| This dissertation develops a methodology for the estimation of structural reliability under cumulative damage. The central idea is to efficiently impose the damage through a grouping operation, by exploiting the statistical correlations between different component failures or by considering the amount of accumulated damage.A computational procedure is developed to correctly construct the nonlinear limit state and estimate the reliability of members in ductile framed structures. The proposed method uses three criteria based on the statistical relationships among the members to efficiently identify those damage states that significantly affect the reliability of the desired member.A fast failure mode identification algorithm for large ductile structural systems is proposed using the grouping idea. Based on the branch and bound method, one more operation, named the grouping operation, is added to the original two operations (branching and bounding). This grouping operation makes use of the statistical relationships among element failures. The proposed method imposes failures on a group of the elements identified by the grouping operation such that the analysis is substantially accelerated.The failure path approach is also used for time-variant system reliability estimation of brittle structures. The significant failure sequences are identified by the branch and bound method, and the damage states in these sequences are grouped together into discrete damage levels ranging from intact structure to system collapse.Finally, analytical and approximate formulations are developed for the estimation of system reliability under a certain load sequence. The material can be ductile, semi-brittle or brittle. All the proposed methods are demonstrated for application to frame and truss structures, and validated using Monte Carlo simulation. |
