On Design of Electro-Thermally Compliant MEMS for Strength

In this paper, meso and micro scale electro-thermally compliant electro mechanical systems are synthesized for strength with polysilicon as the structural material. Local temperature and/or stress constraints are imposed in the topology optimization formulation. This is done to keep the topology thermally intact and also to keep local stresses below their allowable limit. Relaxation performed on both temperature and stress constraints allows them to be ignored when the material densities approach their non-existing states. Noting that both local constraints can be large in number with the number of cells, an active constraint strategy is employed. Honeycomb parameterization, which is a staggered arrangement of hexagonal cells, is used to represent the design region. This ensures at least a common edge between any two neighboring cells and thus avoids the appearance of both checkerboard and zero-stiffness singularities without any additional computational load.