Object-oriented modelling of a flexible beam including geometric nonlinearities

Davide Invernizzi
Politecnico Di Milano, Dipartimento di Scienze e Tecnologie Aerospaziali, Via La Masa 34, 20156 Milano, Italy

Bruno Scaglioni
Politecnico Di Milano, Dipartimento di Elettronica, Informazione e Bioingegneria DEIB, Via Ponzio 34/5, 20133 Milano, Italy

Gianni Ferretti
Politecnico Di Milano, Dipartimento di Elettronica, Informazione e Bioingegneria DEIB, Via Ponzio 34/5, 20133 Milano, Italy

Paolo Albertelli
Politecnico Di Milano, Dipartimento di Meccanica, Via La Masa 1, 20156 Milano, Italy

Ladda ner artikelhttp://dx.doi.org/10.3384/ecp17132735

Ingår i: Proceedings of the 12th International Modelica Conference, Prague, Czech Republic, May 15-17, 2017

Linköping Electronic Conference Proceedings 132:80, s. 735-744

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Publicerad: 2017-07-04

ISBN: 978-91-7685-575-1

ISSN: 1650-3686 (tryckt), 1650-3740 (online)


In this paper, an efficient approach for the modelling and simulation of slender beams subject to heavy inertial loads is presented. The limitations imposed by a linear formulation of elasticity are overcome by a second order expansion of the displacement field, based on a geometrical exact beam model. In light of this, the nonlinearities of the elastic terms are shifted as inertial contributions, which yields an expression of the equations of motion in closed form. Thanks to the formulation in closed form, the proposed model is implemented in Modelica, with particular care to the suitability of the model with respect to the Modelica Multibody library. After describing the model formulation and implementation, the paper presents some simulation results, in order to validate the model with respect to benchmarks, widely adopted in literature.


Nonlinear beams, flexible multibody, geometric stiffening, Modelica flexible


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