  24. [24]
    Jones, R. M. Mechanics of Composite Materials, 2nd ed., Philadelphia, USA (1980)Google Scholar
  25. [25]
    Hu, H. T. and Lin, B. H. Buckling optimization of symmetrically laminated plates with various geometries and end conditions. Composites Science and Technology, 55, 277–285 (1995)CrossRefGoogle Scholar

Copyright information

© Shanghai University and Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  • Jiang-hong Xue (薛江红)
    • 1
    • 2
  • Qing-zi Luo (罗庆姿)
    • 1
    • 2
  • Feng Han (韩峰)
    • 3
  • Ren-huai Liu (刘人怀)
    • 1
    • 2
  1. 1.Department of Mechanics and Civil EngineeringJinan UniversityGuangzhouP. R. China
  2. 2.Key Lab of Disaster Forecast and Control in EngineeringMinistry of EducationGuangzhouP. R. China
  3. 3.State Key Laboratory of Explosion Science and TechnologyBeijing Institute of TechnologyBeijingP. R. China

Personalised recommendations