Fuzzy structural analysis based on fundamental reliability concepts

Fuzzy structural analysis is oriented to estimate the membership function of an output structural variable given the membership functions of the input ones, which are discretized in so-called α-cut levels. Such an estimation requires the solution of two optimization problems for each of them. In this paper an alternative approach is presented. It consists in solving a single optimization problem for the entire problem, which is that of FORM (first-order reliability analysis). It is shown that FORM solution has a valuable property, namely that it allows organizing the order statistics of the output variable along the design point vector. This property is exploited by a nonlinear projection of a large amount of standard Gaussian numbers, truncated according to the membership functions, onto a bi-dimensional space. From this mapping the samples necessary for directly solving the optimization problems are easily drawn using two curves, whose equations are derived from a similar transformation of the second-order approximation of the limit state function. A detailed structural example shows that the desired membership function of the response can be accurately estimated by the proposed method.