TY - JOUR
T1 - A finite element beam model including cross-section distortion in the absolute nodal coordinate formulation
AU - Shen, Zhenxing
AU - Li, Pei
AU - Liu, Cheng
AU - Hu, Gengkai
PY - 2014/8
Y1 - 2014/8
N2 - A new class of beam finite elements is proposed in a three-dimensional fully parameterized absolute nodal coordinate formulation, in which the distortion of the beam cross section can be characterized. The linear, second-order, third-order, and fourth-order models of beam cross section are proposed based on the Pascal triangle polynomials. It is shown that Poisson locking can be eliminated with the proposed higher-order beam models, and the warping displacement of a square beam is well described in the fourth-order beam model. The accuracy of the proposed beam elements and the influence of cross-section distortion on structure deformation and dynamics are examined through several numerical examples. We find that the proposed higher-order models can capture more accurately the structure deformation such as cross-section distortion including warping, compared to the existing beam models in the absolute nodal coordinate formulation.
AB - A new class of beam finite elements is proposed in a three-dimensional fully parameterized absolute nodal coordinate formulation, in which the distortion of the beam cross section can be characterized. The linear, second-order, third-order, and fourth-order models of beam cross section are proposed based on the Pascal triangle polynomials. It is shown that Poisson locking can be eliminated with the proposed higher-order beam models, and the warping displacement of a square beam is well described in the fourth-order beam model. The accuracy of the proposed beam elements and the influence of cross-section distortion on structure deformation and dynamics are examined through several numerical examples. We find that the proposed higher-order models can capture more accurately the structure deformation such as cross-section distortion including warping, compared to the existing beam models in the absolute nodal coordinate formulation.
KW - Absolute nodal coordinate formulation
KW - Cross-section distortion
KW - Higher-order beam models
KW - Warping displacement
UR - http://www.scopus.com/inward/record.url?scp=84905100963&partnerID=8YFLogxK
U2 - 10.1007/s11071-014-1360-y
DO - 10.1007/s11071-014-1360-y
M3 - Article
AN - SCOPUS:84905100963
SN - 0924-090X
VL - 77
SP - 1019
EP - 1033
JO - Nonlinear Dynamics
JF - Nonlinear Dynamics
IS - 3
ER -