Probabilistic failure path approach on structural system-reliability-based design optimization of fatigue-induced failure

Abstract

Reliability analysis with unknown system event definition such as sequence of member failures requires a failure-path approach to determine the component events that will induce overall system failure. In particular, redundant structures prone to fatigue-induced sequential failure needs a system-level analysis employing a failure-path approach to account for stress redistribution. Thus, there can be a high computational cost of incorporating such probabilistic constraints into a System-Reliability-based Design Optimization (SRBDO) framework against fatigue limit states. A structural system reliability analysis procedure, namely, the Branch-and-Bound method employing system reliability Bounds (termed the B3 method) is integrated into an optimization algorithm. A gradient-based optimizer is used to find the optimum, and a modified Sequential Compounding Method (SCM) together with Chun-Song-Paulino (CSP) sensitivity analysis method is used to calculate the gradient with respect to the design variables. Additionally, a new bounding rule of the B3 method is introduced to increase efficiency. To demonstrate the applicability, it is applied to a hypothetical structure of multilayer Danielﾒs system. As a result, the system failure probability of the optimal design obtained from the proposed method is found to be lower than the target probability and is verified through Monte Carlo simulation. The calculated gradient of the system failure probability accurately leads to the optimal design. It is confirmed that the proposed method can allocate limited materials throughout the structure. Moreover, the system reliability analysis of fatigue-induced sequential failure is explicitly incorporated into the design optimization, thereby resulting in cost-efficient and safer structures.