有限元模型刚度修正的加权广义逆法

Stiffness Matrix Correction Using Weighted Moore-Penrose Inverse

针对有限元模型刚度矩阵修正中通常引起的修正矩阵为满阵的不足,提出了有限元模型刚度修正的加权广义逆法,该方法是对排列方程法的扩展,而且在公式推导过程中采用矩阵的形式,简洁明了.由于对被修正矩阵的零元素不进行修正,因而保持了原结构矩阵的窄带性和稀疏性,数值计算表明了方法的有效性.

For the problem that corrected stiffness matrix is a full matrix in finite element model updating, a generalized inverse method with weighted coefficients is presented in this paper. The proposed method is an expansion to AEA （arranging equation approach）. It is concise due to adopting matrix form in the formula derivation. Since the zero-valued elements in banded-state matrix are not corrected, the improved stiffness matrix will still keep its banded-state and sparse characteristics after the matrix is modified.