根据Voronoi胞的几何性质，获得了积分点的二阶Voronoi胞顶点的表达式，并对各邻近结点相关的顶点进行排序以使其生成的二阶Voronoi胞切割面为凸多边形，从而获得各切割凸多边形面域的面积表达式；最后，基于复合函数链式求导法则，获得了三维自然单元法non-Sibson插值形函数导数的显式格式。相比Lasserre算法，该方法具有直观、便于编程且计算量小的特点。悬臂梁的算例结果进一步说明了该方法的可靠性，证实了文献[2，7，8]关于自然单元法具有比有限元中常应变单元更高的精度，理论上和双线性单元的精度同阶的结论。%For an integral point x within three-dimension model ,the vertex coordinate expression of its second-order Voronoi cell is deduced firstly by using the geometric properties of Voronoi diagram .And then ,those second-order Voronoi cell vertexes related to some a neighbor node is further reordered to make the second-order Voronoi cell segment area domain generated become a protrusive polygon so that the segment area expression can be conveniently obtained .Based on the expression of segment area do-main and the definition of non-Sibson shape function ,the derivative expression of the shape function for three-dimension natural element methods is deduced by making use of the chain derivative rule of com-pound function .Compared with the Lasserre algorithm ,this algorithm is more of intuitionistic characte-ristic and can be conveniently programmed .Finally ,through a cantilever beam case ,the reliability of com-puter results by NEM is further verified .And the precision of NEM is higher than that of the tetrahed-ron element with FEM and the same as that of the hexahedron with FEM in theory ,which discussed in detail in reference [2-4] .
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