Analysis-suitable Geometry

CAD models aren’t always ideal for use in CAE. CAD geometry often has slivers and tolerance errors that require many man-hours to cleanup and make watertight before it can be used for analysis. For over a decade, the Coreform team has pursued research and commercialization of analysis-suitable geometry for use in engineering simulation, resulting in their invention of U-splines.

U-splines (“unstructured” splines) are a novel approach to the construction of a spline basis for representing smooth objects in Computer-Aided Design (CAD) and Computer-Aided Engineering (CAE). U-splines are different from existing spline constructions, such as Non-Uniform Rational B- splines (NURBS), subdivision surfaces, T-splines, and hierarchical B-splines, in that they can accommodate local geometrically exact adaptivity in h (element size), p (polynomial degree), and k (smoothness) simultaneously over a highly-varied mesh topology. U-splines also support mixed element meshes (triangle and quadrilateral elements in the same surface mesh).

For many reasons, analysis-suitable geometry based on U- splines provides a significantly better approximation of the model than faceted meshes. U-splines satisfy the smoothness and exactness requirements of CAD, while satisfying the rigorous requirements for FEA. The invention of U-splines was an important step in the development of analysis-suitable geometry for spline-based simulation.

U-splines are compatible with Bezier, NURBS, T-splines, FEA quad-dominant meshes.

U-splines offer many promising attributes, including

  • Local adaptivity
  • Refinement at extraordinary points
  • Integration of triangles (quad-dominant meshes)
  • Extension to volumes
  • Backwards compatibility with T-splines and NURBS
  • Optimal approximation properties when used as a basis for analysis

Read a preprint of the U-splines technical paper.