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| Calculation of the derivative of interpolation shape function for three dimension natural element method |
| Received:November 12, 2012 Revised:February 20, 2014 |
| View Full Text View/Add Comment Download reader |
| DOI：10.7511/jslx201403015 |
| KeyWord:natural element method non-Sibson interpolation chain derivative rule of compound function Voronoi cell |
| Author | Institution |
| 夏晓舟 |
河海大学 力学与材料学院, 南京 |
| 章青 |
河海大学 力学与材料学院, 南京 |
| 蒋群 |
河海大学 力学与材料学院, 南京 ;江西科技师范大学 通信与电子学院, 南昌 |
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| Abstract: |
| 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 domain 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 compound 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 computer results by NEM is further verified.And the precision of NEM is higher than that of the tetrahedron 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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