A 3D hexahedral spline element

Based on the tetrahedral volume coordinates and the B-net method, a 3D hexahedral spline element with 21 nodes is proposed, which includes an internal node and achieves the second order completeness in the Cartesian coordinates. Some numerical examples are employed to evaluate the performance of the proposed element. The numerical results show that the 21-node element has much better performance than that of the isoparametric 20-node Serendipity element especially for the distorted meshes, and it is comparable to the 27-node Lagrange element. It has also been demonstrated that the spline finite element method is an efficient tool for developing high accuracy elements.

► The 21-node hexahedral spline element possesses the second order completeness in the Cartesian coordinates.
► The element has higher accuracy and is less affected by mesh distortions than the 20-node Serendipity element.
► There is no mapping or coordinate transformation required and thus no Jacobian matrix and its inverse are evaluated.