Mathematical and numerical modeling of structures in the presence of multiphysics linear couplings

Abstract : This thesis is devoted to the enrichment of the usual mathematical model of smart structures, taking into account the thermal effects, and to its analytical and numerical study. These are typically structures in the form of sensors or actuators, piezoelectric and/or magnetostrictive, whose properties depend on the temperature. We first present existence and uniqueness results for two problems posed on a three-dimensional domain: the dynamic problem and the quasi-static problem. Based on the quasi-static problem, we deduce a two-dimensional model of plate thanks to the asymptotic expansion method by considering four different types of boundary conditions, each one aiming to model a behavior of sensor and/or actuator type. Each of the four problems turns out to be decoupled into a membrane problem and a bending problem. The latter is an evolution problem which takes into account a rotational inertia effect. We then focus our attention on this problem and present a mathematical and numerical study. The analysis is supported by numerical experiments performed under the FreeFEM++ environment.
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Francesco Bonaldi. Mathematical and numerical modeling of structures in the presence of multiphysics linear couplings. Functional Analysis [math.FA]. Université de Montpellier, 2016. English. ⟨tel-01786352v1⟩

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