Mixing the explicit Vertex Morphing method with rigid body parameters for node-based shape optimization

The combination of a node-based shape parameterization with parametric design is presented. The Vertex Morphing method is blended with rigid body parameters, including additional non-Euclidean geometric transformations. A rigid body representation is chosen, suitable for gradient-based shape optimization, which uses existing nodal sensitivity information. Inspired by the discretization-independent approach for the Vertex Morphing method based on the shape morphing functions, the effect of different design variable scaling strategies on gradient-based optimization with the selected rigid body parameterization is studied. In order to control the smoothness in the transition between design subdomains, that is, the regions that are controlled by the different design variables, we introduce blending functions. The variable scaling strategy is extended for the mixed parameterization to stabilize the influences of the design variables. Convergence speedups by mitigating the ill-conditioning with the help of the variable scaling approach are demonstrated in academic geometrical examples, and optimization improvements by selecting better local minima are presented in a structural problem. Furthermore, an industrial CFD application case supports the work.