有限元模型修正问题的不精确最速下降迭代解

在结构动力分析中,往往需利用结构振动测试所得的实际测量数据(如振动频率和振型),对结构分析模型进行最优修正,使之更能合理反映结构的实际性能,其实质即为计算数学中的特征值反问题.本文考虑有阻尼结构振动中的-类反问题,用一组不完备的模态测量数据修正系统质量矩阵、刚度矩阵和阻尼矩阵,通过等价正交投影思想将原问题转化成-个闭凸锥上的正交投影问题,构造-个不精确最速下降迭代法求解,并讨论了收敛性.算例表明算法是有效的.

An Inexact Steepest Descent Method for Finite Element Model Updating Problem

In structure dynamics analysis, the finite element model(FEM) updating prob-lem is to make a updating for the structural analytical model so that the model could have the closest match with the real structure. In this paper, we consider a FEM updating problem with damping action. A set of incomplete test data is used to adjust the mass, stiff-ness and damping matrixes. The primal problem is deformed equivalently into a problem about finding a metric projection onto a closed convex cone. An inexact steepest descent iterate method and a proof of its convergence are presented. Through the two numerical experiments, we can find the method is effective.