A review on feature-mapping methods for structural optimization

In this review we identify a new category of methods for implementing and solving structural optimization problems that has emerged over the last 20 years, which we propose to call feature-mapping methods. The two defining aspects of these methods are that the design is parameterized by a high-level geometric description and that features are mapped onto a non-body-fitted mesh for analysis. One motivation for using these methods is to gain better control over the geometry to, for example, facilitate imposing direct constraints on geometric features, while avoiding issues with re-meshing. The review starts by providing some key definitions and then examines the ingredients that these methods use to map geometric features onto a fixed mesh. One of these ingredients corresponds to the mechanism for mapping the geometry of a single feature onto a fixed analysis grid, from which an ersatz material or an immersed-boundary approach is used for the analysis. For the former case, which we refer to as the pseudo-density approach, a test problem is formulated to investigate aspects of the material interpolation, boundary smoothing, and numerical integration. We also review other ingredients of feature-mapping techniques, including approaches for combining features (which are required to perform topology optimization) and methods for imposing a minimum separation distance among features. A literature review of feature-mapping methods is provided for shape optimization, combined feature/free-form optimization, and topology optimization. Finally, we discuss potential future research directions for feature-mapping methods.