一种精确积分的四边形四结点等参单元

An Accurately Integrated 4-Node Quadrilateral Element

针对平面问题四边形四结点单元，提出一种新的等参变换方法。采用平行四边形母单元和相应的形函数，推导出四边形四结点等参单元刚度矩阵的精确积分解。理论和数值分析表明，该方法从根本上克服了数值积分带来的误差，计算单元刚度矩阵的速度比传统的高斯两点积分方法快近三倍。

In this paper, a new isoparametric transformation of a parallel quadrilateral parent element and the associated shape function is constructed to derive the accurately integerated stiffness matrix of the 4-nodes quadrilateral element. It has been demonstrated by theoretical and numerical analysis that the error of numerical integration is overcome by using the method and the computing speed ofthe method is almost three times of that of the two-point Gauss' integration.