Geometrically exact isogeometric Bernoulli-Euler beam based on the Frenet-Serret frame
From MaRDI portal
Publication:2683427
DOI10.1016/j.cma.2022.115848OpenAlexW4313334218MaRDI QIDQ2683427
Michael H. Gfrerer, Aleksandar Borković, Benjamin Marussig
Publication date: 10 February 2023
Published in: Computer Methods in Applied Mechanics and Engineering (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/2210.00001
Frenet-Serret framegeometrically exact analysisspatial Bernoulli-Euler beamrotation-free beamstrongly curved beam
Related Items (2)
A new exhaustive semi-analytical method to calculate stress distribution on the surface of a curved beam with circular cross section, with an application to helical compression springs ⋮ An efficient displacement-based isogeometric formulation for geometrically exact viscoelastic beams
Uses Software
Cites Work
- Unnamed Item
- Unnamed Item
- On a virtual work consistent three-dimensional Reissner-Simo beam formulation using the quaternion algebra
- Invariant Hermitian finite elements for thin Kirchhoff rods. II: The linear three-dimensional case
- An implicit \(G^1\) multi patch B-spline interpolation for Kirchhoff-Love space rod
- A consistent 3D corotational beam element for nonlinear dynamic analysis of flexible structures
- B-spline interpolation of Kirchhoff-Love space rods
- The interpolation of rotations and its application to finite element models of geometrically exact rods
- A total Lagrangian Timoshenko beam formulation for geometrically nonlinear isogeometric analysis of spatial beam structures
- Isogeometric analysis: CAD, finite elements, NURBS, exact geometry and mesh refinement
- A comparison of finite elements for nonlinear beams: the absolute nodal coordinate and geometrically exact formulations
- A frame-invariant scheme for the geometrically exact beam using rotation vector parametrization
- Rotation manifold \(\mathrm{SO}(3)\) and its tangential vectors
- A finite strain beam formulation. The three-dimensional dynamic problem. I
- A three-dimensional finite-strain rod model. II. Computational aspects
- On the dynamics in space of rods undergoing large motions - A geometrically exact approach
- On a consistent theory, and variational formulation of finitely stretched and rotated 3-D space-curved beams
- On finite deformations of space-curved beams
- On the choice of finite rotation parameters
- Large-deformation analysis of flexible beams
- On a geometrically exact curved/twisted beam theory under rigid cross-section assumption
- An objective 3D large deformation finite element formulation for geometrically exact curved Kirchhoff rods
- A locking-free finite element formulation and reduced models for geometrically exact Kirchhoff rods
- Dynamics of geometrically nonlinear rods. I: Mechanical models and equations of motion
- On finite element implementation of geometrically nonlinear Reissner's beam theory: Three-dimensional curved beam elements
- Geometrically exact 3D beam theory: Implementation of a strain-invariant finite element for statics and dynamics
- A consistent co-rotational finite element formulation for geometrically nonlinear dynamic analysis of 3-D beams
- Linear static isogeometric analysis of an arbitrarily curved spatial Bernoulli-Euler beam
- On the analytical approach to the linear analysis of an arbitrarily curved spatial Bernoulli-Euler beam
- A geometrically exact isogeometric beam for large displacements and contacts
- Isogeometric analysis of 3D beams for arbitrarily large rotations: locking-free and path-independent solution without displacement DOFs inside the patch
- Invariant isogeometric formulation for the geometric stiffness matrix of spatial curved Kirchhoff rods
- A low order, torsion deformable spatial beam element based on the absolute nodal coordinate formulation and Bishop frame
- On the geometrically exact formulations of finite deformable isogeometric beams
- Geometrically exact static isogeometric analysis of an arbitrarily curved spatial Bernoulli-Euler beam
- Isogeometric configuration design sensitivity analysis of geometrically exact shear-deformable beam structures
- Isogeometric collocation for implicit dynamics of three-dimensional beams undergoing finite motions
- Weak coupling of nonlinear isogeometric spatial Bernoulli beams
- A large rotation finite element analysis of 3D beams by incremental rotation vector and exact strain measure with all the desirable features
- Invariant isogeometric formulations for three-dimensional Kirchhoff rods
- Geometrically nonlinear multi-patch isogeometric analysis of spatial Euler-Bernoulli beam structures
- An isogeometric finite element formulation for geometrically exact Timoshenko beams with extensible directors
- A non-linear symmetric \(\mathrm{G}^1\)-conforming Bézier finite element formulation for the analysis of Kirchhoff beam assemblies
- Isogeometric collocation for three-dimensional geometrically exact shear-deformable beams
- A unified approach for beam-to-beam contact
- Isogeometric collocation methods for Cosserat rods and rod structures
- Locking-free isogeometric collocation formulation for three-dimensional geometrically exact shear-deformable beams with arbitrary initial curvature
- Rotation-free isogeometric analysis of an arbitrarily curved plane Bernoulli-Euler beam
- Nonlinear isogeometric spatial Bernoulli beam
- Isogeometric rotation-free bending-stabilized cables: statics, dynamics, bending strips and coupling with shells
- Consistent tangent operator for an exact Kirchhoff rod model
- An isogeometric implicit \(G^1\) mixed finite element for Kirchhoff space rods
- A novel four-field mixed FE approximation for Kirchhoff rods using Cartan's moving frames
- Mechanics of Structural Elements
- A beam finite element non-linear theory with finite rotations
- There is More than One Way to Frame a Curve
- Parametrization of finite rotations in computational dynamics: a review
- Objectivity of strain measures in the geometrically exact three-dimensional beam theory and its finite-element implementation
- An updated Lagrangian Bézier finite element formulation for the analysis of slender beams
- Torsion At An Inflection Point of a Space Curve
This page was built for publication: Geometrically exact isogeometric Bernoulli-Euler beam based on the Frenet-Serret frame