Modélisation mathématique et numérique de structures en présence de couplages linéaires multiphysiques

Abstract : This thesis is devoted to the enrichment of the usual mathematical model of smart structures, by taking into account thermal effects, and to its mathematical and numerical study. By the expression "smart structures" we refer to structures acting as sensors or actuators, whose properties depend on the temperature. We present at first the results of existence and uniqueness concerning two problems posed on a three-dimensional domain: the dynamic problem and the quasi-static problem. Based on the quasi-static problem, we infer a two-dimensional plate model by means of the asymptotic expansion method by considering four different sets of boundary conditions, each one featuring a sensor-like or an actuator-like behavior. Each of the four problems decouples into a membrane problem and a flexural problem. The latter is an evolution problem that accounts for a rotational inertia effect. Attention is then focused on this problem by presenting a mathematical and numerical study of it. Our numerical analysis is complemented with numerical tests carried out under the FreeFEM++ environment.
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Francesco Bonaldi. Modélisation mathématique et numérique de structures en présence de couplages linéaires multiphysiques. Analyse numérique [math.NA]. Université Montpellier, 2016. Français. ⟨NNT : 2016MONTS027⟩. ⟨tel-01786352v3⟩

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