Design of Electrothermally Compliant MEMS With Hexagonal Cells Using Local Temperature and Stress Constraints

Abstract

In this paper, meso- and microscale electrothermally compliant 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 optimal solutions thermally intact and also to keep the local stresses below their allowable limit. Constraint relaxation performed on both temperature and stress constraints allows them to be ignored when the cell material densities approach their nonexisting states. As both local constraints are large in number with the number of cells, an active constraint strategy is employed with gradient based optimization. Honeycomb parametrization, which is a staggered arrangement of hexagonal cells, is used to represent the design region. This ensures at least an edge connection between any two adjacent cells, and thus prevents the appearance of both checkerboard and point flexure singularities without any additional computational load. Both SIMP and SIGMOID material assignment functions are explored to obtain the optimal solutions.