Theory And Applications Of Structural Reliability In Affine Space

This dissetation has established numerical theories and methods for structural reliability in the affine random space. On the basis of structural reliability theory, the dissetation calculations the structure reliability combining with the stochastic finite element, and compares with the traditional method, Monte Carlo simulation method and stochastic finite element method in generalized random space.The results show that this algorithm has the better efficiency and accuracy.The main contributions of the thesis are as follows:1 .Directing towards the shortcoming of structure reliability computed that the correlated random variables should be converted to uncorrelated random variables by an orthogonal transformation method ,this dissetation applies the affine coordinates knowledge in mathematics to research accurate geometry meaning of reliability index under correlated variables in the affine space and establish the expression and iterative computed formul of reliability index. And this dissetation has established the optimized mode of structure reliability analysis, confirmed this method accuracy with the optimization algorithm.2. Combining the method of this dissetation with the stochastic finite element method, this dissetation analysis the structure reliability under the correlation random variable and combinins the results with the Monte-Carlo method, the traditional stochastic finite element method and the numerical methods.The results show that optimization algorithm has the better efficiency and accuracy.3. The rule of random field discretized and the influence of the correlated length to structure reliability index are summarized, the computed dresults indicate that the relevance has the remarkable influence to the structure reliability index,and is the noticeable factor in the structural engineering design.