LAUSR

A hybrid level set method is proposed for devising structures with embedded components, where the supporting structure as well as the positions and orientations of the components are optimized simultaneously. Two different types of level sets, namely the explicit and implicit level set are introduced to respectively represent the components and supporting structure. In this fashion, smooth geometries and clear interfaces for both the components and their underpinning structure can be obtained, which can facilitate the following analysis or manufacture of the optimized design. The positions and orientation of the components are described by a set of explicit level sets. To facilitate the solution of these multiconstraint optimization problems, a parametric mechanism is formulated by approximating the implicit level sets with the Gaussian radial basis function. Distinguished from the existing approaches, we use two different sets of design variables in a uniform optimization loop, that is, the geometric parameters for the positions and orientations of the components, and the expansion coefficients of the level set interpolation for the supporting structure. In this way, the overall design variables for the optimization problem can be greatly reduced. Several examples are provided to demonstrate the effectiveness and efficiency of the proposed method.