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.

Bayesian Optimisation (BO) is a sample-efficient method for optimising expensive black-box functions, making it particularly suitable for engineering problems where gradients are unavailable and evaluating the objective or constraints is computationally costly. However, such problems often involve high-dimensional inputs and a large number of constraints, posing significant challenges for standard BO frameworks. While prior research has addressed scalability with respect to high-dimensional inputs in constrained settings, efficiently handling large numbers of constraints, i.e. high-dimensional outputs, remains an open problem. This work introduces Autoencoder-Enhanced Joint Dimensionality Reduction for Constrained BO (AERO-BO), a framework that performs dimensionality reduction in both the input (design variable) and output (objective and constraint) spaces via autoencoders. These autoencoders are trained online, requiring no pre-training, and their respective latent representations are connected through Gaussian Processes, which serve as surrogate models during optimisation. By operating in a joint latent space, AERO-BO enables scalable and efficient optimisation in settings with hundreds of design variables and thousands of black-box constraints.

This paper aims to develop a reduced-order modelling methodology for nonlinear, unsteady, aerodynamic loads for active control transonic aeroelastic instabilities. To this end, a NACA0012 airfoil equipped with a flap is chosen as the test configuration. The aim here is to understand the interaction between the transonic shock dynamics and flap actuation at various amplitudes and frequencies. The high-fidelity simulations are carried out for two angles of attack, i.e. a = 0.0°, 4.0°. It is found that transonic buffet characteristics significantly change with airfoil geometry. Additionally, the flap is seen to be ineffective in the separated flow regions, thereby making the Ci-fi slopes highly nonlinear. However, increasing the frequencies of flap oscillations, increases flap effectiveness, increases control over buffet motion and moves towards linear lift responses. Furthermore, we also evaluate the performance of several Bayesian Filters that are crucial in the state-estimation process of the active control of nonlinear systems. It is observed that nonlinear filters such as Unscented Karman Filter perform better than the traditional linear Kalman Filter as system response to flap actuation becomes nonlinear in the presence of separated boundary layer.

In the development of large battery-electric aircraft, integrating the batteries into the wing is a crucial decision, as it results in a lighter wing structure due to bending relief. To understand the influence of wing-integrated batteries on wing structures, this paper presents a study on the wing structural design and sizing of the Elysian E9X aircraft configuration. In this study, the baseline wing design is defined, and the critical load cases for wing sizing are identified. Wing structural sizing is performed using an in-house aeroelastic optimization tool. The objective of the optimization is to minimize wing mass by adjusting the thickness of the wing design sections, subject to various design constraints, including structural strength, buckling, and aeroelastic instability. Sensitivity studies on wing mass with respect to key design parameters are conducted. The study results confirm that placing the batteries in the wing results in a significant wing structural mass reduction compared to housing the batteries in the fuselage. The wing mass sensitivities to other design parameters, such as the spanwise position of the main landing gear, may serve as input for the next round of aircraft design.

This study investigates the aerodynamic benefits of integrating trailing edge camber morphing on the strut of a regional strut-braced wing aircraft designed to cruise at Mach number of 0.5. Strut-braced wings are recognized for their weight advantages in high aspect ratio designs compared to the equivalent cantilever wings since the strut decreases the main wing’s bending moment. Hence, the induced drag component can be reduced due to the high aspect ratio without increasing the weight of the main wing. However, the strut increases the parasite drag component highlighting the need for innovative methods to improve the strut-braced wing overall aerodynamic efficiency. Recent studies have shown the significance of strut shape in the overall drag reduction and the necessity of maintaining high aerodynamic efficiency in off-design conditions. In this work, a genetic algorithm was utilized in conjunction with a mid-fidelity aerodynamic model to optimize the morphing strut trailing edge geometry across a range of climb and cruise conditions. The optimization objective was the minimization of drag and the design variables were the equivalent trailing edge deflection angles in seven sections of the strut. The results demonstrate a drag reduction of 0.5% to 3% both in climb and cruise. For lift coefficients below 0.8, the drag reduction is mainly attributed to the redistribution of the loading and the induced drag component reduction. In contrast, at lift coefficients above 0.8, the parasite drag component decreases due to the increased region of laminar flow over the upper wing surface.

