Variational Lie group formulation of geometrically exact beam dynamics: synchronous and asynchronous integration

Leitz T, Ober-Blöbaum S, Leyendecker S (2014)

Publication Language: English

Publication Type: Book chapter / Article in edited volumes

Publication year: 2014

Publisher: Springer

Edited Volumes: Computational Methods in Applied Sciences

City/Town: Berlin

Book Volume: 35

Pages Range: 175-203

DOI: 10.1007/978-3-319-07260-9_8

Abstract

For the elastodynamic simulation of a geometrically exact beam, an asynchronous variational integrator (AVI) is derived from a PDE viewpoint. Variational integrators are symplectic and conserve discrete momentum maps and since the presented integrator is derived in the Lie group setting, it intrinsically preserves the group structure without the need for constraints. The discrete Euler-Lagrange equations are derived in a general manner and then applied to the beam. A decrease of computational cost is to be expected in situations, where the time steps have to be very low in certain parts of the beam but not everywhere, e.g. if some regions of the beam are moving faster than others. The implementation allows synchronous as well as asynchronous time stepping and shows very good energy behavior, i.e. there is no drift of the total energy for conservative systems.

Authors with CRIS profile

Thomas Leitz Institute of Applied Dynamics Sigrid Leyendecker Institute of Applied Dynamics

Related research project(s)

Space time discretization for flexible multibody systems and multisymplectic variational integrators Oct. 1, 2011 - Sept. 30, 2018

Involved external institutions

Universität Paderborn DE Germany (DE)

How to cite

APA:

Leitz, T., Ober-Blöbaum, S., & Leyendecker, S. (2014). Variational Lie group formulation of geometrically exact beam dynamics: synchronous and asynchronous integration. In Computational Methods in Applied Sciences. (pp. 175-203). Berlin: Springer.

MLA:

Leitz, Thomas, Sina Ober-Blöbaum, and Sigrid Leyendecker. "Variational Lie group formulation of geometrically exact beam dynamics: synchronous and asynchronous integration." Computational Methods in Applied Sciences. Berlin: Springer, 2014. 175-203.

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