中文摘要：

在这份报纸，一个 13 节点金字塔花键元素被使用四面体体积坐标和 B 网方法导出，它在笛卡儿的坐标完成第二顺序完全性。一些适当例子被采用评估建议元素的表演。当网孔被弄歪时，数字结果证明花键元素特别与 isoparametric 易遇奇缘的运气元素 Q20 和它的退化金字塔元素 P13 相比有好一些的性能，并且它比得上 Lagrange 元素 Q27。这被表明了有限元素方法是的花键为开发高精确性元素的一个有效工具。

英文摘要：

In this paper,a 13-node pyramid spline element is derived by using the tetrahedron volume coordinates and the B-net method,which achieves the second order completeness in Cartesian coordinates.Some appropriate examples were employed to evaluate the performance of the proposed element.The numerical results show that the spline element has much better performance compared with the isoparametric serendipity element Q20 and its degenerate pyramid element P13 especially when mesh is distorted,and it is comparable to the Lagrange element Q27.It has been demonstrated that the spline finite element method is an efficient tool for developing high accuracy elements.