Numerical Techniques For Structural Reliability Analysis Of Thin-Walled Box Girders In Generalized Random Space

This dissertation established numerical theories and methods for structural reliability in generalized random space. On the basis of structural reliability theory, Monte Carlo simulation method and stochastic finite element method, The numerical methods about stochastic analysis for thin-walled box girders are investigated systematically.The main contributions of the thesis are as follows:1. Three methods dealing with the problem of non-normal correlative variables, i.e. JC method, mapping transformation and Rosenblatt transformation are summarized and compared. On the same time, numerical computed method is utilized to solve the normal distribution function for the precision of computer. Structural reliability usually is analyzed in Descartes coordinates in which the correlated random variables should be converted to uncorrelated random variables by an orthogonal transformation method. As such, structure reliability analysis in generalized random space is presented without the orthogonal transformation.2. Sampling methods for uniform random numbers and commonprobability distribution functions are proposed. Combining the Monte-Carlo simulation technique with finite element method, the Monte Carlo-finite element method for stochastic analysis and the reliability computation are proposed in this thesis. Neumann Monte Carlo method is also proposed which combined Neumann expansion with Monte-Carlo simulation techniques in order to obtain better efficiency and accuracy.3. The methods for stochastic analysis and reliability analysis of thin-walled box girders is established, as following, one dimensional discretized Monte Carlo method, one dimensional discretized stochastic finite element method and Neumann Monte Carlo method. Results show that random properties of parameters take more effect on the thin-walled box-girders.