Efficient Reliability-Based Design and Inspection of Stiffened Panels Against Fatigue

This paper develops an efficient computational technique to perform reliability-based optimization of structural design and an inspection schedule for fatigue crack growth. Calculating structural reliability in the presence of inspection is computationally challenging because crack size distribution has to be updated after each inspection to simulate replacement. An exact evaluation using Monte Carlo simulation is time consuming because large sample size is required for estimating accurately a low probability of failure. In this paper a less expensive approximate method is proposed to calculate reliability with inspection, combining Monte Carlo simulation and a first-order reliability method. We use Monte Carlo simulation with a small sample to update the probability distribution of cracksizesafterinspectionanda first-orderreliabilitymethodtocalculatethefailureprobabilityatanytimebetween inspections. The application of this methodology is demonstrated by optimizing structural design and an inspection scheduleforminimumlifecyclecostofstiffenedpanelssubjecttouncertaintyinmaterialpropertiesandloading.The effect of the structural design and the inspection schedule on the operational cost and reliability is explored and the costofstructuralweightistradedagainstinspectioncosttominimizetotalcost.Optimizationrevealedthattheuseof inspections can be very cost effective for maintaining structural safety. Nomenclature As = area of a stiffener, m 2 ATotal = total cross sectional area of panel, m 2 a = crack size, mm ac = critical crack size, mm acH = critical crack length due to hoop stress, mm acL = critical crack length for transverse stress, mm acY = critical crack length causing yield of net section of panel, mm ah = crack size at which probability of detection is 50%, mm ai = initial crack size, mm ai;0 = crack size due to fabrication defects, mm aN = crack size afterN cycles of fatigue loading, mm b = panel length, m Ctot