TY - GEN

T1 - A 3D shear deformable beam element based on the absolute nodal coordinate formulation applied to classical buckling problems

AU - Nachbagauer, Karin

AU - Gerstmayr, Johannes

PY - 2012

Y1 - 2012

N2 - The absolute nodal coordinate formulation (ANCF) has been developed for the modeling of large deformations in multibody dynamics problems. In contrast to classical nonlinear beam finite elements in literature, the ANCF does not use rotational degrees of freedom and therefore does not necessarily suffer from singularities emerging from angular parameterizations. Compared to the classical formulation, in which the mass matrix is not constant with respect to the generalized coordinates, ANCF elements generally lead to a constant mass matrix, which is advantageous in dynamic analysis. In the present approach, ANCF beam finite elements are presented, in which the orientation of the cross section is parameterized by means of slope vectors. These beam finite elements provide a continuum mechanics as well as a structural mechanics based formulation for the elastic forces. In a previous work, several static problem tests have shown accuracy and high order convergence in statics. The main subject of the present paper is to show the performance of the proposed beam finite elements in complex buckling tests, which can be solved accurately and efficiently.

AB - The absolute nodal coordinate formulation (ANCF) has been developed for the modeling of large deformations in multibody dynamics problems. In contrast to classical nonlinear beam finite elements in literature, the ANCF does not use rotational degrees of freedom and therefore does not necessarily suffer from singularities emerging from angular parameterizations. Compared to the classical formulation, in which the mass matrix is not constant with respect to the generalized coordinates, ANCF elements generally lead to a constant mass matrix, which is advantageous in dynamic analysis. In the present approach, ANCF beam finite elements are presented, in which the orientation of the cross section is parameterized by means of slope vectors. These beam finite elements provide a continuum mechanics as well as a structural mechanics based formulation for the elastic forces. In a previous work, several static problem tests have shown accuracy and high order convergence in statics. The main subject of the present paper is to show the performance of the proposed beam finite elements in complex buckling tests, which can be solved accurately and efficiently.

KW - Absolute nodal coordinate formulation

KW - Beam finite element

KW - Buckling

KW - Framed structures

KW - Right-angle frame

UR - http://www.scopus.com/inward/record.url?scp=84871624931&partnerID=8YFLogxK

M3 - Conference contribution

AN - SCOPUS:84871624931

SN - 9783950353709

T3 - ECCOMAS 2012 - European Congress on Computational Methods in Applied Sciences and Engineering, e-Book Full Papers

SP - 4324

EP - 4333

BT - ECCOMAS 2012 - European Congress on Computational Methods in Applied Sciences and Engineering, e-Book Full Papers

T2 - 6th European Congress on Computational Methods in Applied Sciences and Engineering, ECCOMAS 2012

Y2 - 10 September 2012 through 14 September 2012

ER -