[17] A monolithic approach for topology optimization of electrostatically actuated devices
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G. H. Yoon and O. Sigmund. Computer Methods in Applied Mechanics and Engineering 197, no. 45-48 (2008): 4062-4075
This paper presents a new topology optimization scheme for nonlinear electrostatic systems actuated by Coulomb’s forces. For successful optimization, computational issues such as (i) alternating governing equations with respect to spatially defined design variables, (ii) imposing interaction boundary condi- tions between insulator (air) and conductor (solid) and (iii) control of minimum geometrical feature sizes must be addressed. To address the first two issues, the paper presents a monolithic formulation based on continuum mechanics theory which simultaneously calculates the electric potential and structural dis- placements. To interpolate between insulator and conductor with continuous design variables, the mono- lithic approach distinguishes between the permittivity value of the electric Poisson’s equation and that of Maxwell’s stress tensor. For the optimization, standard material interpolations are used for Young’s mod- ulus and permittivity values. Moreover, a recently developed morphology filter is applied to control elec- trode gaps and other geometrical features.