Reliability Based Design for a Raked Wing Tip of an Airframe

Summary A reliability-based optimization methodology has been developed to design components of an airframe structure. Design is formulated for an accepted level of risk or reliability. The design variables, weight and the constraints became functions of reliability. Uncertainties in the load, strength and the material properties, as well as the design variables, were modeled as random parameters with specified distributions, like normal, Weibull or Gumbel functions. The objective function and constraint, or a failure mode, became derived functions of the risk-level. Solution to the problem produced the optimum design with weight, variables and constraints as a function of the risk- level. Optimum weight versus reliability traced out an inverted-S shaped graph. The center of the graph corresponded to a 50 percent probability of success, or one failure in two samples. Under some assumptions, this design would be quite close to the deterministic optimum solution. The weight increased when reliability exceeded 50 percent, and decreased when the reliability was compromised. A design could be selected depending on the level of risk acceptable to a situation. The reliability-based optimization software was obtained by combining three codes. MSC/Nastran code was the deterministic analyzer . Fast probability integration of the NESSUS software was the probabilistic calculator. NASA Glenn Research Center’s optimization testbed CometBoards was used as the optimizer. The optimization capability required a deterministic finite element structural model and probabilistic models for material properties , thermo-mechanical load and design variables. Reliability-based optimization method was applied to design the raked wing tip of the Boeing 767–400 extended range airliner which is made of composite and metallic materials. The members of the wing tip were grouped to obtain a set of 13 active design variables. For constraint formulation, the structure was separated into a number of subcomponents. Strain constraints were imposed on members in the subcomponents. There were 203 strain constraints for the panels and the spars and 16 additional constraints for the rod members. Three translations and one rotation at the tip of the structure were also constrained. The design model had a total of 227 behavior constraints for two critical load cases. Constraint can be imposed on principal strain or on a failure theory for laminates. Deterministic optimum solution was generated first, followed by stochastic design. The stochastic optimization calculation required continuous running of the code for more than 5 days, but the execution was smooth and eventless. The optimum design exhibited nine active constraints consisting of eight strain and one displacement limitations. The optimization process redistributed the strain field in the structure and achieved up to a 20-percent reduction in weight over traditional design.