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Discrete variational Lie group formulation of geometrically exact beam dynamics (Q2340899)

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English	Discrete variational Lie group formulation of geometrically exact beam dynamics	scientific article

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scholarly article

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Discrete variational Lie group formulation of geometrically exact beam dynamics (English)

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zbMATH Open document ID

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10.1007/s00211-014-0659-4

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François Demoures

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François Gay-Balmaz

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Sina Ober-Blöbaum

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Sigrid Leyendecker

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Numerische Mathematik

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publication date

21 April 2015

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Mathematics Subject Classification ID

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zbMATH DE Number

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zbMATH Keywords

integrator

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discrete momentum maps

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MaRDI profile type

MaRDI publication profile

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full work available at URL

https://doi.org/10.1007/s00211-014-0659-4

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Kirchhoff’s problem for nonlinearly elastic rods

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Nonlinear problems of elasticity

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On the parametrization of finite rotations in computational mechanics. A classification of concepts with application to smooth shells

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

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Constrained dynamics of geometrically exact beams

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Discrete time Lagrangian mechanics on Lie groups, with an application to the Lagrange top

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Discrete Lagrangian reduction, discrete Euler-Poincaré equations, and semidirect products

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Geometric invariance

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Hamilton-Pontryagin integrators on Lie groups. I: Introduction and structure-preserving properties

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Stochastic variational integrators

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Variational time integrators

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Objectivity of strain measures in the geometrically exact three-dimensional beam theory and its finite-element implementation

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Some applications of semi-discrete variational integrators to classical field theories

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Multisymplectic Lie group variational integrator for a geometrically exact beam in \(\mathbb{R}^3\)

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Symmetry reduced dynamics of charged molecular strands

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Nonsmooth Lagrangian Mechanics and Variational Collision Integrators

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Variational principles for spin systems and the Kirchhoff rod

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Reduced variational formulations in free boundary continuum mechanics

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Time integration and discrete Hamiltonian systems

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Geometric Numerical Integration

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Computational aspects of vector‐like parametrization of three‐dimensional finite rotations

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Interpolation of rotational variables in nonlinear dynamics of 3D beams

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Geometrically exact 3D beam theory: Implementation of a strain-invariant finite element for statics and dynamics

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Problems associated with the use of Cayley transform and tangent scaling for conserving energy and momenta in the Reissner-Simo beam theory

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A discrete mechanics approach to the Cosserat rod theory-Part 1: static equilibria

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Geometric discretization of nonholonomic systems with symmetries

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Multi-body dynamics simulation of geometrically exact Cosserat rods

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Numerical aspects in the dynamic simulation of geometrically exact rods

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Computational dynamics of a 3D elastic string pendulum attached to a rigid body and an inertially fixed reel mechanism

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On the dynamics in space of rods undergoing large motions - A geometrically exact approach

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Asynchronous variational integrators

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Objective energy-momentum conserving integration for the constrained dynamics of geometrically exact beams

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The discrete null space method for the energy-consistent integration of constrained mechanical systems. III: Flexible multibody dynamics

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Variational integrators for constrained dynamical systems

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A Variational Approach to Multirate Integration for Constrained Systems

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Discrete mechanics and optimal control for constrained systems

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Multisymplectic geometry, variational integrators, and nonlinear PDEs

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Discrete Euler-Poincaré and Lie-Poisson equations

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Discrete mechanics and variational integrators

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Discrete versions of some classical integrable systems and factorization of matrix polynomials

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Discrete mechanics and optimal control: An analysis

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On one-dimensional finite-strain beam theory: the plane problem

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On One‐Dimensional Large‐Displacement Finite‐Strain Beam Theory

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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

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The interpolation of rotations and its application to finite element models of geometrically exact rods

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The Hamiltonian structure of nonlinear elasticity: The material and convective representations of solids, rods, and plates

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A three-dimensional finite-strain rod model. II. Computational aspects

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Nonintrusive and Structure Preserving Multiscale Integration of Stiff ODEs, SDEs, and Hamiltonian Systems with Hidden Slow Dynamics via Flow Averaging

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