Consistent quaternion interpolation for objective finite element approximation of geometrically exact beam

DOI10.1016/j.cma.2008.09.004zbMath1228.74079OpenAlexW1964288387WikidataQ60585186 ScholiaQ60585186MaRDI QIDQ653645

Juan-Miguel Gracia

Publication date: 19 December 2011

Published in: Computer Methods in Applied Mechanics and Engineering (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.cma.2008.09.004

zbMATH Keywords

objectivityrelative rotationfinite rotationrotation manifoldtangent spacegeometrically exact beampath-independence

Mathematics Subject Classification ID

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

Related Items (18)

On a virtual work consistent three-dimensional Reissner-Simo beam formulation using the quaternion algebra ⋮ An objective 3D large deformation finite element formulation for geometrically exact curved Kirchhoff rods ⋮ A two-director Cosserat rod model using unconstrained quaternions ⋮ Dynamics of spatial beams in quaternion description based on the Newmark integration scheme ⋮ An equilibrium‐based formulation with nonlinear configuration dependent interpolation for geometrically exact 3D beams ⋮ A cell‐centered finite volume formulation of geometrically exact Simo–Reissner beams with arbitrary initial curvatures ⋮ The quaternion beam model for hard-magnetic flexible cantilevers ⋮ A weak form quadrature element formulation of geometrically exact beams with strain gradient elasticity ⋮ Integrating rotation from angular velocity ⋮ A hybrid-mixed finite element formulation for the geometrically exact analysis of three-dimensional framed structures ⋮ A locking-free finite element formulation and reduced models for geometrically exact Kirchhoff rods ⋮ A 3D fibre beam-column element with shear modelling for the inelastic analysis of steel structures ⋮ A frame-invariant scheme for the geometrically exact beam using rotation vector parametrization ⋮ Locking-free isogeometric collocation formulation for three-dimensional geometrically exact shear-deformable beams with arbitrary initial curvature ⋮ Velocity-based approach in non-linear dynamics of three-dimensional beams with enforced kinematic compatibility ⋮ On conservation of energy and kinematic compatibility in dynamics of nonlinear velocity-based three-dimensional beams ⋮ A finite element formulation for a geometrically exact Kirchhoff-Love beam based on constrained translation ⋮ Finite element formulations for constrained spatial nonlinear beam theories

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