Modern aircraft designs aim to enhance overall performance and reduce fuel consumption, thereby minimising costs. The growing interest in high-aspect-ratio wings stems from the potential gains in aerodynamic performance. Concurrently, the utilisation of composite materials in the aircraft primary structure for weight reduction is increasing. Both aspects influence wing flexibility and may result in larger wing deflections than those of existing aircraft during operational conditions. Under appropriate loading conditions, the wing deflections can be large enough to surpass the threshold of geometrically linear analyses. This adds complexity to both structural and aeroelastic analyses.

The primary challenge in nonlinear structural analyses arises due to the replacement of the scalable linear methods with the iterative predictor-corrector methods. This can significantly exacerbate the required computational effort. The same limitation also extends to aeroelastic analyses. Beyond the computational aspects, the larger wing deflections introduce aeroelastic effects that cannot be modelled using the linear methods. Prior studies have demonstrated the influence of geometric nonlinearities on aeroelastic characteristics. Notably, a majority of numerical models used to investigate these effects so far rely on variants of geometrically exact beam theory for incorporating nonlinear structural kinematics. While this approach makes the analyses computationally efficient, it involves transforming finite element models into equivalent beam models.....

Cantilevers find a wide range of applications in the design of scientific equipment and large-scale engineering structures such as aircraft wings. Analysis techniques based on linearization approximations are unable to capture the large amplitude oscillation behaviour of such structures and thus, necessitates development of dedicated nonlinear methods. In this work, the recent developments in the Koiter-Newton model reduction method are utilized to obtain nonlinear reduced order models (ROMs) from full finite element structural models in order to simulate large amplitude dynamics of cantilevers. The method describes a nonlinear system of governing equations comprising quadratic and cubic terms which are obtained as higher order derivatives of the in-plane strain energy. To ensure that the large rotations in cantilevers and the resultant foreshortening effect is also accounted for, a ROM updating algorithm is adopted where the ROM parameters are varied with the structural deflections. Linear eigenmodes of the structure are utilized to form the reduction subspace. To validate the methodology, the ROM solution is compared against experimental results and a convergence study is conducted to identify the number of modes needed to replicate the nonlinear response. Finally, a composite wingbox structure is considered for which time domain simulations are conducted and frequency response curves, obtained through a frequency sweep, are presented.

The evolving designs and requirements of aircraft structural components has recently created an increased interest in application of nonlinear modelling techniques. While the finite element (FE) methods already incorporate the necessary mechanics to model nonlinear behavior in structures, a major drawback is the considerably higher computation cost in comparison to the linear counterparts. Reduced order modelling (ROM) techniques offer a solution to counter this limitation. The work presented here is focused on the Koiter-Newton (K-N) model reduction technique which is based on a cubically nonlinear mechanical model. The K-N method utilizes existing FE models as a starting point to generate equivalent ROM parameters and thus, can be applied to obtain ROMs for generic structures. The model validity is assessed by conducting nonlinear dynamic analyses of two models with different boundary conditions. Nonlinear frequency response analyses are conducted to demonstrate hardening effects in both the test cases. Comparisons to full FE analyses show significant reduction in computational times.