Automatic Generation of T-Splines with Extraordinary Points Based on Domain Decomposition of Quadrilateral Patches

Isogeometric analysis (IGA) is a numerical methodology for solving differential equations by employing basis functions that preserve the exact geometry of the domain. This approach is based on a class of mathematical functions known as NURBS (Non-Uniform Rational B-Splines). Representing a domain with NURBS entities often requires multiple patches, especially for complex geometries. Bivariate NURBS, defined as tensor products, enforce global refinements within a patch and, in multi-patch models, these refinements are propagated to other model patches. The use of T-Splines with extraordinary points offers a solution to this issue by enabling local refinements through unstructured meshes. The analysis of T-Spline models is performed using a Bézier extraction technique that relies on extraction operators that map Bézier functions to T-Spline functions. When generating a T-Spline model, careful attention is required to ensure that all T-Spline functions are linearly independent—a necessary condition for IGA—in order to form T-Splines that are suitable for analysis. In this sense, this work proposes a methodology to automate the generation of bidimensional unstructured meshes for IGA through T-Splines with extraordinary points. An algorithm for generating unstructured finite element meshes, based on domain decomposition of quadrilateral patches, is adapted to construct T-Spline models. Validation models demonstrate the methodology’s flexibility in generating locally refined isogeometric models.