Aggregated Formulation of Geometric Constraints for Node-based Shape Optimization with Vertex Morphing

Node-based shape optimization methods like Vertex Morphing use every node of the surface mesh as design variables. The method’s key advantages are the minimal effort for problem setup and the resulting largest possible design space that allows finding new and innovative shapes. Due to a large number of design variables, the application of gradient-based optimization methods becomes mandatory, and adjoint sensitivity analysis is the preferred way for efficient computation of the shape gradients. For some industrial applications, it is necessary to restrict the large design freedom in some sense, for example by limiting the geometric design space. In recent work, nodal non-penetration constraints have been successfully applied in the context of Vertex Morphing, resulting in a potentially large number of active constraints. Aggregation methods are commonly used to reduce the number of constraints in the optimization problem and are investigated here to combine nodal geometric constraints in a single global constraint function.