随机结构正交展开分析的Ritz动力聚缩法

A Ritz dynamic condensation algorithm of orthogonal expansion analysis for stochastic structures

针对随机结果正交展开理论计算上的弱点 ,本文在分析扩阶矩阵特性的基础上 ,于 Ritz模态向量子空间中对扩阶方程实现动力聚缩 ,大大提高了正交展开理论对实际工程问题的分析能力。分析实例表明 :即使结构参数具有很大变异性 (如δ =0 .4 )时 ,该算法依然能理想地与 Monte Carlo法模拟结果相吻合 ,计算时间则远远小于 Monte Carlo模拟法。同时 。

The applicability of the orthogonal expansion theory of stochastic structures in the practical engineering is severely undermined by its high calculation cost. In order to remedy this disadvantage, on the basis of analyzing the characteristics of the order-expanded equations, a method for condensing the equations in a subspace spanned by Ritz vectors is proposed in this paper. A numerical example demonstrates that the results derived from the dynamic condensation algorithm are in good agreement with Monte Carlo simulation method, even though the variability of structures' physical parameters is very large (esp. δ=0.4). Moreover the calculation time is much shortened. The necessity of considering the variability of structures' parameters in structures' dynamic analysis is also indicated in the paper.