By Seung-Kyum Choi
This booklet presents readers with an figuring out of the basics and purposes of structural reliability, stochastic finite point process, reliability research through stochastic growth, and optimization below uncertainty. It examines using stochastic expansions, together with polynomial chaos growth and Karhunen-Loeve growth for the reliability research of useful engineering difficulties.
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Extra resources for Reliability-based Structural Design
Example text
46153 In Chapter 4, this example will be solved by another approximation method, namely MVFOSM. 3), the probabilistic methods include the stochastic finite element method, the first- and second-order reliability method, sampling methods, the utilization of stochastic expansions based on the random process concept, etc. Each method requires different computational effort and provides different insight into the response variability and levels of accuracy. In this section, we briefly discuss historical developments of the most widely used methods in probabilistic analysis and discuss the advantages and disadvantages of each method.
Classification of a Random Process As previously stated, the random process can be thought of as a random function. Because manipulating random variables is easier than using the random function directly, a series of deterministic functions with random coefficients is frequently used to replace the random function. After its discretization, the continuous random process is an indexed set of an infinite number of random variables. Various methods, including the use of orthogonal polynomials and Taylor series representations, have been devised to replace random functions with random variables, depending on how the functions and the random coefficients are chosen.
The notation g(ǜ) < 0 denotes the failure region. Likewise, g () = 0 and g () > 0 indicate the failure surface and safe region, respectively. The mean and standard deviation of the limit-state, g () , can be determined from the elementary definition of the mean and variance. 3) PR PS where, P R and P S are the means of R and S, respectively. 4) where, U RS is the correlation coefficient between R and S, and V R and V S are the standard deviations of R and S, respectively. 1. 6) V R2 V S2 The safety index indicates the distance of the mean margin of safety from g () = 0.