The traditional finite element analysis for irregular design domains often encounters challenges such as intricate
mesh discretization and inaccurate boundary description. In this paper, we propose a quadtree scaled boundary
finite element method based on NURBS curves where the boundaries can be accurately represented. Quadtree
decomposition, which satisfies the 2:1 rule, is employed to rapidly subdivide the analysis domain. The scaled
boundary finite element method (SBFEM) is utilized to analyze the internal elements and address the
displacement incompatibility issue of hanging nodes in the quadtree. Furthermore, the boundary element is
discretized into boundary curves and internal lines, whose displacement fields are respectively constructed by
the NURBS shape functions and the Lagrange shape functions, and then the subsequent analysis of the boundary
element is completed by SBFEM. Finally, numerical examples are tested to demonstrate the feasibility of the
proposed method, which effectively enhances computational efficiency and accuracy in solving irregular design
domains.
