A high-precision formula for mixed-order polygon elements based on SBFEM

A satisfactory balance between solution precision and computational efficiency can be achieved via mixed-order elements, however, the generality and robustness of commonly used methods can be further optimized. In this paper, a flexible and versatile mixed-order analysis method is developed based on Scaled Boundary Finite Element Method (SBFEM) theory, wherein one-dimensional linear and quadratic functions are combined to interpolate circular boundaries. The applicability and accuracy of the proposed method for different problems are explored and compared, and good accuracy and tolerance of element distortion performance are revealed. Moreover, compared with the quadratic element, computational efforts can be reduced considerably, enabling efficiency to be enhanced. Additionally, a polygon mixed-order formula can be directly derived, benefiting from the advantages of the SBFEM, wherein stronger universalities are rendered. In summary, the proposed method improves the flexibility and robustness of the mixed-order cells, and distinctive superiorities are revealed, providing an alternative option for the efficient and high-precision numerical analysis of vital structures.