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Communication Dans Un Congrès Année : 2006

Explicit dynamic with X-FEM to handle complex geometries

Résumé

Although the calculation capacities have considerably increased these last years, thecomplexity of the numerical simulations in dynamic fields still induce many problems, essentially dueto CPU time calculation. For instance, the use of explicit scheme yields a critical time step. It dependson the greatest structure eigenvalue [1], [2]. Commonly, rather than to identify this eigenvalue, anupper approximation computed corresponds to the smaller characteristic size (if all elements share thesame behavior). These critical time steps are usually induced by mesh constraints. For complexgeometries, very small sized elements may arise. One approach is then to optimize the mesh byremoving elements or by using mass scaling to improve the critical time step.The work is based on the developments suggested for static problems, which are using theeXtended Finite Element Method [3], [4]. Thanks to the unity partition theory, it is possible to addsome specific functions of enrichment to the conventional approximation field of the displacement.These added functions allow, for example, the treatment of cracks, material interfaces, holes, etc.Consequently, this approach authorizes the non-conformity between mesh and discontinuities.This paper presents the work carried out about the X-FEM finite elements, which arededicated to the dynamic explicit problems including holes or external surfaces. In a first part, thedevelopments are presented for 1D cases and for mono-material structures. The objective is topropose the theoretical framework of the X-FEM finite element: a reformulation of the stiffnessmatrix and an adapted mass matrix offer the possibility to increase time step calculation in the case ofnon-meshed surfaces. A generalization of the method is then proposed for the 2D and 3D cases.Validations for different type of structure are exposed. The results in comparison with ABAQUSsoftware are relevant and allows us to present some outlooks.
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hal-01240586 , version 1 (09-12-2015)

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Patrick Rozycki, Eric Béchet, Nicolas Moes. Explicit dynamic with X-FEM to handle complex geometries. III European Conference on Computational Mechanics - ECCM 2006, Jun 2006, Lisbon, Portugal. ⟨10.1007/1-4020-5370-3_401⟩. ⟨hal-01240586⟩
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