On a virtual work consistent three-dimensional Reissner-Simo beam formulation using the quaternion algebra

DOI10.1007/s00707-013-0824-3zbMath1321.74040OpenAlexW2050899174MaRDI QIDQ359438

Dejan Zupan, Eva Zupan, Miran Saje

Publication date: 12 August 2013

Published in: Acta Mechanica (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s00707-013-0824-3

Mathematics Subject Classification ID

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

Related Items (9)

Weak form quadrature elements based on absolute nodal coordinate formulation for planar beamlike structures ⋮ A consistent strain-based beam element with quaternion representation of rotations ⋮ Geometrically exact isogeometric Bernoulli-Euler beam based on the Frenet-Serret frame ⋮ Large-deformation instability behaviors of 3D beams supported with 3D hinge joints subjected to axial and torsional loadings ⋮ An isogeometric finite element formulation for geometrically exact Timoshenko beams with extensible directors ⋮ Variational modeling of plane-strain hyperelastic thin beams with thickness-stretching effect ⋮ A dynamic beam model for the motility of \textit{Listeria monocytogenes} ⋮ Velocity-based approach in non-linear dynamics of three-dimensional beams with enforced kinematic compatibility ⋮ Geometrically exact static isogeometric analysis of an arbitrarily curved spatial Bernoulli-Euler beam

Uses Software

• Matlab

Cites Work

• Unnamed Item
• Unnamed Item
• Flexible multibody dynamics
• Multi-body dynamics simulation of geometrically exact Cosserat rods
• Consistent quaternion interpolation for objective finite element approximation of geometrically exact beam
• Integrating rotation from angular velocity
• The quaternion-based three-dimensional beam theory
• The interpolation of rotations and its application to finite element models of geometrically exact rods
• A finite strain beam formulation. The three-dimensional dynamic problem. I
• Large deformations of thin curved plane beam of constant initial curvature
• A three-dimensional finite-strain rod model. II. Computational aspects
• Kinematics and dynamics of rigid and flexible mechanisms using finite elements and quaternion algebra
• On finite deformations of space-curved beams
• Finite rotation analysis and consistent linearization using projectors
• A non-linear beam space-time finite element formulation using quaternion algebra: Interpolation of the Lagrange multipliers and the appearance of spurious modes
• Large rotations revisited application of Lie algebra
• On locking-free shear deformable beam finite elements
• Work-conjugacy between rotation-dependent moments and finite rotations.
• Finite-element formulation of geometrically exact three-dimensional beam theories based on interpolation of strain measures.
• An excursion into large rotations
• A kinematically exact space finite strain beam model -- finite element formulation by generalized virtual work principle
• Dynamics of spatial beams in quaternion description based on the Newmark integration scheme
• The linearized three-dimensional beam theory of naturally curved and twisted beams: The strain vector formulation
• Analysis of shear locking in Timoshenko beam elements using the function space approach
• Quaternion-based rigid body rotation integration algorithms for use in particle methods
• Large displacement analysis of three-dimensional beam structures
• Simo-Vu Quoc rods using Clifford algebra
• On the differentiation of the Rodrigues formula and its significance for the vector‐like parameterization of Reissner–Simo beam theory
• On One‐Dimensional Large‐Displacement Finite‐Strain Beam Theory
• On large displacement-small strain analysis of structures with rotational degrees of freedom
• Equations of motion for general constrained systems in Lagrangian mechanics

This page was built for publication: On a virtual work consistent three-dimensional Reissner-Simo beam formulation using the quaternion algebra