Probabilistic failure path approach on optimal design of structures against sequential fatigue-induced failure

Structural redundancy acts as a safeguard against localized damage, but it may lead to a variety of potential overall failures. A system-level probabilistic failure path approach is necessary to identify system failure events and account for stress redistribution in structures prone to fatigue-induced damage. Incorporating such probabilistic constraints into a System-Reliability-based Design Optimization (SRBDO) framework comes with a high computational cost. In this study, an innovative method integrates the Branch-and Bound method employing system reliability Bounds (B³ method) and modified Sequential Compounding Method (SCM) to compute the gradient of the system failure probability, particularly those requiring a failure path approach like sequential failure. New compounding rules are introduced in SCM: (a) screening and (b) adaptive compounding to enhance accuracy especially for systems with highly correlated events. This approach allows for the utilization of gradient-based optimizers, offering enhanced computational efficiency in comparison to current gradient-free methods. Additionally, a new bounding rule of the B³ method is introduced to further increase efficiency, and Chun-Song-Paulino (CSP) sensitivity analysis method is used to calculate the derivatives with respect to the design variables. The proposed method is demonstrated through a hypothetical structure of multilayer Daniel’s system and two truss structures of different scales. The semi-analytical formulation of the sensitivity calculation effectively guides the optimization process to the optimum. This new approach accurately calculates the failure probability of the dominant failure sequences and the overall system failure probability as validated by the Monte Carlo simulation. The numerical studies robustly demonstrated efficiency and accuracy of the proposed optimization framework.