High aspect ratio strut-braced wing aircraft can significantly reduce the induced drag while limiting the weight penalty of increasing the wingspan. As part of the Hybrid Electric Regional Wing Integration Novel Green Technologies (HERWINGT) project, a multifunctional morphing strut is being investigated. In this study, an optimization framework is proposed to define the thickness distribution of the morphing trailing edge of the strut to achieve the desired operational shapes while considering laminate manufacturing guidelines and material allowables. The optimizer finds designs capable of achieving the objective shapes and provides load and mass estimations that can be used to make design decisions.

Design optimization offers the potential to develop lightweight aircraft structures with reduced environmental impact. Due to the high number of design variables and constraints, these challenges are typically addressed using gradient-based optimization methods to maintain efficiency, however overlooking the global design space. Moreover, gradients are frequently unavailable. Bayesian optimization presents a promising gradient-free alternative, enabling sample-efficient global optimization through probabilistic surrogate models. Although Bayesian optimization has shown its effectiveness for problems with a small number of design variables, it struggles to scale to high-dimensional problems, particularly when incorporating large-scale constraints. This challenge is especially pronounced in aeroelastic tailoring, where directional stiffness properties are integrated into the structural design to manage aeroelastic deformations and enhance both aerodynamic and structural performance. Ensuring the safe operation of the system requires simultaneously addressing constraints from various analysis disciplines, making global design space exploration even more complex. This study seeks to address this issue by employing high-dimensional Bayesian optimization combined with dimensionality reduction to tackle the optimization challenges in aeroelastic tailoring. The proposed approach is validated through experiments on a well-known benchmark case, as well as its application to the aeroelastic tailoring problem, demonstrating the feasibility of Bayesian optimization for high-dimensional problems with large-scale constraints.

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.

In the development of electric aircraft, due to the use of Distributed Electric Propulsion (DEP), not only the classic wing flutter but also the propeller whirl flutter needs to be considered for wing structural design. To this end, this paper proposes an aeroelastic optimization method within the framework of an in-house tool named PROTEUS, which enables the preliminary design of DEP wing laminates including propeller whirl flutter effect. In this method, a new aeroelastic model is developed for the coupled propeller-wing system, based on a classic whirl flutter analysis model and the wing aeroelastic model implemented in PROTEUS. Further, the required sensitivities of aeroelastic stability constraints are derived and implemented by making use of these implemented in PROTEUS for conventional wing design. The objective of the optimization is to minimize wing mass by aeroelastically tailoring the lamination parameters and thickness of wing laminates, subject to given aerostructural design constraints. The features and usefulness of the proposed optimization approach are demonstrated through two numerical case studies (with and without whirl flutter constraints) focused on sizing the wing structure of a reference DEP aircraft. The necessary inputs regarding propeller mounting stiffness and damping for the case studies are determined through parametric studies of isolated propellers. The results indicate that including whirl flutter effect in wing sizing slightly increases wing mass, and introducing a flexible-mount-propeller leads to the decrease in wing flutter speed. Additionally, a parametric study of investigating propeller mounting stiffness is conducted, which confirms that the propeller mounting properties have a large influence on aeroelastic instability of the coupled propeller-wing system.

Correction notice The CL in the title of Fig. 7(b) was corrected from 0.4 in the original version to CL=1.0. (a) Climb local lift spanwise distribution at CL=1 0 0.2 0.4 0.6 0.8 1 0 5 10 10-3 0 0.2 0.4 0.6 0.8 1 0 5 10 10-3 (b) Solid line (suction side)-dashed line (pressure side) Fig. 7 Local lift coefficient distribution with a selected friction coefficient of one section.

