Semi-analytical gradient-based optimization of exact CAD models using intermediate field representations

This paper proposes an approach to bridge the gap between industrial applications of Computer Aided Design (CAD) and Topology Optimization (TO) by enabling fast and unintrusive gradient-based optimization in nearly any CAD modeling kernel. The proposed approach allows directly optimizing the parameters of a CAD feature tree, thus ensuring that the final optimized design is automatically a CAD model with human-interpretable and editable parameters. This is achieved by introducing an intermediate Signed Distance Field (SDF) representation in the mathematical formulation. This field acts as an interface between the high-level heterogeneous CAD parameters and density field upon which the design's physical performance is evaluated. Derivatives are evaluated through a hybrid scheme of physical adjoint systems and geometrical finite differences, and then chained back to the CAD parameters. We directly optimize the input CAD model and avoid any time-consuming or error-prone shape reinterpretation post-process. The preservation of intentional features in the CAD construction enables designers to guarantee subsequent editing, manufacturing, or assembly interfaces of the optimized designs. We demonstrate the stability and efficiency of the approach through numerical experiments for a variety of 2D and 3D CAD parameterization strategies and optimization objectives.