从矩阵位移法看有限元应力精度的损失与恢复

矩阵位移法在计算杆端力时须叠加一个“固端力”项，而在有限元法中结点（应）力是直接对位移求导获得的，丢失了“固端力”一项，致使应力的精度大为下降．其实，对于一维有限元，同样可以对结点力叠加一个“固端力”项，使结点内力的精度与位移不相上下，而且这一做法几乎可以直接推广到半解析的有限元线法的二维问题中．本文简要介绍这一最新研究的思路、做法和一些初步的数值结果．

THE LOSS AND RECOVERY OF STRESS ACCURACY IN FEM AS SEEN FROM MATRIX DISPLACEMENT METHOD

In the matrix displacement method, a “fixed end force” term is added for computing the member end forces, while in the finite element method (FEM) the nodal stresses are calculated directly from the derivatives of the element displacements without including the fixed end force term. This has been found to be a major source of the stress accuracy loss in FEM. For one dimensional problems, however, a similar “fixed end force” term can also be added in FEM, resulting super convergent nodal stresses that ...