Construction of n-sided polygonal spline element using area coordinates and B-net method |
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Authors: | Juan Chen Chong-Jun Li and Wan-Ji Chen |
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Institution: | Juan Chen · Chong-Jun Li · Wan-Ji Chen School of Mathematical Sciences,Dalian University of Technology,116024 Dalian,China.State Key Laboratory for Structural Analysis of Industrial Equipment,China.Institute for Structural Analysis of Aerocraft,Shenyang Institute of Aeronautical Engineering,110136 Shenyang,China |
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Abstract: | 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. |
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Keywords: | Finite element method · n-sided polygonal element · Bivariate spline interpolation · The second order completeness |
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