A flexible mixed-order formula for tetrahedron elements based on SBFEM

The tetrahedrons offer advantages in terms of its adaptability to complex geometries and high-efficiency of automated discretization. However, the performance is greatly limited by the weak accuracy suffered from firstorder elements, as well as the significant computational burden required for quadratic cells. In this paper, a flexible mixed-order tetrahedron element is constructed on the basis of SBFEM theory, specifically, a formula for the interpolation of circumferential boundary is developed with the union of quadratic and first-order seamlessly, benefiting the combination of triangle area coordinates and the line drawing approach. Additionally, a flexural angle index of tetrahedral edges and regional customization are proposed as the modification method for determining order conversion. Subsequently, the accuracy of the proposed method in addressing various issues is investigated. The results show that the performance of tetrahedrons is satisfactorily enhanced through the utilization of 64 distinct order combination modes; and compared with its quadratic form, the calculation workload has been effectively decreased with no loss of accuracy. In summary, the analytical performance of tetrahedrons can be enhanced reasonably, which provides an effective approach for rapid and accurate analysis for critical structures.