计算复合材料有效弹性模量的重心有限元方法

采用几何法构造出任意边数多边形单元的重心插值形函数, 应用Galerkin法提出了求解弹性力学问题的重心有限元方法。用重心有限元方法对SiC/Ti和B/Al 2种纤维复合材料横向截面的有效弹性模量进行了预报。计算模型取纤维呈六边形排列且为各向同性的代表性单胞, 对其杨氏模量、 剪切模量和体积模量在较大的体积分数范围内进行了数值模拟。通过与解析公式和传统有限元的计算结果对比, 重心有限元方法的计算结果符合解析公式解的趋势, 与传统有限元的计算结果吻合较好。与传统有限元方法相比, 重心有限元方法的单元划分不受三角形或四边形的形状限制, 能够再现材料的真实结构。由于单元较大且数目较少, 本文方法具有很高的计算效率。 

Barycentric finite element method for predicting the effective elastic moduli of composite materials

Applying a geometrical method to construct the shape functions of the polygonal element, a barycentric finite element method (BFEM) for solving elastic problems was presented. The effective moduli in the transverse section of SiC/Ti and B/Al fiber composites were simulated numerically by BFEM. The computational modeling of BFEM was isotropic hexagonal representative unit cell in the transverse section of the material. The Youngs moduli, shear moduli and the bulk moduli were simulated numerically using BFEM and FEM in a wide range of volume fractions. The effective moduli in BFEM computation are in good agreement with the analytical prediction and the FEM results. In contrast to the FEM, the shapes of the elements in BFEM can be arbitrary polygons with the number of sides larger than four. So BFEM can realize the numerical simulation based on real mesostructure of the composite materials. The numerical examples demonstrate that the BFEM has higher computational efficiency and accuracy.