KSME International Journal

, Volume 14, Issue 6, pp 666–674 | Cite as

Nonlinear finite element analysis of composite shell under impact

  • Chongdu Cho
  • Guiping Zhao
  • Chang Boo Kim
Materials & Fracture · Solids & Structures · Dynamics & Control · Production & Design


Large deflection dynamic responses of laminated composite cylindrical shells under impact are analyzed by the geometrically nonlinear finite element method based on a generalized Sander’s shell theory with the first order transverse shear deformation and the von-Karman large deflection assumption. A modified indentation law with inelastic indentation is employed for the contact force. The nonlinear finite element equations of motion of shell and an impactor along with the contact laws are solved numerically using Newmark’s time marching integration scheme in conjunction with Akay type successive iteration in each step. The ply failure region of the laminated shell is estimated using the Tsai-Wu quadratic interaction criteria. Numerical results, including the contact force histories, deflections and strains are presented and compared with the ones by linear analysis. The effect of the radius of curvature on the composite shell behaviors is investigated and discussed.

Key Words

Composite Shell Impact Non-Linear Finite Element Analysis Damage 


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  1. Aggour, H. and Sun, C. T., 1988, “Finite Element Analysis of a Laminated Composite Plate Subjected to Circularly Distributed Central Impact Loading,”Computers & Structures, Vol. 28, No. 6, pp. 729–736.MATHCrossRefGoogle Scholar
  2. Akay, H. U., 1980, “Dynamic Large Deflection Analysis of Plates Using Mixed Finite Elements,”Computers & Structures, Vol. 11, pp. 1–11.MATHCrossRefGoogle Scholar
  3. Bachrach, W. E. and Hansen, R. S., 1988, “Mixed Finite-Element Method for Composite Cylinder Subjected to Impact,”AIAA J., Vol. 27, No. 5, pp. 632–638.CrossRefGoogle Scholar
  4. Chen, J. K. and Sun, C. T., 1985, “Dynamic Large Deflection Response of Composite Laminates Subjected to Impact,”Composite Structures, Vol. 4, pp. 59–73.CrossRefGoogle Scholar
  5. Cho, C. and Zhao, G., 1999, “Dynamic Response and Damage of Composite Shell under Impact,”KSME Int. J., Vol. 13, No. 9, pp. 596–608.Google Scholar
  6. Choi, I. H. and Hong, C. S., 1994, “New Approach for Simple Prediction of Impact Force History on Composite Laminates,”AIAA J., Vol. 32, No. 10, pp. 2067–2072.CrossRefGoogle Scholar
  7. Crook, A. W., 1952, “A Study of Some Impacts Between Metal Bodies by a Piezoelectric Method,” Proceedings of the Royal Society, London, Series A, Vol. 212, p. 377.CrossRefGoogle Scholar
  8. Gibson, R. F., 1994,Principles of Composite Material Mechanics, McGraw Hill, pp. 110–111.Google Scholar
  9. Gong, S. W., Toh, S. L. and Shim, V. P. W., 1994, “The Elastic Response of Orthotropic Laminated Cylindrical Shells to Low-Velocity Impact,”Composite Engineering, Vol. 4, No. 2, pp. 247–266.CrossRefGoogle Scholar
  10. Matemilola, S. A. and Stronge, W. J., 1997, “Impact Response of Composite Cylinders,”Int. J. of Solids and Structures, Vol. 34, pp. 2669–2684.MATHCrossRefGoogle Scholar
  11. Rajagopalan, K., 1993,Finite Element Buckling Analysis of Stiffened Cylindrical Shells, A. A. Balkema (Rotterdam), pp. 27–28.Google Scholar
  12. Reddy, J. N., 1997,Mechanics of Laminated Composite Plates: Theory and Analysis, CRC Press Inc., pp. 141–142.Google Scholar
  13. Shivakumar, K. N., Elber, W. and Illg, W., 1985, “Prediction of Impact Force and Duration Due to Low-Velocity Impact on Circular Composite Laminates,”J. Applied Mechanics, Vol. 52, pp. 674–680.CrossRefGoogle Scholar
  14. Tan, T. M. and Sun, C. T., 1985, “Use of Statical Indentation Law in the Impact Analysis of Laminated Composite Plate,”J. Applied Mechanics, Vol. 52, pp. 6–12.CrossRefGoogle Scholar
  15. Willis, J. R., 1966, “Hertzian Contact of Anisotropic Bodies,”Journal of Mechanics and Physics of Solids, Vol. 14, pp. 163–176.MATHCrossRefMathSciNetGoogle Scholar
  16. Wu, E. B. and Yen, C. S., 1994, “The Contact Behavior Between Laminated Composite Plates and Rigid Spheres,”J. Applied Mechanics, Vol. 61, pp. 60–66.CrossRefGoogle Scholar
  17. Yang, S. H. and Sun, C. T., 1982, “Indentation Law for Composite Laminates,”Composite Materials: Testing and Design, ASTM STP 787, ASTM, pp. 425–449.Google Scholar
  18. Zhao, G., 2000,Impact Response and Postbuckling Behavior of Composite Cylindrical Shell, Ph. D. Thesis, Inha University, pp. 11–18.Google Scholar

Copyright information

© The Korean Society of Mechanical Engineers (KSME) 2000

Authors and Affiliations

  1. 1.School of MechanicalAerospaceNam Ku, InchonKorea
  2. 2.School of MechanicalAutomation Engineering Inha UniversityNam Ku, InchonKorea

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