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.

针对涉及修剪几何形状的二维弹性问题，提出了一种多边形尺度边界等几何分析的新方法。该方法解决了直接在分析过程中有效处理修剪几何形状的挑战。它采用Newton-Raphson方法来搜索NURBS曲面的修剪曲线和等参曲线之间的交点。该方法涉及将由等参曲线段界定的未修剪内部网格以及由修剪曲线和等参曲线段界定的修剪元素映射到缩放边界元素中。场变量近似是使用 NURBS 基函数实现的。通过虚功语句导出系统方程，并在求解过程中引入混合变量。该方法保留了经典SBFEM的降维和半解析特性。IGA 的细化策略（ h -、 k -、 p - 细化）应用于在多边形单元级别实现高阶连续性边界单元。该方法能够处理任意复杂的问题域，而无需子域划分。它可以用很少的控制点准确地表示弯曲单元，从而比 SBFEM 提高计算精度。所提出的方法已被证明是正确、准确和高效的。它具有推进基于 IGA 的数值方法的潜力，并为 IGA 和 SBFEM 框架下的大规模集成软件的开发提供有价值的指导。