Comptes Rendus
Topological approach to solve frame structures using topological collections and transformations
Comptes Rendus. Mécanique, Volume 342 (2014) no. 8, pp. 466-477.

The present work tackled the modeling of frame structures using a topological approach based on the concepts of topological collections and transformations. The topological collections are used to specify the interconnection law between the frame structures and the transformations that are used to describe their behavior. As a language allowing the application of this approach, we applied the MGS (Modeling of General System) language. To validate this approach, we studied the case of two- and three-dimensional frame structures. Then, the results obtained using the MGS language are presented and compared to those obtained by the structural calculation software by the finite-element method RDM6. For both studied cases, we find that the results obtained by MGS language based on the notions of topological collections and transformations and those obtained by the RDM6 software based on the finite element method are very close, which validates our approach. Using this topological approach, any structure can be characterized by local relations between its elements, thus making it possible to dissociate its topology and its physics. Indeed, in our topological approach, we separately define the topology of the studied frame structure and the local behavior law as well as the equilibrium equations of its various components. Therefore, this topological approach might be generalized to model complex systems which can be considered as a set of local elements linked by a neighborhood relationship.

Published online:
DOI: 10.1016/j.crme.2014.05.005
Keywords: Topological collections, Transformations, Frame structures, MGS language

Mariem Miladi Chaabane 1, 2; Régis Plateaux 2; Jean-Yves Choley 2; Chafik Karra 1; Alain Rivière 2; Mohamed Haddar 1

1 Mechanical, Modeling and Manufacturing Unit, National Engineering School of Sfax (ENIS), BP 1173, 3038 Sfax, Tunisia
2 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
     author = {Mariem Miladi Chaabane and R\'egis Plateaux and Jean-Yves Choley and Chafik Karra and Alain Rivi\`ere and Mohamed Haddar},
     title = {Topological approach to solve frame structures using topological collections and transformations},
     journal = {Comptes Rendus. M\'ecanique},
     pages = {466--477},
     publisher = {Elsevier},
     volume = {342},
     number = {8},
     year = {2014},
     doi = {10.1016/j.crme.2014.05.005},
     language = {en},
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AU  - Alain Rivière
AU  - Mohamed Haddar
TI  - Topological approach to solve frame structures using topological collections and transformations
JO  - Comptes Rendus. Mécanique
PY  - 2014
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EP  - 477
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PB  - Elsevier
DO  - 10.1016/j.crme.2014.05.005
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%A Jean-Yves Choley
%A Chafik Karra
%A Alain Rivière
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Mariem Miladi Chaabane; Régis Plateaux; Jean-Yves Choley; Chafik Karra; Alain Rivière; Mohamed Haddar. Topological approach to solve frame structures using topological collections and transformations. Comptes Rendus. Mécanique, Volume 342 (2014) no. 8, pp. 466-477. doi : 10.1016/j.crme.2014.05.005.

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