SUMMARYThis study presents a general procedure of creating pure equilibrium tetrahedral finite elements for use under the elastostatic hypothesis. These pure equilibrium elements are of the Fraeijs de Veubeke type and the degree of the polynomial approximation functions of their internal stress field is the parameter generating this new elements family. The spurious kinematic modes (SKM), inherent in the equilibrium approach, are eliminated at the element level by converting each tetrahedron into a super-element defined as an assembly of four tetrahedral primitive elements. A mathematical discussion on the number of SKM of the primitive elements as well as their elimination by the super-element technique has been carried out. The development of first and second degree elements is presented here in detail and their efficiency in the frame of global error estimation by dual analysis is emphasized by two numerical applications. The main attribute of the error estimation by dual analysis is that it provides an upper bound on the global discretization error.

L'analyse duale pure a été l'une des premières méthodes utilisées pour estimer l'erreur de discrétisation globale commise lors d'un calcul par éléments finis. Elle repose sur la comparaison de deux solutions éléments finis, la première obtenue à partir d'un modèle cinématiquement admissible classique et la seconde issue d'un modèle statiquement admissible (approche de type équilibre). Nous présentons dans ce travail deux méthodes permettant de créer des éléments équilibre. La première qui peut être qualifiée d'hybride, permet d'étudier des problèmes bidimensionnels avec des éléments équilibre de degré élevé. La seconde, pour laquelle nous présentons dans ce travail l'extension récente aux problèmes 3D à maillages tétraédriques, est de type équilibre pur. Ces deux approches nous ont permis de présenter quelques résultats d'estimation de l'erreur globale par analyse duale.ABSTRACT. The pure dual analysis is one of the first methods developed to perform the estimation of the global discretization error of finite elements analysis. It is based on the comparison of two finite elements solutions, one of which being of the displacement type (kinematically admissible), the second one being of the equilibrium type (statically admissible). This work presents two methods allowing to create equilibrium elements. The first one which can be seen as an hybrid method, allows to compute high-order equilibrium solutions of 2D problems. The second method is of the pure equilibrium type. Its recent extension to 3D problems with tetrahedral mesh is presented here. Those approaches enabled us to present some results of global error estimation by dual analysis. MOTS-CLÉS : estimation d'erreur globale, analyse duale, modèles équilibre.

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Hydrogen storage remains a key issue for the high scale deployment of fuel cell applications. Gaseous hydrogen storage at high pressure with type IV vessels is the best technology. But it is necessary to reach a significant cost reduction of these storage systems. An optimization of the composite structure can be reached by numerical simulation. The goal of the OSIRHYS IV project is to develop and validate models and methods for composite high pressure design and optimization with behavior uncertainties knowledge. It was decided to limit this study to a particular topology, material and winding process. First burst simulations have been performed and results of linear static computations have been compared to experimental data. The numerical simulation models are compared with regards to vessel component masses, burst pressure, burst mode and local displacements. Results show that linear static analyses using axisymmetric and volume FE models could already predict with a reasonable accuracy the radial behavior of the tank in the case of a safe burst mode. Nevertheless, improvements of partner models are needed to reach better agreement with test data. These improvements need to be based on material and vessel geometry knowledge, behavior modelling and the FE model.