A frame-invariant scheme for the geometrically exact beam using rotation vector parametrization
type: Item
instance of: scholarly article
title: A frame-invariant scheme for the geometrically exact beam using rotation vector parametrization
zbMATH Open document ID: 1162.74386
author: J. Martínez
published in: Computational Mechanics
publication date: 2009-06-08T00:00:00Z
Mathematics Subject Classification ID: 74K10
Mathematics Subject Classification ID: 74S05
zbMATH DE Number: 5562515
zbMATH Keywords: geometrically exact beam
zbMATH Keywords: finite rotation
zbMATH Keywords: rotation manifold
zbMATH Keywords: tangent space
zbMATH Keywords: relative rotation
zbMATH Keywords: objective strain
zbMATH Keywords: path-independence
MaRDI profile type: Publication
full work available at URL: s00466-008-0358-z
OpenAlex ID: W2050666945
Wikidata QID: Q60585174
cites work: A finite strain beam formulation. The three-dimensional dynamic problem. I
cites work: A three-dimensional finite-strain rod model. II. Computational aspects
cites work: On the Dynamics of Flexible Beams Under Large Overall Motions—The Plane Case: Part I
cites work: A beam finite element non-linear theory with finite rotations
cites work: On the dynamics in space of rods undergoing large motions - A geometrically exact approach
cites work: A geometrically-exact rod model incorporating shear and torsion-warping deformation
cites work: Computational aspects of vector‐like parametrization of three‐dimensional finite rotations
cites work: On finite element implementation of geometrically nonlinear Reissner's beam theory: Three-dimensional curved beam elements
cites work: A kinematically exact space finite strain beam model -- finite element formulation by generalized virtual work principle
cites work: Statically and kinematically exact nonlinear theory of rods and its numerical verification
cites work: Total Lagrangian Reissner's geometrically exact beam element without singularities
cites work: Simo-Vu Quoc rods using Clifford algebra
cites work: An exact conserving algorithm for nonlinear dynamics with rotational DOFs and general hyperelasticity. I: Rods
cites work: Integrating finite rotations
cites work: Frame-indifferent beam finite elements based upon the geometrically exact beam theory
cites work: A triangular finite shell element based on a fully nonlinear shell formulation
cites work: Parametrization of finite rotations in computational dynamics: a review
cites work: A natural classification of vibration modes of polygonal ducts based on group theoretic analysis
cites work: On the differentiation of the Rodrigues formula and its significance for the vector‐like parameterization of Reissner–Simo beam theory
cites work: On the choice of finite rotation parameters
cites work: On the role of frame invariance in structural mechanics models at finite rotations
cites work: Objectivity of strain measures in the geometrically exact three-dimensional beam theory and its finite-element implementation
cites work: Geometrically exact 3D beam theory: Implementation of a strain-invariant finite element for statics and dynamics
cites work: The interpolation of rotations and its application to finite element models of geometrically exact rods
cites work: 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
cites work: Consistent quaternion interpolation for objective finite element approximation of geometrically exact beam
cites work: On one-dimensional finite-strain beam theory: the plane problem
cites work: Ordinary differential equations of non-linear elasticity. I: Foundations of the theories of non-linearly elastic rods and shells
cites work: Q4527707
cites work: Interpolation of rotational variables in nonlinear dynamics of 3D beams
cites work: On the BCH-formula in \(\mathfrak{so}(3)\)
cites work: Large displacement analysis of three-dimensional beam structures
DOI: 10.1007/S00466-008-0358-Z
description: scientific article; zbMATH DE number 5562515