Three‐dimensional spline scaled boundary finite elements with high‐order completeness

Abstract

AbstractIn this paper, we construct two three‐dimensional (3D) scaled boundary finite elements (SBFEM) combined with the quadratic and cubic quadrilateral spline elements, which possess the second‐ and third‐order completeness in Cartesian coordinates, respectively. The two‐dimensional quadrilateral spline elements have the same nodes as the Serendipity elements, and the accuracy can be comparable with the Lagrange elements. The surface elements in the 3D SBFEM adopt the two‐dimensional quadrilateral spline elements in the B‐net form. Then the computation of derivatives, integrals, and products of the element shape functions in the SBFEM can be significantly simplified by using the Bézier coefficients. Moreover, no mapping or coordinate transformation is required when using the spline elements as the surface elements. This paper gives two algorithms for the implementation of the SBFEM. The numerical results show that the proposed spline scaled boundary finite elements have high‐order completeness and good precision with fewer nodes.