Nonlinear Dynamics

, Volume 47, Issue 4, pp 389–403 | Cite as

Nonlinear transient dynamic response of damped plates using a higher order shear deformation theory

Original Article

Abstract

Damped transient dynamic elasto-plastic analysis of plate is investigated. A finite element model based on a C 0 higher order shear deformation theory has been developed. Nine noded Lagrangian elements with five degrees of freedom per node are used. Selective Gauss integration is used to evaluate energy terms so as to avoid shear locking and spurious mechanisms. Von Mises and Tresca yield criteria are incorporated along with associated flow rules. Explicit central difference time stepping scheme is employed to integrate temporal equations. The mass matrix is diagonalized by using the efficient proportional mass lumping scheme. A program is developed for damped transient dynamic finite element analysis of elasto-plastic plate. Several numerical examples are studied to unfold different facets of damping of elasto-plastic plates.

Keywords

Damping Dynamics Elasto-plastic Lumped mass Plate Transient 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Reissner, E.: The effects of transverse shear deformation on the bending of elastic plates. ASME J. Appl. Mech. 12, A69–A77 (1945)MathSciNetGoogle Scholar
  2. 2.
    Mindlin, R.D.: Influence of rotatory inertia and shear and flexural motions on isotropic elastic plates. ASME J. Appl. Mech. 18(1), 31–38 (1951)MATHGoogle Scholar
  3. 3.
    Kant, T.: Numerical analysis of thick plates. Comput. Methods Appl. Mech. Eng. 31, 1–18 (1982)MATHCrossRefGoogle Scholar
  4. 4.
    Lo, K.H., Christensen, R.M., Wu, E.M.: A higher order theory of plate deformation-Part 1 Homogeneous plates. ASME J. Appl. Mech. 99, 663–668 (1977)Google Scholar
  5. 5.
    Hinton, E., Owen, D.R.J., Shantaram, D.: Dynamic transient linear and nonlinear behavior of thick and thin plates. In: J. R. Whiteman (ed.) Mathematics of Finite Elements and Applications, MAFELAP II: Academic press, London, pp. 423–438 (1977)Google Scholar
  6. 6.
    Owen, D.R.J., Hinton, E., Shantaram, D.: Nonlinear dynamic transient analysis of plates using parabolic isoparametric elements. In: Finite Element Methods in Engineering. The University of Adelaide 44/1–16 (1976)Google Scholar
  7. 7.
    Paul, D.K., Huq, M.M., Hinton, E.: Nonlinear static and transient dynamic analysis of Mindlin plates. In: First International Conference on Numerical Methods for Nonlinear Problems, University College of Swansea, pp. 221–235 (1980)Google Scholar
  8. 8.
    Shantaram, D., Owen, D.R.J., Zeinkiewicz, O.C.: Dynamic transient behavior of two-and three-dimensional structures including plasticity, large deformation effects and fluid interaction. Earthquake Eng. Struct. Dyn., 4, 561–578 (1976)CrossRefGoogle Scholar
  9. 9.
    Kant, T., Mallikarjuna: Nonlinear dynamics of laminated plates with a higher order theory and C0 finite elements. Int. J. Non-Linear Mech. 26(3/4), 335–343 (1991)CrossRefGoogle Scholar
  10. 10.
    Kant, T. Kommineni, J.R.: Large amplitude free vibration analysis of cross-ply composite and sandwich laminates with a refined theory and $C^{0}$ finite elements. Comput. Struct. 50, 123–134 (1994)MATHCrossRefGoogle Scholar
  11. 11.
    Tresca, H.: Surl'ecoulement des corps solides soumis a de fortes pression. C. R. Acad. Sci., Paris, 59, 754 (1864)Google Scholar
  12. 12.
