Skip to main content
SpringerLink
Log in

Static and Free Vibration Analysis of Composite Plates and Shells Using a Flat Shell Element

  • Conference paper
Contemporary Research in Engineering Science

  • 266 Accesses

Abstract

Finite element static and free vibration analysis of thin laminated plates and shells using a three noded triangular flat shell element is presented. The flat shell element is a combination of the Discrete Kirchhoff Theory (DKT) plate bending element and a membrane element derived from the Linear Strain Triangular (LST) element with a total of 18 degrees of freedom (3 translations and 3 rotations per node). Explicit formulations are used for the membrane, bending and membrane-bending coupling stiffness matrices. The results are presented for (i) static analysis of simply supported square plates under doubly sinusoidal and uniformly distributed loads; (ii) simply supported spherical shells under an uniformly distributed load; and (iii) free vibration analysis of (a) square cantilever plates, (b) skew cantilever plates and (c) simply supported spherical shells. The results presented are in good agreement with those available in the literature.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 84.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 109.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. J. L.. Meek and H. S. Tan, A Faceted Shell Element With Roof Nodes, International Journal of Numerical Methods In Engineering, Vol. 23 (1986), pp. 49–67.

    Article  MATH  Google Scholar 

  2. O. C. Zienkiewicz, The Finite Element Method, 3rd edition, McGraw-Hill, London, 1977.

    MATH  Google Scholar 

  3. D. J. Allman, A Compatible Triangular Element Including Vertex Rotations For Plane Elasticity Analysis, Computers and Structures, Vol. 19 (1984), No. 1-2, pp. 1–8.

    Article  MATH  Google Scholar 

  4. P. G. Bergan and C. A. Fellipa, A Triangular Membrane Element With Rotational Degrees of Freedom, Comput. Methods. Appl. Mech. Eng., Vol. 50 (1985), pp. 24–69.

    Article  Google Scholar 

  5. P. G. Bergan and M. K. Nygard, Finite Elements With Increased Freedom in Choosing Shape Functions, International Journal of Numerical Methods in Engineering, Vol. 20 (1984), pp. 643–664.

    Article  MATH  Google Scholar 

  6. N. Carpenter, H. Stolarski and T. Belytschko, A Flat Triangular Shell Element With Improved Membrane Interpolation, Communications in Applied Numerical Methods, Vol. 1 (1985), pp. 161–168.

    Article  MATH  Google Scholar 

  7. J. Fish and T. Belytschko, Stabilized Rapidly Convergent 18- Degrees of Freedom Flat Shell Triangular Element, International Journal of Numerical Methods in Engineering, Vol. 33 (1992), pp. 149–162.

    Article  Google Scholar 

  8. R. D. Cook, On The Allman Triangle And Related Quadrilateral Element, Computers and Structures, Vol. 22 (1986), No. 6, pp. 1065–1067.

    Article  Google Scholar 

  9. R. D. Cook, A Plane Hybrid Element With Rotational DOF and Adjustable Stiffness, International Journal of Numerical Methods in Engineering, Vol. 24 (1987), pp. 1499–1508.

    Article  MATH  Google Scholar 

  10. T. R. J. Hughes and F. Brezzi, On Drilling Degrees of Freedom, Comput. Methods. Appl. Mech. Eng., Vol. 72 (1989), pp. 105–121.

    Article  MATH  MathSciNet  Google Scholar 

  11. A. Ibrahimbegovic, A Novel Membrane Finite Element With an Enhanced Displacement Interpolation, Finite Elements in Analysis and Design, Vol. 7 (1990), pp. 167–179.

    Article  MATH  Google Scholar 

  12. K. Alvin, M. Horacio de la Fuente, B. Hhaugen and C. A. Fellippa, Membrane Triangles With Corner Drilling Freedoms - I. EFF Element, Finite Elements in Analysis and Design, Vol. 12 (1992), pp. 163–187.

    Article  MATH  Google Scholar 

  13. C. A. Fellipa and C. Militello, Membrane Triangles With Corner Drilling Freedoms - II. ANDES Element, Finite Elements in Analysis and Design, Vol. 12 (1992), pp. 189–201.

    Article  Google Scholar 

  14. C. A. Fellipa and S. Alexander, Membrane Triangles With Corner Drilling Freedoms - III. Implementation and Performance Evaluation, Finite Elements in Analysis and Design, Vol. 12 (1992), pp. 203–239.

    Article  Google Scholar 

  15. R. D. Cook, Some Options For Plane Triangular Elements With Rotational Degrees of Freedom, Finite Elements in Analysis and Design, Vol. 6 (1990), pp. 245–249.

    Article  Google Scholar 

  16. R. D. Cook, Modified Formulations for Nine-D.O.F. Plane Tri-angles That Include Vertex Rotations, International Journal of Numerical Methods in Engineering, Vol. 31 (1991), pp. 825–835.

    Article  MATH  Google Scholar 

  17. R. D. Cook, Further Development of a Three-Node Triangular Shell Element, International Journal of Numerical Methods in Engineering, Vol. 36 (1993), pp. 1413–1425.

    Article  MATH  Google Scholar 

  18. M. M. Hrabok and T. M. Hrudey, A Review and Catalog of Plate Bending Finite Elements, Computers and Structures, Vol. 19 (1984), pp. 479–495.

