Definition of the Limit State Function

To apply the FORM analysis to the coupled fluid-structure problem a realistic failure criterion had to be defined to describe the performance of the simulated wing struc­ture. For this kind of problem the random input is given by a variation of structural parameters. The change of the converged angle of attack aEqSt of the aeroelastic equilibrium state (cp. section 1.2) was used to estimate the impact of random input parameters on the aerodynamic properties of the investigated wing model. The devi­ation A aEqSt/aEqSt can be considered in both positive and negative directions. The higher values of aEqSt caused by a lower Young’s modulus or by reduction in wall thickness, respectively, are assessed to be more critical than smaller ones, caused by a stiffer wing structure.

The probability of deviation of equilibrium state angle of attack is investigated for different values of AaEqSt/aEqSt varying between 0.4% and 1.0%. Each value corresponds to a limit state function in the normal variable space, which is defined as:

G(X’) = A aEqSt – AaEqSt, req (4)

The term AaEqSt req defines the highest permitted deviation of the converged angle of attack. For a discrete limit state function and a distribution of random para­meters (characterized by the coefficient of variance) the FORM algorithm calculates a combination of these parameters for which the reliability index в becomes min­imum. For the inversion of the argument, the probability of the aeroelastic response represented by the limit state function becomes maximal.

An exemplary problem for two random variables X[ and X[ with two limit state functions Gi(X’)) and G2(X) is depicted in fig. 7. Corresponding to the definition of the reliability index в the probability of G1 (X’) is higher then of G2(X’) because of the smaller distance в between the curve and the origin of the standard normal space.