Comptes Rendus
Integration of topological modification within the modeling of multi-physics systems: Application to a Pogo-stick
Comptes Rendus. Mécanique, Volume 346 (2018) no. 5, pp. 351-365.

The present work tackles the modeling of multi-physics systems applying a topological approach while proceeding with a new methodology using a topological modification to the structure of systems. Then the comparison with the Magos' methodology is made. Their common ground is the use of connectivity within systems. The comparison and analysis of the different types of modeling show the importance of the topological methodology through the integration of the topological modification to the topological structure of a multi-physics system. In order to validate this methodology, the case of Pogo-stick is studied. The first step consists in generating a topological graph of the system. Then the connectivity step takes into account the contact with the ground. During the last step of this research; the MGS language (Modeling of General System) is used to model the system through equations. Finally, the results are compared to those obtained by MODELICA. Therefore, this proposed methodology may be generalized to model multi-physics systems that can be considered as a set of local elements.

Published online:
DOI: 10.1016/j.crme.2018.01.004
Keywords: Topological approach, Topological modification, Connectivity, Pogo-stick, MGS language

Nourhene Abdeljabbar Kharrat 1, 2; Régis Plateaux 1; Mariem Miladi Chaabane 2; Jean-Yves Choley 1; Chafik Karra 2; Mohamed Haddar 2

1 Laboratory of Engineering of the Mechanical Structures and Materials, High Institute of Mechanic of Paris (SUPMECA), 3, rue Fernand-Hainaut, 93407 Saint-Ouen cedex, France
2 Laboratory Mechanical, Modeling and Manufacturing, National Engineering School of Sfax (ENIS), BP 1173, 3038 Sfax, Tunisia
     author = {Nourhene Abdeljabbar Kharrat and R\'egis Plateaux and Mariem Miladi Chaabane and Jean-Yves Choley and Chafik Karra and Mohamed Haddar},
     title = {Integration of topological modification within the modeling of multi-physics systems: {Application} to a {Pogo-stick}},
     journal = {Comptes Rendus. M\'ecanique},
     pages = {351--365},
     publisher = {Elsevier},
     volume = {346},
     number = {5},
     year = {2018},
     doi = {10.1016/j.crme.2018.01.004},
     language = {en},
AU  - Nourhene Abdeljabbar Kharrat
AU  - Régis Plateaux
AU  - Mariem Miladi Chaabane
AU  - Jean-Yves Choley
AU  - Chafik Karra
AU  - Mohamed Haddar
TI  - Integration of topological modification within the modeling of multi-physics systems: Application to a Pogo-stick
JO  - Comptes Rendus. Mécanique
PY  - 2018
SP  - 351
EP  - 365
VL  - 346
IS  - 5
PB  - Elsevier
DO  - 10.1016/j.crme.2018.01.004
LA  - en
ID  - CRMECA_2018__346_5_351_0
ER  - 
%0 Journal Article
%A Nourhene Abdeljabbar Kharrat
%A Régis Plateaux
%A Mariem Miladi Chaabane
%A Jean-Yves Choley
%A Chafik Karra
%A Mohamed Haddar
%T Integration of topological modification within the modeling of multi-physics systems: Application to a Pogo-stick
%J Comptes Rendus. Mécanique
%D 2018
%P 351-365
%V 346
%N 5
%I Elsevier
%R 10.1016/j.crme.2018.01.004
%G en
%F CRMECA_2018__346_5_351_0
Nourhene Abdeljabbar Kharrat; Régis Plateaux; Mariem Miladi Chaabane; Jean-Yves Choley; Chafik Karra; Mohamed Haddar. Integration of topological modification within the modeling of multi-physics systems: Application to a Pogo-stick. Comptes Rendus. Mécanique, Volume 346 (2018) no. 5, pp. 351-365. doi : 10.1016/j.crme.2018.01.004.

[1] R. Plateaux Continuité et cohérence d'une modélisation des systèmes mécatroniques basée(s) sur une structure topologique, Superior Engineering Institute of Paris, SUPMECA, 2011 (PhD thesis)

[2] Ø. Bjorke Manufacturing Systems Theory – A Geometric Approach to Connection, The Norwegian Institute of Technology, Tapir Publisher, 1995

[3] M. Chaabane Miladi Modélisation géométrique et mécanique pour les systèmes mécatroniques, National School of Engineers of Sfax and Ecole Centrale Paris, 2014 (PhD thesis)

[4] A. Spicher Transformation de collections topologiques de dimension arbitraire. Application à la modélisation de systèmes dynamiques, University of Évry-Val-d'Essonne, France, 2006 (PhD thesis)

[5] J. Cohen Intégration des collections topologiques et des transformations dans un langage fonctionnel, University of Évry-Val-d'Essonne, France, 2004 (PhD thesis)

[6] J.-L. Giavitto; C. Godin; O. Michel; P. Prusinkiewicz Computational models for integrative and developmental biology, Modelling and Simulation of Biological Processes in the Context of Genomics, Hermès, Paris, 2002

