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Nouveaux algorithmes asymptotiques numériques pour la résolution des problèmes de contact unilatéral

Abstract : This thesis is a contribution to the developpement of efficient numerical methods for unilateral contact problems. We propose new algorithms based upon the Asymptotic Numerical Method (ANM) to solve this kind of problems. Since the contact law is not analytic and not adapted to asymptotic expansions, we use a hyperbolic relation between forces and displacements. The contact forces are considered as external ones determined in the form of series. So as to dicretise the unilateral contact problem, we have chosen two formulations : we have first coupled the ANM with the penalty method and then we have combined the ANM a mixed method involving Lagrange multipliers. To describe the whole solution curve, we use a path folloving technique which is based upon rational fractions called Padé approximants. In order to improve the reliability of the ANM algorithms, we propose to correct the solution at high order when it becomes necessary. We propose new high order predication-correction algorithms for contact problems : a high order predictor is combined with a high order corrector which is built up using a technique which associates series expansions, a homotopy technique and Padé approximants. These new high order prediction-correction algorithms improve significantly the reliability and the efficiency of the classical ANM.
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Wassila Aggoune. Nouveaux algorithmes asymptotiques numériques pour la résolution des problèmes de contact unilatéral. Autre. Université Paul Verlaine - Metz, 2003. Français. ⟨NNT : 2003METZ023S⟩. ⟨tel-01749839⟩



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