Design of Composite Wings Including Uncertainties – A Probabilistic Approach

A probabilistic method is developed to optimize the design of an idealized composite wing through consideration of
the uncertainties in the material properties,fiber-direction angle, and ply thickness. The polynomial chaos expansion
method is used to predict the mean, variance, and probability density function of theflutter speed, making use of an
efficient Latin hypercube sampling technique. One-dimensional, two-dimensional, and three-dimensional
polynomial chaos expansions are introduced into the probabilistic flutter model for different combinations of
material, fiber-direction-angle, and ply-thickness uncertainties. The results are compared with Monte Carlo
simulation and it is found that the probability density functions obtained using second- and third-order polynomial
chaos expansion models compare well but require much less computation. A reliability criterion is defined, indicating
the probability of failure due to flutter, and is used to determine successfully the optimal robust design of the
composite wing.