Trimming with polygonal scaled boundary isogeometric method

A novel approach of polygonal scaled boundary isogeometric analysis is proposed for 2D elasticity problems involving trimmed geometries. The method addresses the challenge of efficiently handling trimmed geometries directly within the analysis process. It employs the Newton-Raphson method to search for intersection points between the trimming curve and isoparametric curves of the NURBS surface. The approach involves mapping untrimmed internal grids bounded by isoparametric curve segments and trimmed elements bounded by trimming curve and isoparametric curve segments into scaled boundary elements. Field variable approximations are achieved using NURBS basis functions. The system equation is derived through the virtual work statement, and a hybrid variable is introduced in the solution procedure. The method preserves the dimension reduction and semi-analytical characteristics of the classical SBFEM. Refinement strategies (h-, k-, p-refinements) for IGA are applied to implement high-order continuity boundary elements at the polygonal element level. The approach is capable of handling arbitrary complex problem domains without the necessity of sub-domain division. It accurately represents curved elements with few control points, thereby enhancing computational accuracy compared to SBFEM. The proposed method has been demonstrated to be correct, accurate, and efficient. It holds the potential to advance IGA-based numerical methods and provide valuable guidance for the development of large-scale integration software in the framework of IGA and SBFEM.