基于Neumann展开的转角信息识别近似算法

Approximate Algorithm Based on Neumann Expansion for Rotational Response Identification

针对结构识别中转角信息难以测量的问题,提出了基于Neumann展开的转角信息识别问题近似算法.在结构识别中,由于各单元刚度参数未知,利用结构有限元分析中按静力凝聚的方法由平移求结构的转角是无法实现的,在结构参数差异不大的情况下,可以采用Neumann展开方法得到逆矩阵,进而得到结构的转角信息.理论分析和数值算例表明:该算法在结构参数差异不大的情况下适用,在材料参数全同的情况下是精确解答.其范数误差一般较小,而绝对量较小的分量误差较大.

Aiming at the problem that the rotational response is difficult to measure in structural identification, an approximate algorithm based on Neumann expansion theory is developed for rotational response identification. The rotational response cannot be calculated according to structural displacement response based on the static condensation algorithm in FEM analysis since the stiffness parameters are unknown in structural identification. When the difference among structural parameters are not big, the inverse matrix is available by introducing Neumann expansion to get the information on rotational response. Theoretic analysis and numerical examples are given to illustrate that the approximate algorithm based Neumann expansion is applicable when structural parameters differ not widely from each other, and an accurate .solution can be obtained if the structural parameters are all the same. The norm errors of the approximate algorithm is generally small, while the smaller the absolute value is, the greater the component errors will be.