A finite element formulation for a geometrically exact Kirchhoff-Love beam based on constrained translation

DOI10.1007/s00466-019-01698-zzbMath1464.74200OpenAlexW2935276859WikidataQ113327119 ScholiaQ113327119MaRDI QIDQ2329620

Markus Böl, Matthias Schulz

Publication date: 18 October 2019

Published in: Computational Mechanics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s00466-019-01698-z

zbMATH Keywords

Kirchhoff rodgeometrically exact theoryKirchhoff-Love beamlocking-free finite element method

Mathematics Subject Classification ID

Rods (beams, columns, shafts, arches, rings, etc.) (74K10) Finite element methods applied to problems in solid mechanics (74S05)

Related Items (2)

A novel four-field mixed FE approximation for Kirchhoff rods using Cartan's moving frames ⋮ Invariant isogeometric formulation for the geometric stiffness matrix of spatial curved Kirchhoff rods

Cites Work

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• A quaternion-based formulation of Euler-Bernoulli beam without singularity
• Invariant Hermitian finite elements for thin Kirchhoff rods. I: The linear plane case
• Invariant Hermitian finite elements for thin Kirchhoff rods. II: The linear three-dimensional case
• B-spline interpolation of Kirchhoff-Love space rods
• A mixed hybrid finite beam element with an interface to arbitrary three-dimensional material models
• Consistent quaternion interpolation for objective finite element approximation of geometrically exact beam
• A new locking-free formulation for planar, shear deformable, linear and quadratic beam finite elements based on the absolute nodal coordinate formulation
• A mixed finite element for three-dimensional nonlinear analysis of steel frames
• A geometrically-exact rod model incorporating shear and torsion-warping deformation
• The interpolation of rotations and its application to finite element models of geometrically exact rods
• 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
• Static analysis of beam structures under nonlinear geometric and constitutive behavior
• 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
• A fully nonlinear theory of curved and twisted composite rotor blades accounting for warpings and three-dimensional stress effects
• Co-rotational beam elements with warping effects in instability problems
• On the choice of finite rotation parameters
• Multiplicative updating of the rotation tensor in the finite element analysis of rods and shells --- a path independent approach
• Finite-element formulation of geometrically exact three-dimensional beam theories based on interpolation of strain measures.
• An objective 3D large deformation finite element formulation for geometrically exact curved Kirchhoff rods
• Nonlinear, three-dimensional beam theory for dynamic analysis
• A locking-free finite element formulation and reduced models for geometrically exact Kirchhoff rods
• Finite element theory for curved and twisted beams based on exact solutions for three-dimensional solids. I: Beam concept and geometrically exact nonlinear formulation. II: Anisotropic and advanced beam models
• Description of elastic forces in absolute nodal coordinate formulation
• An excursion into large rotations
• Dynamics of geometrically nonlinear rods. I: Mechanical models and equations of motion
• Dynamics of geometrically nonlinear rods. II: Numerical methods and computational examples
• A kinematically exact space finite strain beam model -- finite element formulation by generalized virtual work principle
• On finite element implementation of geometrically nonlinear Reissner's beam theory: Three-dimensional curved beam elements
• On the bending and stretching elasticity of biopolymer filaments
• Geometrically exact 3D beam theory: Implementation of a strain-invariant finite element for statics and dynamics
• Resolution of sub-element length scales in Brownian dynamics simulations of biopolymer networks with geometrically exact beam finite elements
• The linearized three-dimensional beam theory of naturally curved and twisted beams: The strain vector formulation
• Nonlinear isogeometric spatial Bernoulli beam
• A solid-beam finite element and non-linear constitutive modelling
• Finite elements, finite rotations and small strains fo flexible shells
• On one-dimensional finite-strain beam theory: the plane problem
• An isogeometric implicit \(G^1\) mixed finite element for Kirchhoff space rods
• A mixed variational formulation based on exact intrinsic equations for dynamics of moving beams
• A consistent co-rotational formulation for nonlinear, three-dimensional, beam-elements
• An explicit expression for the tangent-stiffness of a finitely deformed 3-D beam and its use in the analysis of space frames
• On a non-linear formulation for curved Timoshenko beam elements considering large displacement/rotation increments
• A beam finite element non-linear theory with finite rotations
• Dynamic analysis of finitely stretched and rotated three-dimensional space-curved beams
• Anisotropic beam theory and applications
• A nonlinear dynamical theory for heterogeneous, anisotropic, elasticrods
• Applications of higher order corotational stretch theories to nonlinear finite element analysis
• Large displacement analysis of three-dimensional beam structures
• Interpolation of rotational variables in nonlinear dynamics of 3D beams
• Objectivity of strain measures in the geometrically exact three-dimensional beam theory and its finite-element implementation
• A three‐dimensional non‐linear Timoshenko beam based on the core‐congruential formulation
• Finite element of slender beams in finite transformations: a geometrically exact approach
• 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
• Frame-indifferent beam finite elements based upon the geometrically exact beam theory
• Computational aspects of vector‐like parametrization of three‐dimensional finite rotations
• Non‐linear transient finite element analysis with convected co‐ordinates
• On a Variational Theorem in Elasticity
• ON THE BOUNDS OF EIGENVALUES
• Nonlinear problems of elasticity

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