A stochastic optimization methodology (SDO) has been developed to design air-frame structural components made of metallic and composite materials. The design method accommodates uncertainties in load, strength, and material properties that are defined by distribution functions with mean values and standard deviations. A response parameter, like a failure mode, has become a function of reliability. The primitive variables like thermomechanical loads, material properties, and failure theories, as well as variables like depth of beam or thickness of a membrane, are considered random parameters with specified distribution functions defined by mean values and standard deviations.

The cumulative distribution concept is used to estimate the value of the response parameter like stress, displacement, and frequency for a specified reliability. This solution for stochastic optimization also yields the design and weight of a structure as a function of reliability. Weight versus reliability is traced out in an inverted S-shaped graph. The center of the graph corresponds to 50-percent probability of success, or one failure in two samples.

A heavy design with weight approaching infinity could be produced for a near-zero rate of failure. Likewise, weight can be reduced to a small value for the most failure-prone design. Reliability can be changed for different components of an airframe structure. For example, the landing gear of an airliner can be designed for very high reliability, whereas it can be reduced for a raked wingtip.

The design capability is obtained by combining three codes: MSC/Nastran code (the deterministic analysis tool), the fast probabilistic integration or the FPI module of the NESSUS software (the probabilistic calculator), and NASA Glenn’s optimization testbed CometBoards (the optimizer). For the raked wingtip structure of the Boeing 767-400ER airliner, the stochastic optimization process redistributed the strain field and reduced weight by 17 percent over the traditional design.

This work was done by Shantaram S. Pai and Rula Coroneos of Glenn Research Center and Surya N. Patnaik of Ohio Aerospace Institute. For more information, download the Technical Support Package (free white paper) at www.techbriefs.com/tsp under the Manufacturing & Prototyping category.

Inquiries concerning rights for the commercial use of this invention should be addressed to NASA Glenn Research Center, Innovative Partnerships Office, Attn: Steve Fedor, Mail Stop 4–8, 21000 Brookpark Road, Cleveland, Ohio 44135. Refer to LEW-18497-1.