The absolute nodal coordinate formulation

Johannes Gerstmayr, Alexander Humer, Peter Gruber, Karin Nachbagauer

Research output: Chapter in Book/Report/Conference proceedingsChapterpeer-review

7 Citations (Scopus)


The key idea of the absolute nodal coordinate formulation (ANCF) is to use slope vectors in order to describe the orientation of the cross-section of structural mechanics components, such as beams, plates or shells. This formulation relaxes the kinematical assumptions of Bernoulli–Euler and Timoshenko beam theories and enables a deformation of the cross-sections. The present contribution shows how to create 2D and 3D structural finite elements based on the ANCF by employing different sets of slope vectors for approximating the cross-sections’ orientation. A specific aim of this chapter is to present a unified notation for structural mechanics and continuum mechanics ANC formulations. Particular focus is laid on enhanced formulations for such finite elements that circumvent severe issues like Poisson or shear locking. The performance of these elements is evaluated and a detailed assessment comprising the convergence order, the number of iterations, and Jacobian updates for large deformation benchmark problems is provided.

Original languageEnglish
Title of host publicationCISM International Centre for Mechanical Sciences, Courses and Lectures
Number of pages42
Publication statusPublished - 2016

Publication series

NameCISM International Centre for Mechanical Sciences, Courses and Lectures
ISSN (Print)0254-1971
ISSN (Electronic)2309-3706


  • Absolute Nodal Coordinate Formulation
  • Flexible Multibody System
  • Local Frame
  • Shear Correction Factor
  • Virtual Work


Dive into the research topics of 'The absolute nodal coordinate formulation'. Together they form a unique fingerprint.

Cite this