TY - JOUR
T1 - Two-field formulation of the inertial forces of a geometrically-exact beam element
AU - Sonneville, Valentin
AU - Géradin, Michel
N1 - Publisher Copyright:
© 2022, The Author(s).
PY - 2023/10
Y1 - 2023/10
N2 - An independent velocity field is introduced via Legendre transformation of the kinetic energy of a geometrically-exact beam, leading to a first-order system of twice as many governing equations as a one-field formulation. Nevertheless, the new field does not have to be assembled across elements and can be eliminated at the element level, so that the assembled system has the same size as a one-field formulation. Furthermore, because the new field does not have to satisfy the compatibility equations that the original velocity field is subjected to, its finite-element discretization is simpler and leads to simplified inertial forces.
AB - An independent velocity field is introduced via Legendre transformation of the kinetic energy of a geometrically-exact beam, leading to a first-order system of twice as many governing equations as a one-field formulation. Nevertheless, the new field does not have to be assembled across elements and can be eliminated at the element level, so that the assembled system has the same size as a one-field formulation. Furthermore, because the new field does not have to satisfy the compatibility equations that the original velocity field is subjected to, its finite-element discretization is simpler and leads to simplified inertial forces.
KW - Generalized-α for first-order ODE
KW - Geometrically-exact beam finite element
KW - Legendre transformation
KW - Mechanics on Lie group
UR - http://www.scopus.com/inward/record.url?scp=85145161278&partnerID=8YFLogxK
U2 - 10.1007/s11044-022-09867-4
DO - 10.1007/s11044-022-09867-4
M3 - Article
AN - SCOPUS:85145161278
SN - 1384-5640
VL - 59
SP - 239
EP - 254
JO - Multibody System Dynamics
JF - Multibody System Dynamics
IS - 2
ER -