Research on Structural Random Response Based on C Type Gram-Charlier

摘要

The main research content is a quantitative description of the structural uncertainty problem (Quantification Uncertainty) based on the finite element theory. For the first time, reduction integration method is used to decompose multi-dimensional random response function, the multi-dimensional function is transformed into the combination form of multiple one-dimensional random response function, so the multi-dimensional statistical moments of structural random response expressions can be expressed the sum of one-dimensional function integration; Gaussian integration formula is used to compute one-dimensional random response statistical moments, after the multi-dimensional random structural response statistical moments is gained, C type Gram-Charlier (CGC) Series expansion method is used to approximate the probability density function of random structural response. There is an example about car in this paper, it has two random variables that follow normal distribution and lognormal distribution, respectively, then the car's amplitude is computed, the results are compared with Monte Carlo method. CGC and MCS can match well, the tail of the random response probability distribution can also give an accurate estimate; the results illustrate that the CGC is suitable for normal distributions and lognormal distributions; The total number of computational times of CGC method are far less than the Monte Carlo method, the computation efficiency is much higher than Monte Carlo method. So CGC method in this paper is simple and reasonable.