TY - GEN
T1 - Efficient finite element formulation for geometrically exact beams
AU - Bauchau, Olivier A.
AU - Han, Shilei
N1 - Publisher Copyright:
Copyright © 2019 ASME.
PY - 2019
Y1 - 2019
N2 - This paper proposes a new approach to the modeling of geometrically exact beams based on motion interpolation schemes. Motion interpolation schemes yield simple expressions for the sectional strains and linearized strain-motion relationships at the mesh nodes. The classical formulation of the finite element method starts from the weak form of the continuous governing equations obtained from a variational principle. Approximations, typically of a polynomial nature, are introduced to express the continuous displacement field in term of its nodal values. Introducing these approximations into the weak form of the governing equations then yields nonlinear discrete that can be solved with the help of a linearization process. In the proposed approach, the order of the first two steps of the procedure is reversed: approximations are introduced in the variational principle directly and the discrete equations of the problem then follow. This paper has shown that for geometrically exact beams, the discrete equations obtained from the two procedure differ significantly: far simpler discrete equations are obtained from the proposed approach.
AB - This paper proposes a new approach to the modeling of geometrically exact beams based on motion interpolation schemes. Motion interpolation schemes yield simple expressions for the sectional strains and linearized strain-motion relationships at the mesh nodes. The classical formulation of the finite element method starts from the weak form of the continuous governing equations obtained from a variational principle. Approximations, typically of a polynomial nature, are introduced to express the continuous displacement field in term of its nodal values. Introducing these approximations into the weak form of the governing equations then yields nonlinear discrete that can be solved with the help of a linearization process. In the proposed approach, the order of the first two steps of the procedure is reversed: approximations are introduced in the variational principle directly and the discrete equations of the problem then follow. This paper has shown that for geometrically exact beams, the discrete equations obtained from the two procedure differ significantly: far simpler discrete equations are obtained from the proposed approach.
UR - http://www.scopus.com/inward/record.url?scp=85076468187&partnerID=8YFLogxK
U2 - 10.1115/DETC2019-97639
DO - 10.1115/DETC2019-97639
M3 - Conference contribution
AN - SCOPUS:85076468187
T3 - Proceedings of the ASME Design Engineering Technical Conference
BT - 15th International Conference on Multibody Systems, Nonlinear Dynamics, and Control
PB - American Society of Mechanical Engineers (ASME)
T2 - ASME 2019 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference, IDETC-CIE 2019
Y2 - 18 August 2019 through 21 August 2019
ER -