Amit Kale

Tradeoff of Weight and Inspection Cost in Reliability-Based Structural Optimization

This paper develops a methodology for cost-optimal, reliability-based structural design and inspection planning of aircraft structures subject to fatigue damage growth. An optimization problem is formulated to minimize the expected lifetime cost while maintaining a minimum acceptable reliability level. The effect of structural design and inspection schedule on operational cost and reliability is explored. The optimization parameters are the inspection times, types, and structural thickness. A computational technique using a combination of Monte Carlo simulation to estimate the crack size distribution after inspections and first-order reliability method to calculate failure probability at any time is developed to expedite reliability calculations. The paper shows that the simultaneous design of the structure and inspection regime allows trading the cost of additional structural weight against the inspection cost.

Structural Safety Measures for Airplanes

Passenger aircraft structural design is based on a safety factor of 1.5, and this safety factor alone is equivalent to a probability of failure of between 10 S2 and 10 S3 . Yet airliners are much safer, with crashes caused by structural failure being extremely rare based on accident records. The probability of structural failure of transport aircraft is of the order of 10 S8 per flight segment. This paper looks at two additional contributions to safety—the use of conservative material properties and certification tests—using a simple model of structural failure. We find that the three safety measures together might be able to reduce the calculated probability of failure to about 10 S7 . Additional measures, such as conservative load specifications, might be responsible for the higher safety encountered in practice, explaining why passenger aircraft are so structurally safe. In addition, the paper sheds light on the effectiveness of certification tests for improving safety. It is found that certification tests reduce the calculated failure probabilities by reducing the modeling error. We find that these tests are most effective when safety factors are low and when most of the uncertainty is caused by systemic errors rather than variability.

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

Tradeoff of Structural Weight and Inspection Cost in Reliability Based Optimization using Multiple Inspection Types

This paper develops a methodology for cost optimal reliability based structural design and inspection planning of aircraft structures subjected to fatigue damage growth. The methodology is based on the application of methods of structural reliability analysis. An optimization problem is formulated to minimize expected lifetime cost while maintaining the minimum acceptable reliability level. The effect of structural design and inspection schedule on operational cost and reliability is explored. Also, the paper explores the possibility of trading cost due to additional structural weight with inspection cost to obtain minimum operational cost. The optimization parameters are the inspection times and types and the structural thickness. The important outcome of this methodology is consistent evaluation of consequence of different inspection and handling of uncertainty.

Reliability Based Design and Inspection of Stiffened Panels Against Fatigue

This paper addresses the problem of developing optimum structural design and inspection strategy for fatigue crack growth in stiffened panels subjected to uncertainty in material properties and loading. The approach is based on the application of methods of structural reliability analysis. An optimization problem is formulated to minimize expected lifetime cost while maintaining a minimum acceptable reliability level. The effect of structural design and inspection schedule on operational cost and reliability is explored and tradeoff of structural weight and cost between load carrying structural members (skin and stiffeners) and inspections is conducted. The panel is assumed to be under plane stress condition, and stiffeners are modeled as rectangular bars discretely attached to the panel by fasteners. The stress intensity factor is first determined by enforcing displacement compatibility at fastener locations, fatigue crack growth rate is then obtained by numerical integration. Optimization revealed that improving the structure by designing it for multiple load path capability combined with the use of inspections can be very cost effective compared to unstiffened structure.

Effect of Safety Measures on Reliability of Aircraft Structures Subjected to Damage Growth

This paper demonstrates the effect of various safety measures used to design aircraft structures for damage tolerance. In addition, it sheds light on the effectiveness of measures like certification tests in improving structural safety. Typically, aircraft are designed with a safety factor of 2 on the service life in addition to other safety measures, such as conservative material properties. This paper demonstrates that small variation in material properties, loading and errors in modeling damage growth can produce large scatter in fatigue life, which means that quality control measures like certification tests are not very effective in reducing failure probability. However, it is shown that the use of machined cracks in certification can substantially increase the effectiveness of certification testing.© 2005 ASME

Why are Airplanes so Safe Structurally? Effect of Various Safety Measures on Structural Safety of Aircraft

§Passenger aircraft structural design is based on a safety factor of 1.5, and this safety factor alone is equivalent to a probability of failure of between 10 -2 and 10 -3 . Yet airliners are much safer, with crashes due to structural failure being extremely rare based on accident records. The probability of structural failure of transport aircraft is of the order of 10 -8 per flight segment. This paper looks at two other contributions to safety--the use of conservative material properties and certification tests--using a simple model of structural failure. We find that the three safety measures together may be able to reduce the calculated probability of failure to about 10 -7 , and that additional measures, such as conservative load specifications, may be responsible for the higher safety encountered in practice. In addition, the paper sheds light on the effectiveness of certification tests for improving safety. It is found that certification tests reduce the calculated failure probabilities by reducing the modeling error. We find that these tests are most effective when safety factors are low and when most of the uncertainty is due to systemic errors rather than variability. HIS paper explores the effects of various safety measures taken during aircraft structural design using the deterministic design approach based on FAA regulations. We use Monte Carlo simulations to calculate the effect of these safety measures on the probability of failure of a structural component. The safety measures that we include here are (1) the use of safety factors, (2) the use of conservative material properties (A-basis), and (3) the use of final certification tests. We do not include in this discussion the additional safety due to structural redundancy and due to conservative design load specification. The effect of the three individual safety measures and their combined effect on the probability of structural failure of the aircraft are demonstrated. We start with a structural design employing all considered safety measures. The effect of variability in geometry, loads, and material properties is readily incorporated by the appropriate random variables. However, there is also uncertainty due to lack of knowledge (epistemic uncertainty), such as modeling errors in the analysis. To simulate these epistemic uncertainties, we transform the error into a random variable by considering the design of multiple aircraft models. As a consequence, for each model the structure is different. It is as if we pretend that there are hundreds of companies (Airbus, Boeing, etc.) each designing essentially the same airplane, but each having different errors in their structural analysis. For each model we simulate certification testing. If the airplane passes the test, then an entire fleet of airplanes with the same design is assumed to be built with different members of the fleet having different geometry, loads, and