Problèmes industriels de grande dimension en mécanique numérique du contact : performance, fiabilité et robustesse

Abstract : This work deals with computational contact mechanics between deformable solids. The aim of this work is to improve the performance, the reliability and the robustness of the algorithms and numerical models set in Code_Aster which is finite element code developped by Électricité De France (EDF) for its engineering needs. The proposed algorithms are used to solve high dimensional industrial problems in order to optimize the computational running times. Several solutions techniques are available in the field of computational contact mechanics but they must take into account the difficulties coming from non-smooth aspects due to Signorini-Coulomb laws coupled to large deformations of bodies and material non linearities. Firstly the augmented Lagrangian formulation called " stabilized Lagrangian " is introduced. Successively, the mathematical properties of the discrete operators are highlighted and furthermore a novel energetic function is presented. Secondly the kinematical condition with regard to the normal unknowns are reinforced through unconstrained optimization techniques which result to a novel formulation which is so-called " non standard augmented Lagrangian formulation ". Three types of strategies are implemented in the code. The generalized Newton method is developped : it is a method in which all the non linearities are solved in one loop of iterations. The partial Newton method is an hybrid technique between the generalized Newton one and a fixed point method. Finally, a treatment of cycling effects is implemented : some oscillations on contact point status can lead to non convergent algorithms, hence in this work a control strategy is proposed in order to improve the robustness of solutions techniques.
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Ayaovi Dzifa Kudawoo. Problèmes industriels de grande dimension en mécanique numérique du contact : performance, fiabilité et robustesse. Mécanique des structures [physics.class-ph]. Université de Provence - Aix-Marseille I, 2012. Français. ⟨tel-00773642⟩

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