Frame-indifferent beam finite elements based upon the geometrically exact beam theory

From MaRDI portal
Publication:4785195

DOI10.1002/nme.487zbMath1053.74041OpenAlexW2099748123MaRDI QIDQ4785195

Paul Steinmann, Peter Betsch

Publication date: 17 December 2002

Published in: International Journal for Numerical Methods in Engineering (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1002/nme.487




Related Items (67)

Large deformation analysis of fully incompressible hyperelastic curved beamsWeak form quadrature elements based on absolute nodal coordinate formulation for planar beamlike structuresDirect computation of critical equilibrium states for spatial beams and framesA computational framework for polyconvex large strain elasticity for geometrically exact beam theoryOn the geometrically exact beam model: a consistent, effective and simple derivation from three-dimensional finite-elasticityConsistent tangent operator for an exact Kirchhoff rod model\(\Gamma \)-convergence of variational integrators for constrained systemsValidation of flexible multibody dynamics beam formulations using benchmark problemsConstitutive and geometric nonlinear models for the seismic analysis of RC structures with energy dissipatorsObjective energy-momentum conserving integration for the constrained dynamics of geometrically exact beamsState of the art of ANCF elements regarding geometric description, interpolation strategies, definition of elastic forces, validation and the locking phenomenon in comparison with proposed beam finite elementsImportance and effectiveness of representing the shapes of Cosserat rods and framed curves as paths in the special Euclidean algebraA mortar approach for fluid-structure interaction problems: immersed strategies for deformable and rigid bodiesA Nonlinear Finite Element Framework for Flexible Multibody Dynamics: Rotationless Formulation and Energy-Momentum Conserving DiscretizationA discrete, geometrically exact method for simulating nonlinear, elastic and inelastic beamsA large rotation finite element analysis of 3D beams by incremental rotation vector and exact strain measure with all the desirable featuresFrame-invariance in finite element formulations of geometrically exact rodsA framework for data-driven structural analysis in general elasticity based on nonlinear optimization: the static caseWeak form quadrature element analysis of planar slender beams based on geometrically exact beam theoryInterpolation of rotation and motionDynamics of spatial beams in quaternion description based on the Newmark integration schemeDirector-based beam finite elements relying on the geometrically exact beam theory formulated in skew coordinatesExplicit free-floating beam elementSimulation of viscoelastic Cosserat rods based on the geometrically exact dynamics of special Euclidean strandsA total Lagrangian, objective and intrinsically locking‐free Petrov–Galerkin SE(3) Cosserat rod finite element formulationTwo-field formulation of the inertial forces of a geometrically-exact beam elementA geometrically nonlinear Cosserat shell model for orientable and non-orientable surfaces: discretization with geometric finite elementsAn efficient displacement-based isogeometric formulation for geometrically exact viscoelastic beamsMulti-body dynamics simulation of geometrically exact Cosserat rodsHybrid state-space time integration of rotating beamsInvariant Hermitian finite elements for thin Kirchhoff rods. II: The linear three-dimensional caseNumerical aspects in the dynamic simulation of geometrically exact rodsOn the use of geometrically exact shells in a conserving framework for flexible multibody dynamicsConsistent quaternion interpolation for objective finite element approximation of geometrically exact beamA nonlinear hu-washizu variational formulation and related finite-element implementation for spatial beams with arbitrary moderate thick cross-sectionsThe discrete null space method for the energy-consistent integration of constrained mechanical systems. III: Flexible multibody dynamicsAn exact conserving algorithm for nonlinear dynamics with rotational DOFs and general hyperelasticity. II: ShellsThe quaternion-based three-dimensional beam theoryA Hamiltonian and multi-Hamiltonian formulation of a rod model using quaternionsA hybrid-mixed finite element formulation for the geometrically exact analysis of three-dimensional framed structuresEnergy-consistent numerical integration of mechanical systems with mixed holonomic and nonholonomic constraintsA comparison of finite elements for nonlinear beams: the absolute nodal coordinate and geometrically exact formulationsNonlinear dynamics of slender structures: a new object-oriented frameworkAn isogeometric finite element formulation for geometrically exact Timoshenko beams with extensible directorsOn the global interpolation of motionA discrete mechanics approach to the Cosserat rod theory-Part 1: static equilibriaComputational homogenization of rope-like technical textilesIsogeometric analysis of 3D beams for arbitrarily large rotations: locking-free and path-independent solution without displacement DOFs inside the patchThe rotating rigid body model based on a non-twisting frameA low order, torsion deformable spatial beam element based on the absolute nodal coordinate formulation and Bishop frameSpectral collocation methods for the periodic solution of flexible multibody dynamicsLarge deflection analysis of geometrically exact spatial beams under conservative and nonconservative loads using intrinsic equationsGeometrically exact beam finite element formulated on the special Euclidean group \(SE(3)\)Variational modeling of plane-strain hyperelastic thin beams with thickness-stretching effectAnalysis of 2D flexible mechanisms using linear finite elements and incremental techniquesA frame-invariant scheme for the geometrically exact beam using rotation vector parametrizationVelocity-based approach in non-linear dynamics of three-dimensional beams with enforced kinematic compatibilityAn exact conserving algorithm for nonlinear dynamics with rotational DOFs and general hyperelasticity. I: RodsStatic analysis of beam structures under nonlinear geometric and constitutive behaviorOn conservation of energy and kinematic compatibility in dynamics of nonlinear velocity-based three-dimensional beamsA finite element formulation for a geometrically exact Kirchhoff-Love beam based on constrained translationA 3D Shear Deformable Finite Element Based on the Absolute Nodal Coordinate FormulationA Unified Approach to the Energy-Consistent Numer-ical Integration of Nonholonomic Mechanical Systems and Flexible Multibody DynamicsDiscrete variational Lie group formulation of geometrically exact beam dynamicsFinite element formulations for constrained spatial nonlinear beam theoriesConsistent coupling of positions and rotations for embedding 1D Cosserat beams into 3D solid volumesOn the role of frame invariance in structural mechanics models at finite rotations



Cites Work


This page was built for publication: Frame-indifferent beam finite elements based upon the geometrically exact beam theory