A gradient-based, parameter-free approach to shape optimization

In shape optimization, the independent node movement approach, wherein finite element node coordinates are used directly as design variables, allows the most freedom for shape change and avoids the time-consuming parameterization preprocess. However, this approach lacks a length scale control that is necessary to ensure a well-posed shape optimization problem and avoid numerical instability. Motivated by the success of filtering techniques that impose minimum length scales in topology optimization, we propose a scheme with consistent filtering to introduce a length scale and thereby ensure smoothness in shape optimization while preserving the advantages of the independent node movement approach.