Computational Mechanics

, Volume 64, Issue 4, pp 1115–1131 | Cite as

An objective and path-independent 3D finite-strain beam with least-squares assumed-strain formulation

  • P. Areias
  • M. Pires
  • N. Vu Bac
  • Timon RabczukEmail author
Original Paper


An all-encompassing finite-strain representation of rods, shells and continuum can share a common kinematic/constitutive framework where specific conditions for strain, stress and constitutive updating are applied. In this work, finite strain beams are under examination, with several classical requirements met by cooperative techniques judiciously applied. Specifically: the use of a continuum constitutive law is possible due to the relative strain formulation previously introduced, the rotation singularity problem is absent due to the use of a consistent (quadratic) updated Lagrangian technique. Objectiveness and path-independence of director interpolation are satisfied due to the use of a Löwdin frame. These properties are proved in this work. Moreover, high coarse-mesh accuracy is introduced by the least-squares assumed-strain technique, here specialized for a beam. Examples show the accuracy and robustness of the formulation.


Geometrically exact beams Assumed strains Least-squares Nonlinear Constitutive laws 



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Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2019

Authors and Affiliations

  • P. Areias
    • 1
    • 3
  • M. Pires
    • 2
  • N. Vu Bac
    • 4
  • Timon Rabczuk
    • 5
    Email author
  1. 1.Department of Physics, Colégio Luís António VerneyUniversity of ÉvoraÉvoraPortugal
  2. 2.Department of Mathematics, Colégio Luís António VerneyUniversity of ÉvoraÉvoraPortugal
  3. 3.CERIS/Instituto Superior TécnicoUniversity of LisbonLisbonPortugal
  4. 4.Institute of Structural MechanicsBauhaus-University WeimarWeimarGermany
  5. 5.Institute of Research & DevelopmentDuy Tan UniversityDanangViet Nam

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