An improved high-precision polyhedron SBFEM with combinatorial interpolation strategies

Computational accuracy and solution efficiency are crucial indicators for evaluating the performance of finite element numerical algorithms, and the corresponding improvements in these areas are the motivation for the development of computational science. In this paper, a flexible and high-precision polyhedron algorithm is proposed in conjunction with SBFEM and the triangle/quadrilateral interpolation functions. The main content can be summarized as follows: The construction equations for a mixed-order polyhedron element are derived, meanwhile, a generalized procedural framework is designed for multi-performance applications, including automatic elements type identification, coupled solutions, and dynamic storage, and the integrated development is completed based on self-developed software GEODYNA. The correctness, convergence and practicability of the proposed method are demonstrated through several examples in different dimensions. The results show that the proposed method obtains results with an error of <3 % compared to theoretical solutions and the fine numerical solutions, while significantly reducing computational costs; Besides, the proposed method overcomes the limitations of conventional methods on mesh shape and can be seamlessly integrated with octree algorithms, which offers a powerful technical means for the efficient and high-precision analyses of bending deformation and stress concentration problems. It is foreseeable that a good application potential in high-precision structural analysis would be revealed.