Symmetry-Preserving Formulation of Nonlinear Constraints in Multibody Dynamics

García Orden, Juan Carlos (2018). Symmetry-Preserving Formulation of Nonlinear Constraints in Multibody Dynamics. In: "1ª Conferencia de dinámica estructural", 20-21, Junio, Madrid. ISBN 978-84-09-01733-1. pp. 223-226.


Title: Symmetry-Preserving Formulation of Nonlinear Constraints in Multibody Dynamics
  • García Orden, Juan Carlos
Item Type: Presentation at Congress or Conference (Other)
Event Title: 1ª Conferencia de dinámica estructural
Event Dates: 20-21, Junio
Event Location: Madrid
Title of Book: Proceedings of the DinEst 2018
Date: 2018
ISBN: 978-84-09-01733-1
Freetext Keywords: Nonlinear Dynamics, Multibody, Constraints, Energy-Momentum, Symmetries
Faculty: E.T.S.I. Caminos, Canales y Puertos (UPM)
Department: Mecánica de Medios Continuos y Teoría de Estructuras
Creative Commons Licenses: Recognition - No derivative works - Non commercial

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Practical multibody numerical models are typically composed by a set of bodies (rigid or deformable) linked by joints, represented by constraint equations. Thus, a proper formulation of constraints is an essential aspect in the numerical analysis of the dynamics of these models, and may be incorporated by means of Lagrange multipliers, Augmented Lagrangian or Penalty formulations. On the other hand, geometrical integrators are particular time-stepping schemes that have been successfully employed during the last decades in many applications, including multibody systems. One of them is the so-called Energy-Momentum (EM) scheme, that exhibits excellent stability and physical accuracy, but demanding a specific (consistent) formulation of constraints. In particular, EM penalty formulations are specially simple, based on the application of a discrete derivative of the constraint potential. However, this discrete derivative may take several forms, not all of them being consistent. In particular, when applied to constraint potentials endowed with certain symmetries (associated to the conservation of linear and angular momenta, found in many common practical joints), may produce numerical results that conserves the energy but violates the symmetries, thus obtaining unphysical motions. The discrete derivative proposed in this work, while first introduced several years ago, overcomes this problem, mainly due to its particular implementation. Its discrete properties related with energy and symmetries are analyzed and several numerical results of practical multibody models will be presented.

Funding Projects

Government of SpainDPI2015- 67667-C3-2-RUnspecifiedUnspecifiedModelización del comportamiento termo-mecánico de metales a nivel del cristal

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Item ID: 54605
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Deposited by: Memoria Investigacion
Deposited on: 08 Apr 2019 16:14
Last Modified: 08 Apr 2019 16:14
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