Abstract
In this paper, a unified topological approach for the modeling of complex systems is presented. This approach is based on topological notions such as the topological collections and the transformations. These two topological notions allow the separation between the topological structure (interconnection laws) and the physics (behavioral laws) of the studied system. In fact, regardless of the complexity of the system, interconnection laws are declared through the topological collections and behavioral laws through the transformations. Therefore, a system is considered as local elements linked by neighbor relations to which local behavioral laws are associated. In order to show that the topological modeling approach is independent of the physical nature or the number of elementary components, a 2D beams structure with topological modification is taken as an example. In fact, a beams structure is a well-structured set of beams. Classical modeling consists in considering such structure as a global system and the resolution necessities the computation of the global stiffness matrix and therefore a modification of the beams structure involves the actualization of this matrix. Contrary to the classical approach, the application of the topological collections allow to consider a beams structure as local elements with no assembling terms as it is demonstrated through this paper.
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Acknowledgements
The authors gratefully acknowledge the assistance and the financial support of the project 19PEJC10-12 by the Tunisian Ministry of Higher Education and Scientific Research.
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Miladi Chaabane, M., Plateaux, R., Choley, JY., Karra, C., Riviere, A., Haddar, M. (2020). A Unified Topological Approach for the Modeling: Application to a 2D Beams Structure. In: Barkallah, M., Choley, JY., Louati, J., Ayadi, O., Chaari, F., Haddar, M. (eds) Mechatronics 4.0. MECHATRONICS 2019. Lecture Notes in Mechanical Engineering. Springer, Cham. https://doi.org/10.1007/978-3-030-46729-6_3
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