Application of Computational Topology to the Design of Microelectromechanical Structures

We are applying tools from computational topology and combinatorial geometry in our investigation of computational aspects of engineering design problems. We seek tractable algorithmic solutions by exploiting algebraic formulations of the fundamental computational-topological problems arising in the kinematic and dynamic analysis of microelectromechanical (MEM) structures. In particular, we use concepts from computational topology and geometry to determine the shape of microelectromechanical (MEM) structures, given specifications of their parameterized geometry and their functionality (parametric design). MEM structures are particularly suited for automated parametric design because of (i) their highly specialized and automated production process, which allows only a very limited number of elementary structures, (ii) the tractable geometry and functionality of the devices, and (iii) the possibly large number of devices produced simultaneously in one manufacturing process. Kinematic int..