Development of a Nonlinear Structural Stability Constraint for Aeroelastic Optimization

In recent decades, substantial endeavors have been directed towards developing aircraft structures that enhance fuel efficiency and reduce emissions. Central to these efforts has been aeroelastic optimization, whereby an airframe’s design space is explored with the aid of aeroelastic analysis tools and within the bounds imposed by dozens of constraints, including structural strength and stability. Accurate evaluation of the stability constraints in thin-walled, lightweight constructions is crucial, as these constraints are often active and a driving design factor. Nonetheless, though the pursuit of efficiency has led to increasingly slender, flexible and thus kinematic nonlinear wings, the aeroelastic optimization community still predominantly relies on linear analyses for the evaluation of structural stability constraints. This preference stems from the conservative nature of linear evaluations and from their ease of implementation and evaluation. However, defaulting to linear methods has resulted in overlooking the real nature of the structural problem at hand: as wings become more slender, their stress and stability analyses should account for nonlinearities. Failing to do so results in inaccuracies and excessively conservative estimates of buckling margins. Such conservatism places a glass ceiling on the load-bearing capacity of wing structures, effectively confining the design space in an excessive manner and excluding solutions that could potentially yield significant weight savings. This paper extends our previous research work on the incorporation of nonlinear structural stability analysis into the aeroelastic optimization of wingbox-like structures. Our approach hinges on assessing the positive-definiteness of the tangent stiffness matrix, a key indicator of structural stability. By monitoring the eigenvalues of the tangent stiffness matrix while tracing load-displacement equilibrium paths using arc-length methods, it is possible to pinpoint the real onset of structural instability. Herein, the efficacy of the proposed constraint is demonstrated through the structural optimization of an idealized version of NASA’s CRM (Common Research Model) wingbox. The structure’s thickness distribution is first optimized for minimum mass employing traditional linear buckling constraints, to create a baseline, and then by enforcing nonlinear structural stability constraints. A mass reduction of 29.6% with respect to the linearly optimized structure highlights the potential of the proposed constraint for aeroelastic optimization.