Hybrid-electric aircraft represent a promising solution for the urgent need to decarbonize short-haul flights and bolster aviation sustainability. Nevertheless, the realization of hybrid-electric aircraft demands rigorous environmental impact analysis, given the substantial investments, time, and research required for technology development. This study offers a comprehensive life cycle inventory spanning the years 2030, 2040, and 2050 for both conventional and hybrid-electric aircraft configurations. Our inventory datasets are meticulously constructed through a systematic approach, ensuring data harmonization by drawing upon scientific literature, industry expertise, and primary data sources. This extensive dataset encompasses all pertinent systems necessary to model the environmental footprint of flights covering distances ranging from 200 to 600 nautical miles, utilizing a 50-passenger aircraft with the ATR42 as a reference model. Additionally, we furnish supplemental data for end-of-life considerations and uncertainty analysis. The systems under examination include the airframe, powertrain, power electronics and drives, batteries, fuel cells, hydrogen onboard storage, airport infrastructure, and battery charging stations. Notably, the carbon footprint of conventional aircraft aligns with data from the ecoinvent v3.8 database; however, our provided datasets are more than tenfold more detailed and incorporate a forward-looking perspective. These meticulously curated life cycle inventories can be amalgamated to simulate the potential environmental ramifications of conventional aircraft powered by kerosene or alternative aviation fuels, hybrid-electric aircraft utilizing battery technology, and hybrid-electric aircraft employing hydrogen as a fuel in conjunction with batteries. In this context, our findings play a pivotal role in nurturing the development of technology roadmaps that prioritize environmental sustainability within the realm of regional aviation.

Design optimisation potentially leads to lightweight aircraft structures with lower environmental impact. Due to the high number of design variables and constraints, these problems are ordinarily solved using gradient-based optimisation methods, leading to a local solution in the design space while the global space is neglected. Bayesian Optimisation is a promising path towards sample-efficient, global optimisation based on probabilistic surrogate models. While for problems with a low number of design variables, Bayesian Optimisation methods have demonstrated their strength, the scalability to high-dimensional problems while incorporating large-scale constraints is still lacking. Especially in aeroelastic tailoring where directional stiffness properties are embodied into the structural design of aircraft, to control aeroelastic deformations and to increase the aerodynamic and structural performance, the safe operation of the system needs to be ensured by involving constraints resulting from different analysis disciplines. Hence, a global design space search becomes even more challenging. The present study attempts to tackle the problem by using high-dimensional Bayesian Optimisation in combination with a dimensionality reduction approach to solve the optimisation problem occurring in aeroelastic tailoring, presenting a novel approach for high-dimensional problems with large-scale constraints. Experiments on well-known benchmark cases with black-box constraints show that the proposed approach can incorporate large-scale constraints.

The design and optimisation of aircraft wings are critical tasks in aerospace engineering, requiring a balance between structural integrity, aerostructural performance, and manufacturability. This multifaceted challenge involves the interplay of various disciplines, each with distinct parameters and constraints. Traditional design approaches often fall short, necessitating advanced methodologies like Multidisciplinary Design Optimisation (MDO). MDO integrates aerodynamic, structural, and manufacturability analyses to explore a vast design space and identify optimal solutions that meet performance, safety, and cost criteria. Advancements in manufacturing technologies and material sciences have led to the increased use of composite materials, which offer an excellent weight-to-strength ratio. Aeroelastic Tailoring, which incorporates directional stiffness into structural design, further enhances performance. This study employs lamination parameters to efficiently represent composite layups within a gradient-based optimisation process, aiming to minimise weight while ensuring feasibility across multiple constraints. The work highlights the challenge of optimising aircraft designs using multiple models of varying fidelity. Traditional sequential optimisation approaches, which progressively integrate disciplines, may miss potential superior designs due to limited initial information. Instead, concurrent optimisation schemes are explored, utilising both low-fidelity (beam-based) and high-fidelity (shell-based) models. This approach promises structural feasibility, reduces computational costs, and incorporates high-fidelity information early in the design process. The envisioned methodology bridges different design stages, enabling better overall aircraft performance. By aligning and comparing a beam-based and shell-based model, the study explores their use in multi-fidelity optimisation. The results demonstrate the feasibility and benefits of this approach, offering a robust framework for future aircraft design projects.

This paper presents a method for identifying flight dynamics models for aircraft that includes effects from the flexible structure and the effects from unsteady aerodynamics. In the time domain, the unsteady aerodynamic effects are often modelled using aerodynamic lag states. The proposed method involves first determining the poles that govern the dynamics for these lag states from flight data. This is followed by reconstructing the time signal histories for these lag states so that they can then be used as part of the model fitting procedure. Flight tests were conducted using a scaled Diana2 glider unmanned aerial vehicle (UAV) in order to collect experimental data for modelling. To be able to measure the response of the aircraft and its structure, the glider was instrumented with a wide range of sensors including accelerometers, gyroscopes and strain gauges placed across the aircraft structure. During the flight, various excitation manoeuvres were conducted by the pilot while the aircraft responses were collected. From these measurements, a full flight dynamics model consisting of both lateral and longitudinal dynamics was then identified. Additionally, a model predicting the tail and wing root loads was also identified. First, a rigid aircraft model was fitted that was then extended with states corresponding to the flexible modes and aerodynamic lags. Comparison between the rigid and extended model showed that the addition of structural modes and aerodynamic lag states to the identified models can lead up to 30% improvement in predicting aircraft responses. In conclusion, the method developed and presented in this paper is able to identify flight dynamics models from flight data that more accurately capture the dynamics of flexible aircraft by including effects from the flexible structure and unsteady aerodynamics.

