Stochastic finite element based structural reliability analysis and optimization.

摘要

A stochastic finite element-based procedure is proposed for the reliability analysis of complicated structures which do not have closed-form solutions. Detailed formulations are presented for the reliability analysis of framed structures and applied to steel frames. A procedure is proposed for the reliability analysis of frames with uncertain connection rigidity.; A methodology is also developed for the reliability analysis of structures with distributed parameters that can be modeled as random fields. The random fields are discretized into sets of correlated random variables and the stochastic finite element approach is employed for the reliability analysis. Sensitivity measures are used to enable the consideration of only a few of the distributed parameters as random fields, thus ensuring computational efficiency. The effect of the correlation characteristics of the random field on discretization and reliability analysis are studied using stochastic mesh refinement.; Stochastic finite element-based reliability analysis is used to examine the Load and Resistance Factor Design method for the design of steel framed structures. The reliability of an element in an actual structure is found to be dependent on the statistical properties of the other elements, the location of the element in the overall structural configuration, and the statistical correlations among the stochastic parameters. These effects are ignored by LRFD, resulting in conservative design and nonuniform risk levels in the structure.; A stochastic structural optimization procedure is proposed to remove this deficiency using the reliability indices computed by the Stochastic Finite Element Method. The reliability indices are required to be within a desired narrow range, resulting in a balanced distribution of weight while ensuring uniform risk levels across the structure. A derivative-free algorithm with variable, discrete step sizes is used to search for the optimum solution. The use of several techniques to reduce the number of constraints and to accelerate the convergence makes the algorithm attractive for application to practical design.