Improved functional perturbation method for reliability analysis of randomly heterogeneous beams

The strength reliability of randomly heterogeneous beams is studied. The beams are considered as brittle, and failure by the weakest link criterion is assumed. The structure is statically indeterminate, thus the stress field is a function of the random morphology. The probabilistic beam strength is a coupled functional of morphology and stresses. Correlation between local strength and local modulus is also considered, and its effect on reliability is investigated. Heterogeneity is confined to the longitudinal direction only. An improved analytical solution is found by a new, optimized functional perturbation method (FPM). The improvement is achieved by two operations: generalizing the previously used FPM to account for multifunctional dependency, and choosing the perturbation to be around the proper homogeneous case for each type of morphology. It is shown that the improvement of the optimized method for reliability analysis is significant, and depends on the type of local strength-modulus statistical correlation. In addition, analytical results for very large and very small correlation lengths are obtained, and their validity range is examined by numerical solutions.