A SBFEM formula for the mixed-order hexahedron interpolation based on serendipity elements

Abstract

The hexahedron elements have been widely used in theoretical research and engineering applications because of their simple formulation and fine analytical performance. In this paper, a flexible mixed-order hexahedron interpolation is proposed based on the SBFEM theory, which is summarized as follows: (1) The interpolation functions are constructed for boundary surfaces by introducing the “Serendipity element”, which allows for a combination of linear and quadratic interpolation; (2) Two approaches for order conversion in hexahedron elements have been applied and investigated; (3) The accuracy and applicability of the proposed method are verified using several classical examples and engineering practice. In this way, the proposed method is capable of handling abundant patterns of different order combinations, thus the analysis performance of hexahedron elements has been improved. The precision of the proposed method is demonstrated by comparing it with the theoretical solution and the classical isoparametric FEM. By comparison, the computational efficiency can be improved by approximately 40–55 % with satisfactory accuracy. In general, the proposed method offers a new alternative channel for simulating particular problems, such as bending and stress concentration.