ALBERT

Description: An approach is presented for carrying out reliability-based design of a metallic, plate-like wing to meet strength and flutter requirements that are given in terms of risk/reliability. The design problem is to determine the thickness distribution such that wing weight is a minimum and the probability of failure is less than a specified value. Failure is assumed to occur if either the flutter speed is less than a specified allowable or the stress caused by a pressure loading is greater than a specified allowable. Four uncertain quantities are considered: wing thickness, calculated flutter speed, allowable stress, and magnitude of a uniform pressure load. The reliability-based design optimization approach described herein starts with a design obtained using conventional deterministic design optimization with margins on the allowables. Reliability is calculated using Monte Carlo simulation with response surfaces that provide values of stresses and flutter speed. During the reliability-based design optimization, the response surfaces and move limits are coordinated to ensure accuracy of the response surfaces. Studies carried out in the paper show the relationship between reliability and weight and indicate that, for the design problem considered, increases in reliability can be obtained with modest increases in weight.

Description: approach is presented for carrying out the reliability-based design of a plate-like wing that is part of a wind tunnel model. The goal is to design the wind tunnel model to match the stiffness characteristics of the wing box of a flight vehicle while satisfying strength-based risk/reliability requirements that prevents damage to the wind tunnel model and fixtures. The flight vehicle is a modified F/A-18 aircraft. The design problem is solved using reliability-based optimization techniques. The objective function to be minimized is the difference between the displacements of the wind tunnel model and the corresponding displacements of the flight vehicle. The design variables control the thickness distribution of the wind tunnel model. Displacements of the wind tunnel model change with the thickness distribution, while displacements of the flight vehicle are a set of fixed data. The only constraint imposed is that the probability of failure is less than a specified value. Failure is assumed to occur if the stress caused by aerodynamic pressure loading is greater than the specified strength allowable. Two uncertain quantities are considered: the allowable stress and the thickness distribution of the wind tunnel model. Reliability is calculated using Monte Carlo simulation with response surfaces that provide approximate values of stresses. The response surface equations are, in turn, computed from finite element analyses of the wind tunnel model at specified design points. Because the response surface approximations were fit over a small region centered about the current design, the response surfaces were refit periodically as the design variables changed. Coarse-grained parallelism was used to simultaneously perform multiple finite element analyses. Studies carried out in this paper demonstrate that this scheme of using moving response surfaces and coarse-grained computational parallelism reduce the execution time of the Monte Carlo simulation enough to make the design problem tractable. The results of the reliability-based designs performed in this paper show that large decreases in the probability of stress-based failure can be realized with only small sacrifices in the ability of the wind tunnel model to represent the displacements of the full-scale vehicle.

Description: An approach for conducting reliability-based design and optimization (RBDO) of a Boeing 767 raked wing tip (RWT) is presented. The goal is to evaluate the benefits of RBDO for design of an aircraft substructure. A finite-element (FE) model that includes eight critical static load cases is used to evaluate the response of the wing tip. Thirteen design variables that describe the thickness of the composite skins and stiffeners are selected to minimize the weight of the wing tip. A strain-based margin of safety is used to evaluate the performance of the structure. The randomness in the load scale factor and in the strain limits is considered. Of the 13 variables, the wing-tip design was controlled primarily by the thickness of the thickest plies in the upper skins. The report includes an analysis of the optimization results and recommendations for future reliability-based studies.

Description: An equivalent plate procedure is developed to provide a computationally efficient means of matching the stiffness and frequencies of flight vehicle wing structures for prescribed loading conditions. First, the equivalent plate is used to match the stiffness of a stiffened panel without damage and the stiffness of a stiffened panel with damage. For both stiffened panels, the equivalent plate models reproduce the deformation of a corresponding detailed model exactly for the given loading conditions. Once the stiffness was matched, the equivalent plate models were then used to predict the frequencies of the panels. Two analytical procedures using the lumped-mass matrix were used to match the first five frequencies of the corresponding detailed model. In both the procedures, the lumped-mass matrix for the equivalent plate is constructed by multiplying the diagonal terms of the consistent-mass matrix by a proportionality constant. In the first procedure, the proportionality constant is selected such that the total mass of the equivalent plate is equal to that of the detailed model. In the second method, the proportionality constant is selected to minimize the sum of the squares of the errors in a set of pre-selected frequencies between the equivalent plate model and the detailed model. The equivalent plate models reproduced the fundamental first frequency accurately in both the methods. It is observed that changing only the mass distribution in the equivalent plate model did not provide enough flexibility to match all of the frequencies.