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

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Abstract

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.

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References

  1. Bathe K.-J.: Finite Element Procedures. Prentice-Hall, New Jersey (1995)

    Google Scholar 

  2. Zienkiewicz O.C., Taylor R.L.: The Finite Element Method for Solid and Structural Mechanics. Elsevier Butterworth-Heinemann, Oxford (2005)

    MATH  Google Scholar 

  3. Rakowski J.: The interpretation of the shear locking in beam elements. Comput. Struct. 37, 769–776 (1990)

    Article  Google Scholar 

  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)

    Article  MATH  Google Scholar 

  5. Przemieniecki J.: Theory of Matrix Structural Analysis. McGraw-Hill, New York (1968)

    MATH  Google Scholar 

  6. Tessler A., Dong S.B.: On a hierarchy of conforming Timoshenko beam elements. Comput. Struct. 14, 335–344 (1981)

    Article  Google Scholar 

  7. Reddy J.N.: On locking-free shear deformable beam finite elements. Comput. Methods Appl. Mech. Eng. 149, 113–132 (1997)

    Article  MATH  Google Scholar 

  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)

    Article  MATH  MathSciNet  Google Scholar 

  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)

    Article  MATH  Google Scholar 

  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 

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Authors and Affiliations

  1. Faculty of Civil Engineering, University of Rijeka, Rijeka, Republic of Croatia

    Edita Papa Dukić & Gordan Jelenić

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  1. Edita Papa Dukić
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  2. Gordan Jelenić
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Correspondence to Gordan Jelenić.

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Papa Dukić, E., Jelenić, G. Exact solution of 3D Timoshenko beam problem: problem-dependent formulation. Arch Appl Mech 84, 375–384 (2014). https://doi.org/10.1007/s00419-013-0805-y

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  • DOI: https://doi.org/10.1007/s00419-013-0805-y

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