The scaled boundary finite element method (SBFEM) is a powerful method for solving elastostatics problems based on polygonal elements. In this paper, we firstly construct the quadratic polygonal scaled boundary element only depends on the boundary nodal displacements by transforming the additional degrees of freedom derived from the constant body loads to those by the boundary nodes. Further, combining with the discrete Kirchhoff theory, we construct the polygonal scaled boundary thin plate element, which can possess the second order completeness. The element stiffness matrix for the thin plate problem can be transformed by the stiffness matrix for the plane problem directly by avoiding to compute the shape functions of SBFEM. Numerical examples verify that the proposed polygonal scaled boundary thin plate element has good accuracy.

缩放边界有限元法 (SBFEM) 是解决基于多边形单元的弹性静力学问题的强大方法。在本文中，我们首先通过将由恒定体载荷导出的附加自由度转换为边界节点的附加自由度，构建仅依赖于边界节点位移的二次多边形缩放边界元。进一步结合离散基尔霍夫理论，构造了具有二阶完备性的多边形尺度边界薄板单元。薄板问题的单元刚度矩阵可以直接转换为平面问​​题的刚度矩阵，避免计算 SBFEM 的形状函数。数值算例验证了所提出的多边形缩放边界薄板单元具有良好的精度。