Consistent coupling of positions and rotations for embedding 1D Cosserat beams into 3D solid volumes

@article{Steinbrecher2021ConsistentCO,
  title={Consistent coupling of positions and rotations for embedding 1D Cosserat beams into 3D solid volumes},
  author={Ivo Steinbrecher and Alexander Popp and Christoph Meier},
  journal={ArXiv},
  year={2021},
  volume={abs/2107.11151}
}
The present article proposes a mortar-type finite element formulation for consistently embedding curved, slender beams into 3D solid volumes. Following the fundamental kinematic assumption of undeformable cross-section s, the beams are identified as 1D Cosserat continua with pointwise six (translational and rotational) degrees of freedom describing the cross-section (centroid) position and orientation. A consistent 1D-3D coupling scheme for this problem type is proposed, requiring to enforce… Expand

References

SHOWING 1-10 OF 80 REFERENCES
An objective 3D large deformation finite element formulation for geometrically exact curved Kirchhoff rods
The objective of this work is the development of a new finite element formulation for beams according to the Kirchhoff theory of thin rods, which includes the deformation states of axial tension,Expand
Comparison of the absolute nodal coordinate and geometrically exact formulations for beams
The modeling of flexibility in multibody systems has received increase scrutiny in recent years. The use of finite element techniques is becoming more prevalent, although the formulation ofExpand
Geometrically Exact Finite Element Formulations for Slender Beams: Kirchhoff–Love Theory Versus Simo–Reissner Theory
TLDR
It will be shown that the geometrically exact Kirchhoff–Love beam elements proposed in this work are the first ones of this type that fulfill all essential requirements and provide considerable numerical advantages such as lower spatial discretization error levels, improved performance of time integration schemes as well as linear and nonlinear solvers and smooth geometry representation as compared to shear-deformable Simo–Reissner formulations when applied to highly slender beams. Expand
Geometrically exact beam elements and smooth contact schemes for the modeling of fiber-based materials and structures
TLDR
A novel geometrically exact beam element based on the Simo–Reissner theory is proposed that is capable of treating even the most general cases of slender beam problems in terms of initial geometry and external loads. Expand
A 3D mortar method for solid mechanics
A version of the mortar method is developed for tying arbitrary dissimilar 3D meshes with a focus on issues related to large deformation solid mechanics. Issues regarding momentum conservation, largeExpand
Objectivity of strain measures in the geometrically exact three-dimensional beam theory and its finite-element implementation
  • M. Crisfield, Gordan Jelenić
  • Mathematics
  • Proceedings of the Royal Society of London. Series A: Mathematical, Physical and Engineering Sciences
  • 1999
The paper discusses the issue of discretization of the strain–configuration relationships in the geometrically exact theory of three–dimensional (3D) beams, which has been at the heart of most recentExpand
A dual mortar approach for 3D finite deformation contact with consistent linearization
In this paper, an approach for three-dimensional frictionless contact based on a dual mortar formulation and using a primal-dual active set strategy for direct constraint enforcement is presented. WeExpand
Shear deformable shell elements for large strains and rotations
Well-known finite element concepts like the Assumed Natural Strain (ANS) and the Enhanced Assumed Strain (EAS) techniques are combined to derive efficient and reliable finite elements for continuumExpand
A locking-free finite element formulation and reduced models for geometrically exact Kirchhoff rods
In this work, we suggest a locking-free geometrically exact finite element formulation incorporating the modes of axial tension, torsion and bending of thin Kirchhoff beams with arbitrary initialExpand
Optimal solid shells for non-linear analyses of multilayer composites. II. Dynamics
Abstract We are presenting a simple low-order solid-shell element formulation––having only displacement degrees of freedom (dofs), i.e., without rotational dofs––that has an optimal number ofExpand
...
1
2
3
4
5
...