In line with recent advancements in aviation, which lead to more fuel-efficient aircraft, this paper presents a novel continuous movable parameterisation methodology. The methodology takes advantage of the ability of the doublet lattice method (DLM) to describe aerodynamic forces using downwash. The movables are described in the continuous space using a downwash distribution generated using a B-spline surface. To demonstrate and assess the movable modelling methodology, the U-HARWARD aircraft model has been used, with the performance of the continuous parameterisation compared to a reference movable parameterisation for roll control, manoeuvre load alleviation and cruise performance. The results show that the continuous parameterisation can determine a downwash distribution that is at least equal in performance – during roll – or has better performance – for manoeuvre load alleviation and cruise performance – than the reference parameterisation. The continuous parameterisation showed a 3 percentage points improvement with respect to the reference parameterisation for manoeuvre load alleviation and a 2.4 percentage points improvement for the induced drag coefficient. The results in the paper demonstrated the successful application of a movable parameterisation methodology, which can be applied to an aircraft for which only the planform and initial structural parameters are known.

Recent investigations pertaining to high aspect ratio wings have demonstrated the influence of geometric nonlinearities on structural and aeroelastic response when large deflections occur [1,2]. While utilization of nonlinear analyses techniques is beneficial for more realistic predictions of large deflection behaviour, it is accompanied with the drawback of high computational costs since finite element (FE) solvers are based on iterative predictor-corrector models. Nonlinear reduced order modelling can be an effective tool for conducting efficient analyses in such cases. In the proposed study we aim to exploit the recent developments in the Koiter-Newton (K-N) model reduction technique [3] for nonlinear dynamic response analysis of a high aspect ratio wing and thus, demonstrate the achievable reduction in computational costs in comparison to full FE simulations. The K-N reduction is a FE-based formulation which describes a system of nonlinear governing equations comprising quadratic and cubic stiffness terms. The higher order stiffness terms are evaluated as derivatives of the in-plane strain energy. To ensure that the effect of large rotations is accounted for, the reduced order model (ROM) is updated at fixed load intervals. Linear eigenmodes of the deformed structure are used to formulate the reduction subspace at the different load steps. The test structure chosen in this work is a variant of the Pazy wing [4] which is an experimental benchmark wing designed for nonlinear aeroelastic studies. The Pazy wing variant is based on the dimensions of the original design with minor modifications in the inner geometry. The FE model is constructed entirely using shell elements with 21,712 grid points and 130,272 degrees of freedom. For the initial validation, we conduct a nonlinear static analysis with a concentrated follower force, and compare it to FE solution from MSC Nastran. It is seen that by using just a single degree of freedom ROM, the nonlinear static solution is reproducible within a 2 % error margin for up to 40 % tip deflections. Subsequently, a nonlinear dynamic response analysis is conducted where the wing is subjected to large amplitude transient loads. The preliminary studies show a reduction in simulation time of over 95 % without significant loss in solution accuracy. References [1] Riso, Cristina, and Carlos E. Cesnik. "Low-Order Geometrically Nonlinear Aeroelastic Modeling and Analysis of the Pazy Wing Experiment." AIAA SciTech 2022 Forum. 2022. [2] Hilger, Jonathan, and Markus Raimund Ritter. "Nonlinear aeroelastic simulations and stability analysis of the Pazy wing aeroelastic benchmark." Aerospace 8.10 (2021): 308. [3] Sinha, Kautuk, et al. "Koiter–Newton Based Model Reduction for Large Deflection Analysis of Wing Structures." AIAA Journal (2023): 1-10. [4] Avin, Or, et al. "Experimental aeroelastic benchmark of a very flexible wing." AIAA Journal 60.3 (2022): 1745-1768.

