Shape optimization is typically differentiated into two main categories:

CAD-based methods originate from shape representations of computer graphics technology or computer-aided design (CAD), such as parametric design, Non-Uniform Rational B-Splines (NURBS), morphing boxes, or free-form deformation (FFD). They are characterized by a low number of design variables, which engineers generally intuitively understand. Experienced engineers may even be able to refine the initial CAD parameter model in order to improve the shapes obtainable by optimization. Subjective criteria, such as esthetics, can be controlled by a well-considered parameter model. However, due to the small number of design variables, the resulting design space is compact, and the attainable optima depend significantly on the chosen shape parameters. Engineers can be stuck on their original design concept and are not able to explore the design space more extensively.

The other shape optimization strategy - known as grid-based, node-based, or parameter-free shape optimization - lets the form evolve as freely as possible. The positions of the discretization’s surface nodes are selected as design variables. 

By leveraging the strengths of both methods, mixed shape parameterizations seek to create highly flexible and problem-specific shape design variables while preserving an extensive design space. In node-based optimization, the otherwise limited impact on the final design is enhanced by introducing a small number of additional shape parameters, which help guide the optimizer toward a preferred local optimum. As different shape representations have diverse influences on the shape, design variable scaling strategies are developed to improve the conditioning of the design space.

Research at the Chair of Structural Analysis has focused so far on incorporating rigid body parameters into the Vertex Morphing framework. Further work will be conducted on mixing node-based shape optimization with other shape description methods, such as NURBS or subdivision surfaces.

 

Publications

• Schmölz, David; Geiser, Armin; Stein, Victor P.; Hojjat, Majid; Bletzinger, Kai-Uwe; Wüchner, Roland: Mixing the explicit Vertex Morphing method with rigid body parameters for node-based shape optimization. Structural and Multidisciplinary Optimization 69, 2026, DOI