Archive of Applied Mechanics

, Volume 84, Issue 3, pp 375–384 | Cite as

Exact solution of 3D Timoshenko beam problem: problem-dependent formulation

  • Edita Papa Dukić
  • Gordan JelenićEmail author


Problem-dependent interpolation functions for displacements and rotations are obtained from the exact analytical solution of the 3D Timoshenko beam problem by introducing a full set of boundary conditions. The developed methodology allows us to derive a new solution that coincides with the classical result of the engineering beam theory. In addition, the proposed interpolation enables exact strain recovery at any point within the problem domain.


Linear analysis 3D Timoshenko beam Problem-dependent formulation Boundary conditions 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Bathe K.-J.: Finite Element Procedures. Prentice-Hall, New Jersey (1995)Google Scholar
  2. 2.
    Zienkiewicz O.C., Taylor R.L.: The Finite Element Method for Solid and Structural Mechanics. Elsevier Butterworth-Heinemann, Oxford (2005)zbMATHGoogle Scholar
  3. 3.
    Rakowski J.: The interpretation of the shear locking in beam elements. Comput. Struct. 37, 769–776 (1990)CrossRefGoogle Scholar
  4. 4.
    Yunhua L.: Explanation and elimination of shear locking and membrane locking with field consistence approach. Comput. Methods Appl. Mech. Eng. 162, 249–269 (1998)CrossRefzbMATHGoogle Scholar
  5. 5.
    Przemieniecki J.: Theory of Matrix Structural Analysis. McGraw-Hill, New York (1968)zbMATHGoogle Scholar
  6. 6.
    Tessler A., Dong S.B.: On a hierarchy of conforming Timoshenko beam elements. Comput. Struct. 14, 335–344 (1981)CrossRefGoogle Scholar
  7. 7.
    Reddy J.N.: On locking-free shear deformable beam finite elements. Comput. Methods Appl. Mech. Eng. 149, 113–132 (1997)CrossRefzbMATHGoogle Scholar
  8. 8.
    Mukherjee S., Reddy J.N., Krishnamoorthy C.S.: Convergence properties and derivative extraction of the superconvergent Timoshenko beam finite element. Comput. Methods Appl. Mech. Eng. 190, 3475–3500 (2001)CrossRefzbMATHMathSciNetGoogle Scholar
  9. 9.
    Jelenić G., Papa E.: Exact solution of 3D Timoshenko beam problem using linked interpolation of arbitrary order. Arch. Appl. Mech. 81(2), 171–183 (2011)CrossRefzbMATHGoogle Scholar
  10. 10.
    Zienkiewicz O.C., Taylor R.L., Zhu J.Z.: The Finite Element Method. Its Basis and Fundamentals. Elsevier Butterworth-Heinemann, Oxford (2005)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  1. 1.Faculty of Civil EngineeringUniversity of RijekaRijekaRepublic of Croatia

Personalised recommendations