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.
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