A geometrical nonlinear eccentric 3D-beam element with arbitrary cross-sections

DOI10.1016/S0045-7825(97)00305-8zbMath0951.74065OpenAlexW2083319913MaRDI QIDQ1818052

Roland Sauer, Friedrich Gruttmann, Werner Wagner

Publication date: 2 January 2001

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

Full work available at URL: https://doi.org/10.1016/s0045-7825(97)00305-8

zbMATH Keywords

linearizationstrain measuressymmetric bilinear formorthogonal transformationsGreen-Lagrange strain tensoreccentric space curved beams with arbitrary cross-sectionsTimoshenko beam kinematicstorsion bending coupling

Mathematics Subject Classification ID

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

Related Items

Using finite strain 3D‐material models in beam and shell elements ⋮ On the differentiation of the Rodrigues formula and its significance for the vector‐like parameterization of Reissner–Simo beam theory ⋮ A computational framework for polyconvex large strain elasticity for geometrically exact beam theory ⋮ Constitutive and geometric nonlinear models for the seismic analysis of RC structures with energy dissipators ⋮ Co-rotational beam elements with warping effects in instability problems ⋮ Corotational nonlinear analyses of laminated shell structures using a 4-node quadrilateral flat shell element with drilling stiffness ⋮ Co-rotational finite element formulation for thin-walled beams with generic open section ⋮ Large deflection of composite beams by finite elements with node-dependent kinematics ⋮ Erratum ⋮ Homogenization assumptions for coupled multiscale analysis of structural elements: beam kinematics ⋮ Extension of non-linear beam models with deformable cross sections ⋮ Advances on kinematically exact rod models for thin-walled open-section members: consistent warping function and nonlinear constitutive equation ⋮ An advanced finite element formulation for piezoelectric beam structures ⋮ A mixed hybrid finite beam element with an interface to arbitrary three-dimensional material models ⋮ A nonlinear hu-washizu variational formulation and related finite-element implementation for spatial beams with arbitrary moderate thick cross-sections ⋮ A solid-beam finite element and non-linear constitutive modelling ⋮ A large displacement and finite rotation thin-walled beam formulation including cross-section deformation ⋮ Geometrically exact thin-walled beam including warping formulated on the special Euclidean group \(SE(3)\) ⋮ A geometrically exact beam finite element for curved thin-walled bars with deformable cross-section ⋮ An isogeometric finite element formulation for geometrically exact Timoshenko beams with extensible directors ⋮ On the simultaneous use of simple geometrically exact shear-rigid rod and shell finite elements ⋮ A mixed finite element for three-dimensional nonlinear analysis of steel frames ⋮ A geometrically and materially non-linear piezoelectric three-dimensional-beam finite element formulation including warping effects ⋮ Large deflection analysis of geometrically exact spatial beams under conservative and nonconservative loads using intrinsic equations ⋮ Small-amplitude free vibrations of straight beams subjected to large displacements and rotation ⋮ A simple finite element for the geometrically exact analysis of Bernoulli-Euler rods ⋮ Finite element linear and nonlinear, static and dynamic analysis of structural elements – an addendum – A bibliography (1996‐1999) ⋮ A corotational formulation for thin-walled beams with monosymmetric open section

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• A geometrically-exact rod model incorporating shear and torsion-warping deformation
• Further considerations on the problem of torsion and flexure of prismatical beams
• A three-dimensional finite-strain rod model. II. Computational aspects
• On the geometrical stiffness of a beam in space - A consistent v.w. approach
• On finite deformations of space-curved beams
• Finite rotation analysis and consistent linearization using projectors
• The (symmetric) Hessian for geometrically nonlinear models in solid mechanics: Intrinsic definition and geometric interpretation
• Some considerations on the problem of torsion and flexure of prismatical beams
• An excursion into large rotations
• A consistent co-rotational formulation for nonlinear, three-dimensional, beam-elements
• A beam finite element non-linear theory with finite rotations
• Large displacement analysis of three-dimensional beam structures
• Parametrization of finite rotations in computational dynamics: a review
• A finite rotation shell theory with application to composite structures
• Computational aspects of vector‐like parametrization of three‐dimensional finite rotations
• Non‐linear transient finite element analysis with convected co‐ordinates
• On large displacement-small strain analysis of structures with rotational degrees of freedom
• On large displacement-small strain analysis of structures with rotational degrees of freedom