    von Mises. R.: Mechanicsanik der festen korper in plastisch deformablen zustant. Nachr. Ges. Wiss. Gottingen 582 (1930)Google Scholar
  13. 13.
    Owen, D.R.J., Hinton, E., Finite Elements in Plasticity: Theory and Practice, 1st ed., Pineridge Press, Swansea (1980)Google Scholar
  14. 14.
    Underwood, P.: Dynamic relaxation, In: T. Belytschko and TJR. Hughes (eds.) Computational Methods for Transient Analysis. Elsevier Science Publisher, Amsterdam, pp. 245–265 (1983)Google Scholar
  15. 15.
    Pica, A. and Hinton, E.: Further developments in transient and pseudo-transient analysis of Mindlin plates. Int. J. Num. Methods Eng. 17, 1749–1761 (1981)MATHCrossRefGoogle Scholar
  16. 16.
    Hinton, E., Rock, T., Zienkiewicz, O.C.: A note on mass lumping and related processes in the finite element method. Earthquake Eng. Struct. Dyn. 4, 245–249 (1976)CrossRefGoogle Scholar
  17. 17.
    Khante, S.N., Rode, V.R.: Elasto-plastic dynamic analysis of plates using higher order shear deformation theory. In: P.K., K., Gupta, Manoj (eds.) Structural Engineering and Mechanics. BITS Pilani, pp. 224–234 (2004)Google Scholar
  18. 18.
    Khante, S.N., Rode, V.R.: Effect of tangent modulus on transient non-linear response of plates using higher order shear deformation theory. In: Sudarsana Rao (ed.), Recent Treads in Structural Engineering, JNTU College of Engineering, Anantpur, pp. 222–231 (2004)Google Scholar
  19. 19.
    Reddy, J.N.: Dynamic (transient) analysis of layered anisotropic composite material plates. Int. J. Num. Methods Eng. 19, 237–255 (1983)MATHCrossRefGoogle Scholar
  20. 20.
    Liu, S.C., Lin, T.H.: Elastic-plastic dynamic analysis of structures using known elastic solutions. Earthquake Eng. Struct. Dyn. 7, 147–159 (1979)CrossRefGoogle Scholar
  21. 21.
    Bathe, K.J., Bolourchi, S.A.: Geometric and material nonlinear plate and shell elements. Comput. Struct. 11, 23–48 (1980)MATHCrossRefGoogle Scholar
  22. 22.
    Kant, T., Ravichandran, R.V., Pandya, B.N. Mallikarjuna: Finite element transient dynamic analysis of isotropic and fiber reinforced composite plates using higher order theory. Composite Struct. 19, 319–342 (1988)CrossRefGoogle Scholar
  23. 23.
    Chandrasekharappa, G., Srirangarajan, H.R.: Nonlinear dynamic damped response of an orthotropic circular plate. Comput. Struct. 33(5), 1163–1165 (1989)MATHCrossRefGoogle Scholar
  24. 24.
    Cook, R.D., Malkus, D.S., Plesha, M.E.: Concepts and applications of finite element analysis. Willey, NY (2000)Google Scholar
  25. 25.
    Kant, T., Swaminathan, K.: Analytical solutions for free vibration of laminated composite and sandwich plates based on a higher-order refined theory. Composite Struct. 53, 73–85 (2001)CrossRefGoogle Scholar
  26. 26.
    Kant, T., Swaminathan, K.: Analytical solutions for the static analysis of laminated composite and sandwich plates based on a higher order refined theory. Composite Struct. 56, 329–344 (2002)CrossRefGoogle Scholar
  27. 27.
    Khante, S.N., Rode, V.R.: Non-linear dynamic bending analysis of plates using a higher order shear deformation theory. Nonlinear Dyn. (2006) 43:257–275.Google Scholar

Copyright information

© Springer Science+Business Media, Inc. 2006

Authors and Affiliations

  • Suraj Narendra Khante
    • 1
  • Vijay Rode
    • 1
  • Tarun Kant
    • 1
  1. 1.CE-AMD, Shri G. S. Institute of Technology and ScienceIndoreIndia

Personalised recommendations