Smooth boundary topology optimization for electrostatic problems through the combination of shape and topological design sensitivities

This paper presents a new methodology for topology optimization in which the topology of the design domain considered may change during the shape optimization process, unlike the case of classical shape or topology optimization. To achieve this, the concept of the topological gradient is introduced to compute the sensitivity of an objective function when a small hole is drilled in the domain, and this is successfully connected to the shape sensitivity. A test problem consisting of an elliptic dielectric material with a circular hole has been selected to illustrate the validity of the proposed method.