From CAD to representations suitable for isogeometric analysis: a complete pipeline

Abstract Next generation CAD/CAE systems shall integrate design and analysis procedures as a means to simplify workflows, boost performance, and speed up time to market. In the present paper we demonstrate a proof of concept of such a unification using subdivision surfaces and the enabling technology of isogeometric analysis. In particular, we present a complete pipeline to convert CAD models into smooth $$G^1$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msup> <mml:mi>G</mml:mi> <mml:mn>1</mml:mn> </mml:msup> </mml:math> spline representations, which are suitable for isogeometric analysis. Starting from a CAD boundary representation of a mechanical object, we perform an automatic control cage extraction by means of quadrangular faces, such that its limit Catmull-Clark subdivision surface approximates accurately the input model. We then compute a basis of the $$G^1$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msup> <mml:mi>G</mml:mi> <mml:mn>1</mml:mn> </mml:msup> </mml:math> spline space over the quad mesh in order to carry out least squares fitting over a point cloud, acquired by sampling the original CAD geometry. The resulting surface is a collection of Bézier patches with $$G^1$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msup> <mml:mi>G</mml:mi> <mml:mn>1</mml:mn> </mml:msup> </mml:math> regularity. Finally, we use the basis functions to perform isogeometric analysis simulations of realistic PDEs on the reconstructed $$G^1$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msup> <mml:mi>G</mml:mi> <mml:mn>1</mml:mn> </mml:msup> </mml:math> model. The quality of the construction is demonstrated via several numerical examples performed on a collection of CAD objects presenting various challenging realistic shapes.