NURBS-based and parametric-based shape optimization with differentiated CAD kernel

ABSTRACT

Numerical optimization is becoming an essential industrial method in engineering design for shapes immersed in fluids. High-fidelity optimization requires fine design spaces with many design variables, which can only be tackled efficiently with gradient-based optimization methods. CAD packages that are open-source or commercially available do not provide the required shape derivatives, but impose to compute them with expensive, inaccurate and non-robust finite-differences.

The present work is the first demonstration of obtaining exact shape derivatives with respect to CAD design parametrization by applying algorithmic differentiation to a complete CAD system, in this case the Open Cascade Technology (OCCT) CAD-kernel. The extension of OCCT to perform shape optimization is shown by using parametric models based on explicit parametrizations of the CAD model and on implicit parametrizations based on the BRep (NURBS). In addition, we demonstrate the imposition of geometric constraints for both approaches, a salient part of industrial design, and an intuitive method of storing them in standard CAD format. The proposed method is demonstrated on a turbo-machinery test case, namely the optimization of the TU Berlin Stator.

GRAPHICAL ABSTRACT

Keywords:

• aerodynamic shape optimization
• CAD-based sensitivities
• gradient method

Acknowledgements

This research is a part of the IODA project - Industrial Optimal Design using Adjoint CFD. IODA is Marie Sklodowska-Curie Innovative Training Network. This work was supported by European Commission [Grant Agreement Number 6429].