    Article  Google Scholar 

  19. J. L. Batoz, K. J. Bathe and L. W. Ho, A Study of Three Noded Triangular Plate Bending Elements, International Journal of Numerical Methods in Engineering, Vol. 15 (1980), pp. 1771–1812.

    Article  MATH  Google Scholar 

  20. C. Jeyachandrabose and J. Kirkhope, An Alternative Explicit Formulation for the DKT Plate Bending Element, International Journal of Numerical Methods in Engineering, Vol. 21 (1985), pp. 1289–1293.

    Article  MATH  Google Scholar 

  21. C. Jeyachadrabose and J. Kirkhope, Construction of New Efficient Three-noded Triangular Thin Plate Bending Elements, Computers and Structures, Vol. 23 (1986), pp. 587–603.

    Article  Google Scholar 

  22. C. A. Fellippa and P. G. Bergan, A Triangular Plate Bending Element Based on Energy Orthogonal Free Formulation, Comp. Meth. Appl. Mech. Eng., Vol. 61 (1987), pp. 129–160.

    Article  Google Scholar 

  23. G. P. Bazeley, Y. K. Cheung, B. M. Irons and O. C. Zienkiewicz, Triangular Elements in Plate Bending Confirming and Non-conforming Solutions, Proc. Conf. on Matrix Methods in Structural Mechanics, AFFDL-TR-66-80 (1965), Wright-Patterson Air Force Base, pp. 547–576.

    Google Scholar 

  24. B. Specht, Modified Shape Functions for the Three Noded Plate Bending Element Passing the Patch Test, International Journal of Numerical Methods in Engineering, Vol. 26 (1988), pp. 705–715.

    Article  MATH  Google Scholar 

  25. O. C. Zienkiewicz, R. L. Taylor, P. Papadopoulos and E. Onate, Plate Bending Elements With Discrete Constraints: New Triangular Elements, Computers and Structures, Vol. 35 (1990), pp. 505–522.

    Article  MATH  Google Scholar 

  26. R. D. Cook, Concepts and Applications of Finite Element Analysis (1981), John Wiley and Sons, New York.

    MATH  Google Scholar 

  27. K. J. Bathe and L. W. Ho, A Simple and Effective Element for Analysis of General Shell Structures, Computers and Structures, Vol. 13 (1981), pp. 673–681.

    Article  MATH  Google Scholar 

  28. H. C. Chen, Evaluation of Allman Triangular Membrane Element Used in general Shell Analysis, Computers and Structures, Vol. 43 (1992), pp. 881–887.

    Article  Google Scholar 

  29. A. Ertas, J. T. Krafcik and S. Ekward-Osire, Performance of an Anisotropic Allman/DKT 3-Node Thin Triangular Flat Shell Element, Composite Engineering, Vol. 2 (1992), No. 4, pp. 269–280.

    Article  Google Scholar 

  30. T. T. Yang, Finite Element Structural Analysis, Prentice-Hall, Inc.

    Google Scholar 

  31. N. D. Phan and J. N. Reddy, Analysis of Laminated Composite Plates Using A Higher Order Shear Deformation Theory, International Journal of Numerical Methods in Engineering, Vol. 21 (1985), pp. 2201–2219.

    Article  MATH  Google Scholar 

  32. J. M. Whitney and A. W. Leissa, Analysis of Anisotropic Heterogeneous Plates, Journal of Applied Mechanics, Vol.36 (1969), No.2, Trans. ASME, Vol.91 (1969), Series E, pp. 261–266.

    Google Scholar 

  33. J. N. Reddy, Exact Solutions of Moderately Thick Laminated Shells, J. Engng. Mech. Div., ASCE, Vol. 110 (1984), No. 5, pp. 794–807.

    Article  Google Scholar 

  34. A. Dey, J. N. Bandyopadhyay and P. K. Sinha, Finite Element Analysis of Laminated Composite Parabolaid of Revolution Shells, Computers and Structures, Vol. 44 (1992), No. 3, pp. 675–682.

    Article  Google Scholar 

  35. R. K. Kapania and S. Singhvi, Free Vibration Analysis of Generally Laminated Tapered Skew Plates, Enhancing Analysis Techniques For Composite Materials, ASME, NDE-Vol. 10 (1991), pp. 159–168.

    Google Scholar 

  36. R. M. Jones, Mechanics of Composite Materials, Scripta Book Company, Washington, D. C.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Virginia Polytechnic Institute and State University, Blacksburg, VA, 24061-0219, USA

    R. K. Kapania & P. Mohan

Authors
  1. R. K. Kapania
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. P. Mohan
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. Dept. of Engineering Science and Mechanics, Virginia Polytechnic Institute and State University, 24061-0219, Blacksburg, VA, USA

    Romesh C. Batra

Rights and permissions

Reprints and permissions

Copyright information

© 1995 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Kapania, R.K., Mohan, P. (1995). Static and Free Vibration Analysis of Composite Plates and Shells Using a Flat Shell Element. In: Batra, R.C. (eds) Contemporary Research in Engineering Science. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-80001-6_13

Download citation

  • DOI: https://doi.org/10.1007/978-3-642-80001-6_13

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-80003-0

  • Online ISBN: 978-3-642-80001-6

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics

Search

Navigation