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.
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@article{CRMECA_2014__342_8_466_0,
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},
}
TY - JOUR AU - Mariem Miladi Chaabane AU - Régis Plateaux AU - Jean-Yves Choley AU - Chafik Karra AU - Alain Rivière AU - Mohamed Haddar TI - Topological approach to solve frame structures using topological collections and transformations JO - Comptes Rendus. Mécanique PY - 2014 SP - 466 EP - 477 VL - 342 IS - 8 PB - Elsevier DO - 10.1016/j.crme.2014.05.005 LA - en ID - CRMECA_2014__342_8_466_0 ER -
%0 Journal Article %A Mariem Miladi Chaabane %A Régis Plateaux %A Jean-Yves Choley %A Chafik Karra %A Alain Rivière %A Mohamed Haddar %T Topological approach to solve frame structures using topological collections and transformations %J Comptes Rendus. Mécanique %D 2014 %P 466-477 %V 342 %N 8 %I Elsevier %R 10.1016/j.crme.2014.05.005 %G en %F CRMECA_2014__342_8_466_0
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. https://comptes-rendus.academie-sciences.fr/mecanique/articles/10.1016/j.crme.2014.05.005/
[1] Analysis of structures by system theory, J. Struct. Div., ASCE, Volume 88 (1962), pp. 1-22
[2] Diakoptics, the Piecewise Solution for Large-Scale System, Macdonald, London, 1963
[3] Combinatorial representations in structural analysis, Comput. Civ. Eng., Volume 15 (2001) no. 3, pp. 193-207
[4] The duality relation between mechanisms and trusses, Mech. Mach. Theory, Volume 36 (2001) no. 3, pp. 343-369
[5] Transforming engineering problems through graph representations, Adv. Eng. Inform., Volume 17 (2003) no. 2, pp. 77-93
[6] Need for the definition of a topological structure for the complex systems modelling, CPI'2007, Rabat, Maroc, 22–24 octobre 2007 (2007)
[7] Continuité et cohérence d'une modélisation des systèmes mécatroniques basée(s) sur une structure topologique, Superior Engineering Institute of Paris SUPMECA, 2011 (PhD thesis)
[8] Topological approach to solve 2D truss structure using MGS language, IEEE MECATRONIC REM, 2012, pp. 437-444
[9] Transformation de collections topologiques de dimension arbitraire. Application à la modélisation de systèmes dynamiques, University of Évry–Val d'Essonne, 2006 (PhD thesis)
[10] Intégration des collections topologiques et des transformations dans un langage fonctionnel, University of Évry–Val d'Essonne, 2004 (PhD thesis)
[11] Computational models for integrative and developmental biology, Modelling and Simulation of Biological Processes in the Context of Genomics, Hermès, Paris, 2002
[12] Declarative modeling of a neurulation-like process, Biosystems, Volume 87 (2007) no. 2–3, pp. 281-288
[13] Solutio problematis ad geometriam situs pertinentis, Comment. Acad. Sci. Petropolitanae, Volume 8 (1741), pp. 128-140
[14] A Short Course in Tensor Analysis for Electrical Engineers, Wiley/Chapman & Hall, New York/London, 1942
[15] 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, USA, 1966, pp. 453-491
[16] An application of algebraic topology to numerical analysis: on the existence of a solution to the network problem, Proc. Natl. Acad. Sci. USA, Volume 41 (1955), pp. 518-521
[17] The Finite Element Method: A Practical Course, Butterworth/Heinemann, Boston/Oxford, 2003
[18] Modeling of complex physical systems http://www.modelica.org/
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