A 3D shear deformable finite element based on the absolute nodal coordinate formulation

Karin Nachbagauer, Peter Gruber, Johannes Gerstmayr

Research output: Chapter in Book/Report/Conference proceedingsConference contributionpeer-review

31 Citations (Scopus)


The absolute nodal coordinate formulation (ANCF) has been developed for the modeling of large deformation beams in two or three dimensions. The absence of rotational degrees of freedom is the main conceptual difference between the ANCF and classical nonlinear beam finite elements that can be found in literature. In the present approach, an ANCF beam finite element is presented, in which the orientation of the cross section is parameterized by means of slope vectors. Based on these slope vectors, a thickness as well as a shear deformation of the cross section is included. The proposed finite beam element is investigated by an eigenfrequency analysis of a simply supported beam. The high frequencies of thicknessmodes are of the same magnitude as the shear mode frequencies. Therefore, the thickness modes do not significantly influence the performance of the finite element in dynamical simulations. The lateral buckling of a cantilevered right-angle frame under an end load is investigated in order to show a large deformation example in statics, as well as a dynamic application. A comparison to results provided in the literature reveals that the present element shows accuracy and high order convergence.

Original languageEnglish
Title of host publicationMultibody Dynamics
Subtitle of host publicationComputational Methods and Applications
EditorsJean-Claude Samin, Paul Fisette
Number of pages20
ISBN (Print)9789400754034
Publication statusPublished - 2013
Externally publishedYes
EventECCOMAS Thematic Conference on Multibody Dynamics, 2003 - Barcelona, Spain
Duration: 30 Jun 20033 Jul 2003

Publication series

NameComputational Methods in Applied Sciences
ISSN (Print)1871-3033


ConferenceECCOMAS Thematic Conference on Multibody Dynamics, 2003


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