A space-time finite element formulation for geometrically exact shear-deformable beams
Abstract
We present a space-time finite element formulation for the transient analysis of geometrically exact shear-deformable beams. The formulation treats space and time within a unified finite element framework and employs a mixed approach in which translational and angular velocities are introduced as independent fields. The rotation field is parametrized using nodal rotation (pseudo-)vectors and a suitable objective interpolation of the triad field is employed. The resulting formulation supports generally curved beam structures, including geometric kinks and rigid joints. Furthermore, time-dependent material domains can be represented directly through the geometry of the space-time surface, enabling the treatment of non-material boundaries without modifying the underlying beam formulation. Numerical examples demonstrate convergence to solutions obtained with classical time-stepping schemes, objectivity of the formulation, and the influence of the space-time stabilization. Finally, the sliding spaghetti problem illustrates the applicability of the proposed approach to axially moving continua.
Related
- Mixed finite element discretization of intrinsic geometrically exact beams for multiplier-free multibody dynamics
- Mixed finite element discretization of intrinsic geometrically exact beams for multiplier-free multibody dynamics
- Semidiscrete Modeling of Dislocation-Disclination Systems: Finite Element Formulation
- A Stream-Function Formulation for the Surface Stokes-Helfrich Model - Surface Finite Element Discretization and Validation
- A stabilized, nodal strain finite element method for small and large deformations: formulation, analysis, and impact on remeshing strategies
BibTeX
@misc{steinbrecher2026spacetime,
title = {{A space-time finite element formulation for geometrically exact shear-deformable beams}},
author = {Ivo Steinbrecher and Alexander Humer},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.03285},
eprint = {2610.03285},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.03285},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - A space-time finite element formulation for geometrically exact shear-deformable beams
AU - Ivo Steinbrecher
AU - Alexander Humer
PY - 2026
DA - 2026/10/02
PB - arXiv
DO - 10.48550/arxiv.2610.03285
UR - https://arxiv.org/abs/2610.03285
AB - We present a space-time finite element formulation for the transient analysis of geometrically exact shear-deformable beams. The formulation treats space and time within a unified finite element framework and employs a mixed approach in which translational and angular velocities are introduced as independent fields. The rotation field is parametrized using nodal rotation (pseudo-)vectors and a suitable objective interpolation of the triad field is employed. The resulting formulation supports generally curved beam structures, including geometric kinks and rigid joints. Furthermore, time-dependent material domains can be represented directly through the geometry of the space-time surface, enabling the treatment of non-material boundaries without modifying the underlying beam formulation. Numerical examples demonstrate convergence to solutions obtained with classical time-stepping schemes, objectivity of the formulation, and the influence of the space-time stabilization. Finally, the sliding spaghetti problem illustrates the applicability of the proposed approach to axially moving continua.
ER -