This paper contributes towards the development of a reduced-order modelling methodology for nonlinear, unsteady aerodynamic loads for the active control of transonic aeroelastic flutter. To this end, a 1-DOF torsional NACA0012 airfoil is chosen as the test configuration. The aim is to develop the reduced-order model in nonlinear state-space form to be used in active control scenarios. Hence, a nonlinear coupled differential equation that captures the shock dynamics. The underlying hypothesis of this work is that, once these aerodynamic effects are included in the low-order model, the nonlinear trend in the flutter stability boundary, specifically in the transonic regime, will be predicted purely based on first principles, without the need for numerical or experimental corrections. In this work, we observe that the aeroelastic system could become prematurely unstable as soon as the aerodynamic flow field undergoes a Hopf bifurcation. For low amplitude airfoil pitching below a certain threshold, the aerostructural system is seen to exhibit a coupled oscillator behaviour that has an exact linear analytical formulation. The analytical formulation thus produces an accurate prediction whilst being orders of magnitude faster than the numerical simulation.

This paper presents an experimental investigation into the aeroelastic behavior of an innovative wind turbine design featuring a downwind two-blade rotor with a teetering hub mounted on a tower with adjustable tilt. The rotor model incorporates two sets of elastic blades—stiff and flexible—for scaling purposes, each instrumented with strain gauges and accelerometers. Ground and wind tunnel tests were conducted to analyze the aeroelastic response. Static tests exhibited discrepancies between measured and numerically predicted displacements, with maximum displacements near the tip exceeding numerical predictions by 14% and 31% for flexible and stiff blades respectively. Frequency differences between measured and numerically simulated elastic modes ranged from 0.5% to 18% for both blade sets, as determined by ground vibration tests. Wind tunnel tests revealed the dominance of rotational speed harmonics, particularly the second harmonic, in the blades’ periodic response. A sensitivity analysis was also carried out with respect to tower tilt angle, rotational speed and blade pitch angle, for both blade sets at a range of tip-speed ratio values. The static response of the system, as captured by the generated power and thrust, was primarily sensitive to tower tilt angle variation and to a lesser extent blade pitch angle. Conversely, the tip-speed ratio in conjunction with rotational speed were found to dictate the dynamic response, influencing the azimuthal position and magnitude of the maximum bending moment at the blade root. Finally, no dynamic aeroelastic instability was observed during wind tunnel tests.

This research investigates the application of aeroelastic tailoring to enhance the post-control surface reversal regime on a mid-range aircraft. Conventionally, active Maneuver Load Alleviation (MLA) is achieved through control surface actuation, while passive MLA utilizes structural modifications at the material or layout level to exploit wing wash-out deformation. Previous studies have demonstrated the significance of high control effectiveness in active MLA and the limitations of composite tailoring in passive MLA due to roll control authority constraints which typically result in stiffer wings with moderate mass savings. The aeroelastic optimization framework PROTEUS, developed at TU Delft, is employed to enhance operation in the post-control surface reversal regime. This is done to capitalize on increased control authority and thus promote load alleviation. The approach taken in this study is to identify critical constraints and assess the advantages of this strategy while acknowledging the technology’s immaturity, particularly its challenges in maintaining roll control effectiveness in certain flight envelope sectors. The results demonstrate significant mass savings in active MLA within the post-control surface reversal regime compared to conventional active MLA and highlight the substantial impact of the cruise-twist constraint on enhancing this regime.

This paper introduces a new computationally efficient tool to predict the post buckling behavior of thin-walled aircraft structures, particularly stiffened panels. Focusing on the critical transition where local buckling alters load distribution but retains the structure’s load-carrying capacity, the proposed postbuckling analysis method employs a semi-analytical Rayleigh-Ritz-based model and the perturbation approach. The assumed geometrically compatible displacement field functions are based on hierarchical polynomials, which are able to enhance the versatility and computational efficiency of the semi-analytical model, enabling its application across a wider range of structural configurations and boundary conditions, whereas currently available perturbation-based methodologies are limited to simple boundary conditions. The enhancement in computational efficiency, additionally, provides substantial benefits to the design and optimization processes. The obtained results for the linear case perfectly match the analytical values for buckling load. For the nonlinear case, results come in a good agreement with literature.