结构动力重分析的向量值有理逼近方法

研究动力重分析问题, 针对结构参数大修改, 提出一种 将矩阵摄动法与向量值函数的有理逼近方法组合起来的新方法. 在只增加少许计算量的情况 下, 利用向量值函数的有理逼近方法以及Rayleigh商来改善摄动解的逼近质量并扩大其逼近 范围. 该方法操作简单, 易于辅助. 两个数值例子表明, 所提出的方法对结构参数发生大修 改能够给出高精度的逼近结果. 对结构参数大修改的动力重分析, 向量值有理逼近是一种有 效方法.

Vector-valued Rational Approximate Method for Structural Dynamic Reanalysis

The present paper is presented a new method for problems of structural dynamic reanalysis with very large changes in design variable. This method is based on combining the power-series expansion of eigenvalue problems with the rational approximation of a vector-value function. The use of the rational approximation and the Rayleigh quotient leads to that the quality of power-series expansion is significantly improved and the range of approximation is extended with a few of additional operation counts. The method is simple in operation and easy in implement. Two numerical examples were used to show that the proposed method can provide high quality approximations of the structural behavior for large changes in design variable. For large modification in design variable, the rational approximation of a vector-value function is an efficient method for structural dynamic reanalysis.