Construction of n-sided polygonal spline element using area coordinates and B-net method  

作　　者：Juan Chen Chong-Jun Li Wan-Ji Chen 

机构地区：[1]School of Mathematical Sciences,Dalian University of Technology, 116024 Dalian, China [2]State Key Laboratory for Structural Analysisof Industrial Equipment, Dalian University of Technology,116024 Dalian, China [3]Institute for Structural Analysis of Aerocraft,Shenyang Institute of Aeronautical Engineering,110136 Shenyang, China

出　　处：《Acta Mechanica Sinica》2010年第5期685-693,共9页力学学报（英文版）

基　　金：supported by the National Natural Science Foundation of China (60533060, 10672032, 10726067);Science Foundation of Dalian University of Technology (SFDUT07001)

摘　　要：In general, triangular and quadrilateral elements are commonly applied in two-dimensional finite element methods. If they are used to compute polycrystalline materials, the cost of computation can be quite significant. Polygonal elements can do well in simulation of the materials behavior and provide greater flexibility for the meshing of complex geometries. Hence, the study on the polygonal element is a very useful and necessary part in the finite element method. In this paper, an n-sided polygonal element based on quadratic spline interpolant, denoted by PS2 element, is presented using the triangular area coordinates and the B-net method. The PS2 element is conforming and can exactly model the quadratic field. It is valid for both convex and non-convex polygonal element, and insensitive to mesh distortions. In addition, no mapping or coordinate transformation is required and thus no Jacobian matrix and its inverse are evaluated. Some appropriate examples are employed to evaluate the performance of the proposed element.In general, triangular and quadrilateral elements are commonly applied in two-dimensional finite element methods. If they are used to compute polycrystalline materials, the cost of computation can be quite significant. Polygonal elements can do well in simulation of the materials behavior and provide greater flexibility for the meshing of complex geometries. Hence, the study on the polygonal element is a very useful and necessary part in the finite element method. In this paper, an n-sided polygonal element based on quadratic spline interpolant, denoted by PS2 element, is presented using the triangular area coordinates and the B-net method. The PS2 element is conforming and can exactly model the quadratic field. It is valid for both convex and non-convex polygonal element, and insensitive to mesh distortions. In addition, no mapping or coordinate transformation is required and thus no Jacobian matrix and its inverse are evaluated. Some appropriate examples are employed to evaluate the performance of the proposed element.

关 键 词：Finite element method n-sided polygonalelement - Bivariate spline interpolation The second ordercompleteness 

分 类 号：O241.5[理学—计算数学] TP301.6[理学—数学]