TY - GEN
T1 - A 3D shear deformable finite element based on the absolute nodal coordinate formulation
AU - Nachbagauer, Karin
AU - Gruber, Peter
AU - Gerstmayr, Johannes
N1 - Funding Information:
K. Nachbagauer and P. Gruber acknowledge support from the Austrian Science Funds (FWF): I337-N18, J. Gerstmayr from the K2-Comet Austrian Center of Competence in Mechatronics (ACCM).
Publisher Copyright:
© 2013 Springer Science+Business Media Dordrecht.
PY - 2013
Y1 - 2013
N2 - 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.
AB - 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.
UR - http://www.scopus.com/inward/record.url?scp=84964211640&partnerID=8YFLogxK
U2 - 10.1007/978-94-007-5404-1_4
DO - 10.1007/978-94-007-5404-1_4
M3 - Conference contribution
AN - SCOPUS:84964211640
SN - 9789400754034
T3 - Computational Methods in Applied Sciences
SP - 77
EP - 96
BT - Multibody Dynamics
A2 - Samin, Jean-Claude
A2 - Fisette, Paul
PB - Springer
T2 - ECCOMAS Thematic Conference on Multibody Dynamics, 2003
Y2 - 30 June 2003 through 3 July 2003
ER -