Geometric continuity constraints of automatically derived parametrisations in CAD-based shape optimisation

ABSTRACT

CAD geometries are most often exchanged between analysis tools using NURBS patches to represent the boundary (BRep). We present a method where the control points of the BRep are used to automatically derive parametrisations suitable for shape optimisation with gradient-based methods. Particular focus is on ensuring geometric continuity between the NURBS patches through formulation of discrete constraints. Design variables then arise from an orthogonal basis to the remaining design space using a singular value decomposition (SVD). The manuscript presents the extension of earlier work on B-spline surfaces to full NURBS surfaces and investigates the effect of the SVD cut-off on the optimisation results. An estimation of the effective rank is proposed which allows to automatically determine a suitable cut-off value. The effectiveness of the algorithm is demonstrated for the minimisation of total pressure loss over a section of an automotive climate duct, and a U-bend cooling channel.

KEYWORDS:

• Continuity constraints
• nullspace
• singular value decomposition
• CAD
• NURBS
• shape optimisation

Disclosure statement

No potential conflict of interest was reported by the authors.

Notes

1. http://aboutflow.sems.qmul.ac.uk/events/munich2016/benchmark/

Additional information

Funding

The authors would like to thank the funding from China Scholarship Council [grant numbers  201306230097,  201206280018] and Queen Mary University of London for this research. The third author acknowledges the support from the European Union's Seventh Framework Programme FP7 People: Marie-Curie Actions (FP7/2007-2013) under REA grant agreement no 371006.