Reliability-Based Structural Design of Aircraft Together with Future Tests

Abstract

Traditional optimization changes variables that are available in the design stage to optimize objectives, such as aircraft structural reliability. However, there are many post-design measures, such as tests and structural health monitoring that reduce uncertainty andfurther improve the reliability. In this paper, a new reliability-based design framework that can include post-design uncertainty reduction variables is proposed. Among many post-design variables, this paper focuses on the number of coupon tests and the number of structural element tests. Uncertainty in the failure stress prediction, variability due to the finite number of coupon tests, and uncertainties in geometry and service conditions are studied in detail. The Bayesian technique is used to update the failure stress distribution based on results of the element tests. Tradeoff plots of the number of tests, weight and probability of failure in certification and in service are generated, and finally reliability-based design of future tests together with aircraft structure is performed for minimum lifecycle cost. Nomenclature A = load carrying area (width times thickness) of a small part of the overall structure be ef = bound of associated with failure criterion used while predicting failure in the structural element tests b t = bound of error in the design thickness, e t b w = bound of error in the design width, e w e ef = error associated with failure criterion used while predicting failure in the structural element tests e f = error in predicting failure of the entire structure in certification or proof testec e p = error in load calculation e σ = error in stress calculation e t = error in the design thickness due to construction errors e w = error in the design width due to construction errors DOC = direct operating cost E( ) = expected value (i.e., mean value) k d = knockdown factor at coupon level due to use of conservative (B-basis) material properties k f = additional knockdown factor at the structural level (nominal value is taken as 0.95) n c = number of coupon tests (nominal value is taken as 50) American Institute of Aeronautics and Astronautics2 n e = number of element tests (nominal value is taken as 3) N a = number of aircraft in a fleet (taken as 1,000) N mat = number of materials for which coupon testing is done (taken as 80) N elem = number of different types of structural elements tested (taken as 100) p = cost saving by reducing the structural weight by one unit P calc = calculated design load P d = true design load based on the FAA specifications (e.g., gust load specification) P f = probability of failure PFCT = probability of failing certification test σ ca = allowable stress (B-basis) from coupon testing σ ea = allowable stress (B-basis) from element testing σ a = allowable stress (B-basis) of the entire structure σ cf = failure stress from coupon testing σ ef = failure stress of the structural element (σ ef ) test = element failure stress measured in tests (σ ef ) calc = calculated (or predicted) element failure stress (σ ef...

Simultaneous Design of a Stiffened Fuselage Panel and Number of Structural Tests

“…That is, if very large or very small fracture toughness values are obtained from the element tests, the company may want to increase or reduce the panel thickness and stiffener area of the elements. We did not find published data on redesign practices, and so we use a common sense approach that we devised in our earlier work [5][6][7]. We assumed that if the B-basis value obtained after element tests, ea KIC , is more than 5% higher than the B-basis value obtained from coupon tests, ca KIC , then the panel thickness and stiffener area are both reduced such that ea KIC is reduced by 5%.…”

“…The effect of element tests on fracture toughness distribution is modeled using Bayesian updating, which is used to update the mean fracture toughness distribution as in our earlier work [5][6][7]. If Bayesian updating were used directly within an MCS loop of probability of failure calculation, the computational cost would be very high.…”

“…Note here that it is more convenient to define the error to be measured from the calculated values of the fracture toughness as shown in Fig B1. As in our earlier work [5][6][7], we neglect the effect of coupon tests and assumed the initial distribution of the mean fracture toughness ( )…”

“…The cost model used in this study is based on the paper by Kaufmann et al [18], and used in our earlier work [6,7]. The DOC of the aircraft structure is defined as …”

“…They also found that it is possible to perform a probabilistic design and at the same time satisfy the Federal Aviation Administration Regulations for deterministic design. In follow up studies, Acar et al [6,7] showed that it is possible to design the structural tests together with the structure (by trading off the cost of more weight against the cost of additional tests) through simulating all possible outcomes of future tests in a Bayesian framework.…”