Reliability-based aeroelastic design of composite plate wings using a stability margin

Abstract

Reliability-based design is concerned with ensuring that constraints are enforced with acceptable probability under inherent variability in properties. In aircraft design, such a constraint may be that aeroelastic instability does not occur at velocities encountered by the aircraft. This approach can be complicated, as the aeroelastic instability speed is a discontinuous function of material properties, on account of particular modes only becoming unstable for some parameter values. In reliability analysis, it is common to use surrogate models due to the computational expense associated with Monte Carlo Simulation, however, such methods can be inaccurate when emulating discontinuous functions such as the aeroelastic instability speed. In this paper, an alternative approach is proposed in which Gaussian process surrogate models are fitted directly to each of the modal eigenvalues at the design air-speed, and used to emulate a stability margin based upon the most critical eigenvalue. Using this approach, it is shown that the reliability may be estimated for the aeroelastic stability using smooth emulators, thereby overcoming the problems associated with discontinuities. The method is demonstrated for layup optimisation of composite plate wings with uncertain ply angles, in which the probability of aeroelastic instability occurring is minimised for a prescribed air-speed. In uncertainty quantification, a good agreement is found with Monte Carlo Simulation with an order of two magnitudes reduction in model runs. Through reliability-based design, reductions in the probability of failure of up to 99.8% are achieved by increasing the stability margin at the design speed.

Optimal Design of Plated/Shell Structures under Flutter Constraints—A Literature Review

“…Pettit, Beran [44] analysed oscillations of an aerofoil with uncertain pitching stiffness and angle of attack. Scarth, Cooper [45] investigated the influence of material variability on stability margins in flutter characteristics. Various linear and nonlinear aeroelastic problems were formulated and solved with the aid of the reliability based design optimization methods in Refs [46][47][48][49][50][51][52][53] and even the results were compared with the results obtained with the use of deterministic optimization methods Nikbay et al [46,52,53].…”

Probabilistic Control Optimization of Aeroservoelastic Systems with Uncertainty

“…The probability of flutter was assessed using a combination of polynomial chaos (PC) expansions and Monte-Carlo simulations. Likewise, Scarth and Cooper [14] used Gaussian process surrogate models to estimate the probability of failure of a composite plate and used reliability-based design to reduce the probability of failure and increase the stability margin. Similar work was also considered by Stanford and Beran [15], but with uncertainty in the panel boundary conditions.…”

Effect of delamination on the stochastic natural frequencies of composite laminates

“…The aspect of delamination in composites has also received adequate attention in the deterministic domain . Stochastic analysis of composite and sandwich structures considering sourceuncertainty is found to be studied by many researchers including the aspects of multi-scale analysis, optimization and reliability assessment [40][41][42][43][44][45][46][47][48][49][50][51][52][53][54][55][56][57][58][59]. However, the compound effect of delamination and sourceuncertainty has not been investigated yet for the dynamic responses of composite structures.…”