[7] A. Spicher; O. Michel Declarative modeling of a neurulation-like process, Biosystems, Volume 87 (2007) no. 2–3, pp. 281-288

[8] L. Euler Solutio problematis ad geometriam situs pertinentis, Comment. Acad. scientiar. Petropolit., Volume 8 (1741), pp. 128-140

[9] G. Kron Diakoptics: The Piecewise Solution for Large-Scale System, Macdonald, London, 1963

[10] J.-P. Roth An application of algebraic topology to numerical analysis: on the existence of a solution to the network problem, Proc. Natl. Acad. Sci., Volume 41 (1955), pp. 518-521

[11] F. Branin The algebraic-topological basis for network analogies and the vector calculus, Proceedings of the Symposium on Generalized Networks, Polytechnic Press of the Polytechnic Institute of Brooklyn, Brooklyn, NY, 1966, pp. 453-491

[12] F.A. Firestone A new analogy between mechanical and electrical systems, J. Acoust. Soc. Am., Volume 4 (1933) no. 13, pp. 249-267

[13] H.M. Trent Isomorphisms between oriented linear graphs and lumped physical systems, J. Acoust. Soc. Am., Volume 27 (1955) no. 3, pp. 500-527

[14] E. Tonti, A classification diagram for physical variables, 2003.

[15] E. Tonti A direct discrete formulation of field laws: the cell method, Comput. Model. Eng. Sci., Volume 2 (2001) no. 2, pp. 237-258

[16] O. Maurice Introduction d'une théorie des jeux dans des topologies dynamiques, Université de Limoges, France, 2013

[17] A. Van der Schaft The Hamiltonian formulation of energy conserving physical systems with ports, Arch. Electron. Übertrag. Tech., Volume 49 (1995), pp. 362-371

[18] A. van der Schaft Port-Hamiltonian systems: an introductory survey, Proceedings of the International Congress of Mathematicians, vol. III, European Mathematical Society Publishing House (EMS Ph), 2006, pp. 1339-1365

[19] H. Paynter Analysis and Design of Engineering Systems, MIT Press, Cambridge, UK, 1961

[20] M. Magos Rivera Sur la modélisation des systèmes dynamiques à topologie variable, École doctorale d'électronique électrotechnique et automatique, Lyon, France, 2005 (PhD thesis)

[21] C. Valentin; M. Magos; B. Maschke A port-Hamiltonian formulation of physical switching systems with varying constraints, Automatica, Volume 43 (2007) no. 7, pp. 1125-1133

[22] M. Chaabane Miladi; R. Plateaux; J.-Y. Choley; C. Karra; A. Rivière; M. Haddar Topological approach to solve 2D truss structure using MGS language, 9th France–Japan & 7th Europe–Asia Congress on Mechatronics (MECATRONICS)/Research and Education in Mechatronics, REM, Paris, 2012

[23] M. Chaabane Miladi; R. Plateaux; J.-Y. Choley; C. Karra; A. Riviere; M. Haddar Topological modeling of a one stage spur gear transmission, Chin. J. Mech. Eng., Volume 27 (2014), pp. 900-908

[24] F. Harary; G. Gupta Dynamic graph models, Math. Comput. Model., Volume 25 (1997) no. 7, pp. 79-87

[25] D.D. Šiljak Dynamic graphs, Nonlinear Anal. Hybrid Syst., Volume 2 (2008) no. 2, pp. 544-567

[26] J.L. Gross; J. Yellen Graph Theory and Its Applications, CRC Press, Boca Raton, FL, USA, 2005

[27] J.A. Bondy; U.S.R. Murty Graph Theory with Applications, vol. 290, Macmillan, London, 1976

[28] W.L. Roque; A.C.A. de Souza; D.X. Barbieri The Euler–Poincaré characteristic applied to identify low bone density from vertebral tomographic images, Rev. Bras. Reumatol., Volume 49 (2009) no. 2, pp. 140-145

[29] History of Topology (I.M. James, ed.), Elsevier, 1999

[30] J. Bertin; J.-P. Demailly; L. Illusie; C. Peters Introduction à la théorie de Hodge, Société mathématique de France, 1996

[31] (Modelica, Modeling of Complex Physical Systems)

[32] N. Abdeljabbar Kharrat; R. Plateaux; M. Chaabane Miladi; C. Karra; J.-Y. Choley; M. Haddar Topological modeling of 2D piezoelectric truss structure using the MGS language, CMSM'2017 (2017), pp. 349-360 (chapter 35)

[33] N. Abdeljabbar Kharrat, R. Plateaux, M. Chabaane Miladi, C. Karra, J.-Y. Choley, M. Haddar, Topological modeling of a wind turbine, in: IEEE International Symposium on Systems Engineering, Vienna, Austria, 11–13 October 2017.

Cited by Sources:

Comments - Policy