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

2021 ◽  
Vol 374 ◽  
pp. 113475
Author(s):  
Thomas Leitz ◽  
Rodrigo T. Sato Martín de Almagro ◽  
Sigrid Leyendecker
Keyword(s):  
Lie Group ◽  
Beam Dynamics ◽  
Variational Integrators ◽  
Shear Locking ◽  
Dual Quaternion ◽  
Geometrically Exact Beam ◽  
Quaternion Interpolation

scholarly journals Discrete variational Lie group formulation of geometrically exact beam dynamics

2014 ◽  
Vol 130 (1) ◽  
pp. 73-123 ◽  
Author(s):  
F. Demoures ◽  
F. Gay-Balmaz ◽  
S. Leyendecker ◽  
S. Ober-Blöbaum ◽  
T. S. Ratiu ◽  
...  
Keyword(s):  
Lie Group ◽  
Beam Dynamics ◽  
Geometrically Exact Beam

scholarly journals Multisymplectic variational integrators and space/time symplecticity

2016 ◽  
Vol 14 (03) ◽  
pp. 341-391 ◽  
Author(s):  
François Demoures ◽  
François Gay-Balmaz ◽  
Tudor S. Ratiu
Keyword(s):  
Lie Group ◽  
Numerical Scheme ◽  
Variational Integrators ◽  
Beam Model ◽  
Structure Preserving ◽  
Dimensional Spacetime ◽  
Geometrically Exact Beam ◽  
Temporal And Spatial ◽  
Group Symmetries

Multisymplectic variational integrators are structure-preserving numerical schemes especially designed for PDEs derived from covariant spacetime Hamilton principles. The goal of this paper is to study the properties of the temporal and spatial discrete evolution maps obtained from a multisymplectic numerical scheme. Our study focuses on a (1+1)-dimensional spacetime discretized by triangles, but our approach carries over naturally to more general cases. In the case of Lie group symmetries, we explore the links between the discrete Noether theorems associated to the multisymplectic spacetime discretization and to the temporal and spatial discrete evolution maps, and emphasize the role of boundary conditions. We also consider in detail the case of multisymplectic integrators on Lie groups. Our results are illustrated with the numerical example of a geometrically exact beam model.

scholarly journals Asynchronous variational Lie group integration for geometrically exact beam dynamics

PAMM ◽  
2013 ◽  
Vol 13 (1) ◽  
pp. 45-46 ◽  
Author(s):  
Francois Demoures ◽  
Francois Gay-Balmaz ◽  
Thomas Leitz ◽  
Sigrid Leyendecker ◽  
Sina Ober-Blöbaum ◽  
...  
Keyword(s):  
Lie Group ◽  
Beam Dynamics ◽  
Geometrically Exact Beam ◽  
Group Integration ◽  
Lie Group Integration

scholarly journals Multisymplectic Lie group variational integrator for a geometrically exact beam in

2014 ◽  
Vol 19 (10) ◽  
pp. 3492-3512 ◽  
Author(s):  
François Demoures ◽  
François Gay-Balmaz ◽  
Marin Kobilarov ◽  
Tudor S. Ratiu
Keyword(s):  
Lie Group ◽  
Variational Integrator ◽  
Geometrically Exact Beam
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