Optimal design of electrostatically actuated microsystems

This thesis addresses the application of numerical optimization techniques to devices classified as Micro-Electro-Mechanical-Systems (MEMS). The finite element (FEM) based analysis and sensitivity analysis capabilities for the fully-coupled electro-mechanical problem, which results from electrostatically actuated MEMS, are developed and implemented. Specifically, shape and topology optimization, using gradient based algorithms, are applied to the design of MEMS. Topology optimization generates optimal topology without the requirement of close-to-optimal initial designs. It is proposed to extend the current state of the art in topology optimization to a fully-coupled electro-mechanical problem, in which the electrostatic and structural domains occupy distinct regions of space. The difficulty in allowing the conducting interface between the domains to freely evolve during the topology optimization process is addressed. Additionally, the prediction of the instability phenomena known as 'pull-in', by an eigenvalue analysis, is incorporated into the proposed design methodology. The design optimization of realistic MEMS devices is the driving force behind the application of all developed computational tools.