A monolithic approach for topology optimization of electrostatically actuated devices

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 conditions 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 displacements. To interpolate between insulator and conductor with continuous design variables, the monolithic 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 modulus and permittivity values. Moreover, a recently developed morphology filter is applied to control electrode gaps and other geometrical features.