Geometrically exact static isogeometric analysis of an arbitrarily curved spatial Bernoulli–Euler beam

A. Borković*, B. Marussig, G. Radenković

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review


The objective of this research is the development of a geometrically exact model for the analysis of arbitrarily curved spatial Bernoulli–Euler beams. The complete metric of the beam is utilized in order to include the effect of curviness on the nonlinear distribution of axial strain over the cross section. The exact constitutive relation between energetically conjugated pairs is employed, along with four reduced relations. The isogeometric approach, which allows smooth connections between finite elements, is used for the spatial discretization of the weak form. Two methods for updating the local vector basis are applied and discussed in the context of finite rotations. All the requirements of geometrically exact beam theory are satisfied, such as objectivity and path-independence. The accuracy of the formulation is verified by a thorough numerical analysis. The influence of the curviness on the structural response is scrutinized for two classic examples. If the exact response of the structure is sought, the curviness must be considered when choosing the appropriate beam model.

Original languageEnglish
Article number114447
JournalComputer Methods in Applied Mechanics and Engineering
Publication statusPublished - 15 Feb 2022


  • Analytical constitutive relation
  • Geometrically exact analysis
  • Spatial Bernoulli–Euler beam
  • Strongly curved beams

ASJC Scopus subject areas

  • Computational Mechanics
  • Mechanics of Materials
  • Mechanical Engineering
  • Physics and Astronomy(all)
  • Computer Science Applications


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