An objective FE-formulation for Cosserat rods based on the spherical Bézier interpolation

Cites Work

Assumed-metric spherically interpolated quadrilateral shell element
On natural strain measures of the non linear micropolar continuum
On a stress resultant geometrically exact shell model. I: Formulation and optimal parametrization
Flexible multibody dynamics
Consistent quaternion interpolation for objective finite element approximation of geometrically exact beam
The quaternion-based three-dimensional beam theory
Geometrically exact beam finite element formulated on the special Euclidean group \(SE(3)\)
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
A frame-invariant scheme for the geometrically exact beam using rotation vector parametrization
A finite strain beam formulation. The three-dimensional dynamic problem. I
A three-dimensional finite-strain rod model. II. Computational aspects
On finite deformations of space-curved beams
The (symmetric) Hessian for geometrically nonlinear models in solid mechanics: Intrinsic definition and geometric interpretation
The vectorial parameterization of rotation
Multiplicative updating of the rotation tensor in the finite element analysis of rods and shells --- a path independent approach
A formulation and implementation of geometrically exact curved beam elements incorporating finite strains and finite rotations
An objective 3D large deformation finite element formulation for geometrically exact curved Kirchhoff rods
On the role of frame invariance in structural mechanics models at finite rotations
The Cosserat surface as a shell model, theory and finite element formulation
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
Statically and kinematically exact nonlinear theory of rods and its numerical verification
Isogeometric shape optimization of nonlinear, curved 3D beams and beam structures
Dynamic multi-patch isogeometric analysis of planar Euler-Bernoulli beams
Geometrically exact static isogeometric analysis of an arbitrarily curved spatial Bernoulli-Euler beam
A new deformation measure for the nonlinear micropolar continuum
Optimal design of vascular stents using a network of 1D slender curved rods
Isogeometric collocation for implicit dynamics of three-dimensional beams undergoing finite motions
A non-linear symmetric \(\mathrm{G}^1\)-conforming Bézier finite element formulation for the analysis of Kirchhoff beam assemblies
Energy pairs in the micropolar continuum
Generalized continua -- from the theory to engineering applications. Papers based on the presentations at the course, Udine, Italy, September 19--23, 2011
Isogeometric collocation for three-dimensional geometrically exact shear-deformable beams
Isogeometric collocation methods for Cosserat rods and rod structures
An isogeometric collocation method for frictionless contact of Cosserat rods
Locking-free isogeometric collocation formulation for three-dimensional geometrically exact shear-deformable beams with arbitrary initial curvature
On one-dimensional finite-strain beam theory: the plane problem
Floating tangents for approximating spatial curves with \(G^1\) piecewise helices
A beam model for duoskelion structures derived by asymptotic homogenization and its application to axial loading problems
Constitutive models for strongly curved beams in the frame of isogeometric analysis
A continuum-mechanics interpretation of Reissner's non-linear shear-deformable beam theory
A discrete mechanics approach to the Cosserat rod theory-Part 1: static equilibria
Geodesic finite elements for Cosserat rods
Total Lagrangian Reissner's geometrically exact beam element without singularities
A beam finite element non-linear theory with finite rotations
Kirchhoff’s problem for nonlinearly elastic rods
Large displacement analysis of three-dimensional beam structures
Objectivity of strain measures in the geometrically exact three-dimensional beam theory and its finite-element implementation
An intrinsic beam model based on a helicoidal approximation—Part I: Formulation
Truss Modular Beams with Deformation Energy Depending on Higher Displacement Gradients
An objective finite element approximation of the kinematics of geometrically exact rods and its use in the formulation of an energy-momentum conserving scheme in dynamics
On the differentiation of the Rodrigues formula and its significance for the vector‐like parameterization of Reissner–Simo beam theory
Lie Groups, Lie Algebras, and Representations
On One‐Dimensional Large‐Displacement Finite‐Strain Beam Theory

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