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

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

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review


We present a geometrically exact nonlinear analysis of elastic in-plane beams in the context of finite but small strain theory. The formulation utilizes the full beam metric and obtains the complete analytic elastic constitutive model by employing the exact relation between the reference and equidistant strains. Thus, we account for the nonlinear strain distribution over the thickness of a beam. In addition to the full analytical constitutive model, four simplified ones are presented. Their comparison provides a thorough examination of the influence of a beam's metric on the structural response. As a benchmark result, an analytical solution for a pure bending of a strongly curved cantilever beam is derived. We show that the appropriate formulation depends on the curviness of a beam at all configurations. Furthermore, the nonlinear distribution of strain along the thickness of strongly curved beams must be considered to obtain a complete and accurate response.

Original languageEnglish
Article number108539
JournalThin-Walled Structures
Publication statusPublished - Jan 2022


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

ASJC Scopus subject areas

  • Civil and Structural Engineering
  • Building and Construction
  • Mechanical Engineering


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