Optimal design of an electrostatically actuated microbeam for maximum pull-in voltage

We consider optimizing the shape of a capacitive micro-beam for maximum pull-in voltage. The problem is discretized using finite elements. The normal flow algorithm is used to trace the nonlinear voltage displacement curve and find the pull-in point. Optimal width and thickness distributions are obtained for different beam boundary conditions using a resizing scheme based on optimality criterion. The results indicate that substantial increase in pull-in voltage can be achieved by varying the width and/or thickness distribution.