Multisymplectic Galerkin Lie group variational integrators for geometrically exact beam dynamics based on unit dual quaternion interpolation -- no shear locking

DOI10.1016/j.cma.2020.113475zbMath1506.37107OpenAlexW3112329814WikidataQ115358885 ScholiaQ115358885MaRDI QIDQ2021224

Rodrigo T. Sato Martín de Almagro, Thomas Leitz, Sigrid Leyendecker

Publication date: 26 April 2021

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.2020.113475

zbMATH Keywords

Lie groupmultisymplecticvariational integratorhigh-order integrationgeometrically exact beamspacetime discretization

Mathematics Subject Classification ID

Rods (beams, columns, shafts, arches, rings, etc.) (74K10) Variational methods for problems in mechanics (70G75) Discretization methods and integrators (symplectic, variational, geometric, etc.) for dynamical systems (37M15) Symmetries, Lie group and Lie algebra methods for problems in mechanics (70G65)

Related Items (2)

Multisymplectic Hamiltonian variational integrators ⋮ A Lie group variational integration approach to the full discretization of a constrained geometrically exact Cosserat beam model

Cites Work

• Unnamed Item
• Unnamed Item
• Construction and analysis of higher order Galerkin variational integrators
• Exponential and Cayley maps for dual quaternions
• A Hamiltonian and multi-Hamiltonian formulation of a rod model using quaternions
• A finite strain beam formulation. The three-dimensional dynamic problem. I
• Discrete versions of some classical integrable systems and factorization of matrix polynomials
• Multisymplectic geometry, variational integrators, and nonlinear PDEs
• Construction and analysis of higher order variational integrators for dynamical systems with holonomic constraints
• Galerkin Lie-group variational integrators based on unit quaternion interpolation
• Multisymplectic Lie group variational integrator for a geometrically exact beam in \(\mathbb{R}^3\)
• Discrete variational Lie group formulation of geometrically exact beam dynamics
• Spectral variational integrators
• Lie group variational integrators for the full body problem
• Computational geometric optimal control of rigid bodies
• Variational integrators and the finite element method
• Multisymplectic variational integrators and space/time symplecticity
• Discrete mechanics and variational integrators
• Backward Error Analysis for Numerical Integrators
• The Mathematical Theory of Finite Element Methods

This page was built for publication: Multisymplectic Galerkin Lie group variational integrators for geometrically exact beam dynamics based on unit dual quaternion interpolation -- no shear locking