Reduction of initial stress stiffening by topology optimization

Topology optimization is a rigorous method of obtaining non-intuitive designs. We use it to obtain a capacitive RF switch that stiffens little in response to an increase of the in-plane biaxial stresses that typically develop during MEMS fabrication. The actuation voltage is closely related to the membrane's stiffness, and is more stable for a stress insensitive switch. We employ the Solid Isotropic Material with Penalization (SIMP) method with the Method of Moving Asymptotes (MMA) and a robust formulation to minimize the ratio between the compliance at a low stress level and that at a high stress level. We include a volume constraint and a compliance constraint. Topology optimized designs are compared to an intuitively-designed RF switch. The switches contain similar features. The compliance constraint is varied such that the topology optimized switch performance approaches the intuitively-designed one. Finally, the importance of the compliance constraint and of the robust formulation are discussed.