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| Barycentric finite element method and its application in elasticity theory |
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Abstract Abstract The basis functions of mean value interpolation on arbitrary polygonal element are constructed by geometric method. The formations of the basis functions were identical. The barycentric finite element method (BFEM) was brought by the Galerkin method. And the BFEM was applied in elasticity problems. The functions of BFEM were conforming on irregular polygons. Because of the property, essential boundary conditions can be imposed exactly. The functions have uniform expression for different edge number polygons, consequently the programs could be written conveniently. This provides greater flexibility to solve partial differential equations on complicated geometries. In this paper, BFEM was used in elasticity problems — the patch test, cantilever beam and the effective moduli of composite material. In the patch test, the error was realized the machine precision accuracy. The numerical results using the BFEM were in good agreement with beam theory predictions. The moduli of the composite material were simulated by BFEM. Compared the theory predictions and solution of FEM, the results showed the good consistency and had reasonable changing trend.
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Received: 23 June 2009
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2010, Vol. 31 
