Analysis-suitable unstructured T-splines: Multiple extraordinary points per face

Analysis-suitable T-splines (AST-splines) are a promising candidate to achieve a seamless integration between the design and the analysis of thin-walled structures in industrial settings. In this work, we allow multiple extraordinary points per face, i.e., we remove the restriction of preceding works that required extraordinary points to be at least four rings apart from each other. We do so by mathematically showing that AST-splines with multiple extraordinary points per face are linearly independent and their polynomial basis functions form a non-negative partition of unity. This extension of the subset of AST-splines drastically increases the flexibility to build geometries using AST-splines; e.g., much coarser meshes can be constructed around small holes. The AST-spline spaces detailed in this work have C1 inter-element continuity near extraordinary points and C2 inter-element continuity elsewhere. For the convergence studies performed in this paper involving second- and fourth-order linear elliptic problems with manufactured solutions, we have not found any drawback caused by allowing multiple EPs per face in either the first refinement levels or the asymptotic behavior. To illustrate a possible isogeometric framework that is already available, we design the B-pillar and the side outer panel of a car using T-splines with the commercial software Autodesk Fusion360, import the control nets into our in-house code to build AST-splines, and import the Bézier extraction information into the commercial software LS-DYNA to solve eigenvalue problems. The results are compared with conventional finite elements and good agreement is found between AST-splines and conventional finite elements. •Smooth splines with multiple extraordinary points per face are studied.•A mathematical proof of linear independence is provided.•Excellent convergence from level 0 is obtained.•Geometries with arbitrary topological genus are built.•Comparisons with the commercial software LS-DYNA are included.