Nguyen-Nhat-Binh TRINH : Asymptotic modeling of a micro-mirror array and software design for automatically derived multiscale models

Abstract :This Ph.D. thesis is in the context of the development of mathematical tools for software which aim is to automatically derive asymptotic models of MEMS Arrays using a symbolic computation and a reuse concept. The contribution covers three aspects: asymptotic modeling, numerical simulations, and software design. The derivation of asymptotic models for the coupled electromechanical problem in the micro-mirror array MIRA is achieved by employing the two-scale transformation method. With the goal to capture a larger family of asymptotic models, we consider the case where the array is actuated by two different voltages in two zones. As a result, the model includes periodic sub-models and boundary corrector sub-models for the lateral boundary, interfaces, inner edges and outer edges. With these models, the simulation of the network is feasible despite its large size. Numerical simulations of the electrostatic part are implemented in finite element software. In addition, the system design is optimized to minimize pull-in voltage. In terms of software design, new forms of data structure and rewriting strategies are designed using abstract syntax trees. This leads on the one hand to the standardization of the data structure and to make it more flexible and on the other hand to make the strategies more general which allows to decrease their number and thus the complexity of the software. The data structure is constructed with a recursive form that broadens the capability of description of families of asymptotic models. Finally, a concurrent system made with the rewriting system and a description logic framework is investigated. This is the first step in building an efficient knowledge representation in software for asymptotic model building

Jury Composition :

Michel LENCZNER, Professor, Université Bourgogne Franche-Comté, PhD Director

Frédéric  ZAMKOTSIAN , Directeur de recherche, Laboratoire d’Astrophysique de Marseille (LAM, Aix-Marseille University, CNRS, CNES), PhD Co-director

Antonio GAUDIELLO, Professor, Université de Naples Federico II, Reporter

Horatiu  CIRSTEA, Professor, Université de Lorraine, Reporter

Renata BUNOIU-SCHILTZ, Maîtresse de conférences, Université de Lorraine, Reviewer

Localization : ENSMM 26 rue de l'Epitaphe 25000 BESANCON - Room Transfert 1