Dynamics of a flexible body: a two-field formulation

Dynamics; Flexible body; Model reduction; Multibody dynamics; Superelement; Convection velocity; Elastic body; Field formulation; Flexible bodies; Legendre transformations; Position-orientation; Reference axis; Velocity field; Modeling and Simulation; Aerospace Engineering; Mechanical Engineering; Computer Science Applications; Control and Optimization

Abstract :

[en] A two-field formulation of the nonlinear dynamics of an elastic body is presented in which positions/orientations and the resulting velocity field are treated as independent. Combining a nonclassical description of elastic velocity that includes the convection velocity due to elastic deformation with floating reference axes minimizing the relative kinetic energy due to elastic deformation provides a fully uncoupled expression of kinetic energy. A transformation inspired by the classical Legendre transformation concept is introduced to develop the motion equations in canonical form. Finite element discretization is achieved using the same shape function sets for elastic displacements and velocities. Specific attention is brought to the discretization of the gyroscopic forces induced by elastic deformation. A model reduction strategy to construct superelement models suitable for flexible multibody dynamics applications is proposed, which fulfills the essential condition of orthogonality between a rigid body and elastic motions. The problem of expressing kinematic connections at superelement boundaries is briefly addressed. Two academic examples have been developed to illustrate some of the concepts presented.

Disciplines :

Aerospace & aeronautics engineering
Mechanical engineering

Author, co-author :

Géradin, Michel ; Université de Liège - ULiège > Département d'aérospatiale et mécanique ; TUM-IAS, Garching, Germany

Language :

English

Title :

Dynamics of a flexible body: a two-field formulation

Publication date :

2021

Journal title :

Multibody System Dynamics

ISSN :

1384-5640

eISSN :

1573-272X

Publisher :

Springer Science and Business Media B.V.

Volume :

Issue :

Pages :

1-29

Peer reviewed :

Peer reviewed

Additional URL :

https://link.springer.com/content/pdf/10.1007/s11044-021-09801-0.pdf

Funders :

TUM - Technische Universität München [DE]

Funding text :

The author acknowledges the support of the Technical University of Munich’s Institute for Advanced Study (TUM-IAS). He also thanks Dr. Alejandro Cosimo (Conicet, Argentina and University of Liège, Belgium) for providing the simulations with the ODIN software.The author acknowledges the support of the Technical University of Munich’s Institute for Advanced Study (TUM-IAS). He also thanks Dr. Alejandro Cosimo (Conicet, Argentina and University of Liège, Belgium) for providing the simulations with the ODIN software.

Available on ORBi :

since 07 February 2023

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