Proof of concept of a nonlinear structural stability constraint for aeroelastic optimisation

In the past few decades, substantial work has been directed towards the design of aircraft structures that maximise fuel efficiency, improve performance and curtail emissions. Aeroelastic optimisation offers an effective way to devise lightweight and fuel efficient structures, with structural stability constraints often driving the design. To date, the aeroelastic optimisation community has relied mostly on linear buckling predictions for the evaluation of structural stability constraints, mainly because of their conservativeness, computational efficiency and simplicity of implementation. This approach typically leads to overly conservative buckling margins, and this over-conservativeness places a glass ceiling over the load carrying capacity of wing structures, consequently restricting the exploration of regions within the design space where considerable weight savings could be achieved.

By contrast to previous works that predominantly rely on linear buckling constraints, the present paper introduces a method to incorporate nonlinear structural stability analysis into aeroelastic optimisations of wingbox-like structures. The method relies on the evaluation of the positive-definiteness of the tangent stiffness matrix, which is an indicator of structural stability. The sign of the stiffness eigenvalues is monitored while tracing the load-displacement equilibrium paths by means of the arc-length method, thus pinpointing the onset of instability. The proposed constraint is tested in a proof of concept structural optimisation of an idealised version of the CRM wingbox. This optimisation shows a 10.9 % reduction in mass with respect to a baseline design that is optimal with a linear buckling approach, promising great potential for application to more realistic aeroelastic optimisations.