TY - JOUR
T1 - Hamel's field variational integrator for simulating dynamics of thin-walled geometrically exact beams with warping effects
AU - Chen, Ju
AU - Huang, Ziheng
AU - Tian, Qiang
N1 - Publisher Copyright:
© 2023 Elsevier Ltd
PY - 2023/12
Y1 - 2023/12
N2 - Using discrete variational principle, a Hamel's field variational integrator (HFVI) for simulating dynamics of thin-walled geometrically exact beams with warping effects is originally proposed. Firstly, a spacetime independent interpolation way for thin-walled beam elements is established on SE(3) × R space by using Hamel's formalism. Then, a new discretization formulation of convective velocity and convective strains on Lie algebra is proposed by using frame operators, which helps to reduce the system's nonlinearity. After that, the variations of discrete convective velocity and discrete convective strain are decoupled from the cross-section configuration variables. This way can avoid the computation of nonlinear exponential map's tangent map and reduce the computation complexity significantly. According the Hamiltonian form of proposed HFVI, the warping variables and discrete convective strains can be independently solved by using discrete compatibility equations on Lie algebra. Finally, the efficiency and accuracy of HFVI is validated by six static and dynamic examples.
AB - Using discrete variational principle, a Hamel's field variational integrator (HFVI) for simulating dynamics of thin-walled geometrically exact beams with warping effects is originally proposed. Firstly, a spacetime independent interpolation way for thin-walled beam elements is established on SE(3) × R space by using Hamel's formalism. Then, a new discretization formulation of convective velocity and convective strains on Lie algebra is proposed by using frame operators, which helps to reduce the system's nonlinearity. After that, the variations of discrete convective velocity and discrete convective strain are decoupled from the cross-section configuration variables. This way can avoid the computation of nonlinear exponential map's tangent map and reduce the computation complexity significantly. According the Hamiltonian form of proposed HFVI, the warping variables and discrete convective strains can be independently solved by using discrete compatibility equations on Lie algebra. Finally, the efficiency and accuracy of HFVI is validated by six static and dynamic examples.
KW - Dynamic analysis
KW - Frame operator
KW - Geometrically exact thin-walled beam
KW - Hamel's field variational integrator
KW - Warping and Wagner effect
UR - http://www.scopus.com/inward/record.url?scp=85167786143&partnerID=8YFLogxK
U2 - 10.1016/j.mechmachtheory.2023.105462
DO - 10.1016/j.mechmachtheory.2023.105462
M3 - Article
AN - SCOPUS:85167786143
SN - 0094-114X
VL - 190
JO - Mechanism and Machine Theory
JF - Mechanism and Machine Theory
M1 - 105462
ER -