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.

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Double-curved composite structures that are manufactured via automated fiber placement, such as pressure vessels, can take advantage of tow steering to reduce weight. This design freedom comes with the cost of adding internal normal stresses to the tow, possibly leading to wrinkles or pull up. The present work investigates tow pull up both experimentally and analytically and details a correlation between tow pull up and the minimum critical steering radius, where the material tackiness and the modelled plate’s length are found to be the most influential parameters. The experimental determination of the material tackiness is the next step to improve the predictive capabilities of the proposed model.@en

The authors regret to inform that an error has been identified in the numerical dataset presented in the original paper (Appendix C.1) for square tubular structures. The mean force values were taken for the entire range (including the peak) instead of the plateau phase of the crushing due to a scripting error. This has an effect on some of the coefficient of determination values, error ranges in Table 2 and causes a change in the generalized equation. However, the coefficient of determination of the generalized model remains unchanged. This corrigendum presents the changes in text and the updated figures and tables. The authors would like to apologise for any inconvenience caused.

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Carbon emissions from commercial aircraft are expected to reach more than twice as much as the current levels by 2050. Unconventional aircraft, such as the Flying-V, are projected to achieve more than 20% fuel savings when compared to conventional configurations. However, these unconventional aircraft configurations pose a unique set of design challenges, being one of them the crashworthiness of wing-fuselage structures, which have an oval-shaped cross section that leads to a significant reduction in space underneath the cabin floor. Evaluating the feasibility of a design early in the design phase is vital to avoid cost overruns and minimize the need for drastic design changes. For assessing crashworthiness early in the design phase, the development of low-fidelity models is an attractive as well as a viable option because these models offer both low computational cost and the capability to conduct parametric studies on the crash structure. To develop and implement such low-fidelity models, we propose to explore the analytical modeling of various energy-absorbing mechanisms, namely axial crushing, plastic bending, and joint failure. In the present study, we present the modelling of plastic bending for beam-like structural members. We also present an envisaged method applying user-defined elements to simulate plastic bending in structural members for cases where the location of plastic hinges cannot be predetermined.@en

To design crash structures for disruptive aircraft designs, it is required to have fast and accurate methods that can predict crashworthiness of aircraft structures early in the design phase. Axial crushing is one of the key energy absorbing mechanisms during a crash event. In this study, various analytical models proposed for calculation of mean crushing force for thin-walled tubular structures are compared with a database of numerical and experimental values to ascertain their accuracy. Improvements to some of the models have also been proposed. Finally a generalized model based on the studied and improved analytical models for prediction of mean crushing force for closed section thin-walled tubular structures is introduced. The generalized model demonstrates high accuracy when compared against experimental/numerical dataset as evidenced by a high coefficient of determination (R²) value of 0.97 and can therefore be used to estimate the mean crushing force for closed-section thin-walled metallic tubular structures with various cross-sectional shapes and crushing modes early in the design phase.

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As of present the Urban Air Mobility market has been dominated by fully electric aircraft. However, hydrogen vehicles have remained relatively undeveloped in this segment, also because hydrogen poses additional design complexities and uncertainties concerning crashworthiness, fuel cell cooling, and low volumetric density. Nevertheless, hydrogen might yield advantages in mission performance owing to its superior gravimetric energy density and greater sustainability when compared to batteries. In this paper, the design procedure of a four-passenger long-range hydrogen eVTOL using Multidisciplinary Analysis and Design Optimization (MADO) is presented. Using MADO, the mission energy of the eVTOL was minimized while abiding by the constraints rooting from the use of hydrogen. Based on this design, the conclusion can be made that the implementation of hydrogen eVTOLs in urban air mobility is feasible whilst taking into account constraints resulting from the use of hydrogen at the preliminary design stage. This led to an aircraft which excels at longer range due to the increased scalability of hydrogen fuel, but having a weight penalty due to auxiliary equipment which hampers its performance and results in a large fuselage and maximum takeoff weight.@en

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.@en

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.

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The Vibration Correlation Technique (VCT) is a non-destructive method to predict buckling loads for imperfection-sensitive structures. While successfully used to validate numerical models and predict experimental buckling loads, recommendations for defining the VCT experiment are scarce. Here, its sensitivity towards the number of load steps and the maximum load level measured is studied, and an uncertainty quantification of the measured frequency affecting the VCT prediction is performed First, a series of finite element (FE) models representing nominally identical cylinders, and validated by buckling experiments, are used to perform a sensitivity study. When no frequency deviations are introduced in the FE results, a positive correlation between the VCT predictions and the maximum load used for measurements is found, the number of load steps used being only relevant in reducing the errors. Introducing frequency deviations deterred the predictions correlation with the maximum load, while using more load steps reduced this influence. Second, a sensitivity study based on experimental data confirmed most of the trends previously observed using the FE results, the exception being a poor prediction sensitivity as a function of the maximum load, owing to several cylinders for which the VCT method gave predictions that progressively decreased with increasing the load.

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Modular structures come with the promise of efficient manufacturing and reduced maintenance costs. The amount of modularization is usually limited by weight efficiency, meaning that the minimum weight always lies on the most customized design, where all the structural elements are allowed to be different across the structural domain. This work studies a new design approach and structural and aeroelastic optimization of wings using truss-based modular structures. Furthermore, the work proposes a new approach to structural topology, eliminating traditional elements, such as spars and ribs, and replacing them with modular truss-based structures, which are connected by spherical joints at their ends. The topological mesh of the structures are created from the Delaunay triangulation and tessellation. The structural model is based on two types of finite elements: beam and quadrilateral elements. The beam elements are defined from consistent Timoshenko elements and the quadrilaterals are based on Mindlin-Reissner kinematics using bi-linear interpolation and reduced integration to prevent shear locking. The Doublet-Lattice Method is used to predict the unsteady subsonic aerodynamics, and the P-K method is used to compute the aeroelastic system solution. For the examples and case studies, a reference wing geometry from the FLEXOP project is used as a baseline. Two optimizations are proposed, where in all the objective functions are to minimize the structural weight of the wing and to maximize the flutter speed. The first optimization has as design variables the number of control points, or nodes, in each airfoil and the number of sections along the span. In the second optimization, the external diameters and thicknesses of each of the modular structures are individually optimized, even eliminating unnecessary ones. The results show that it is possible to obtain relatively light wings that meet the structural and aeroelastic requirements; however, the definition of the optimization parameters directly influence the mesh generation and computational cost of the optimization. Above all, modular structures have proved to be a good strategy in the design of structures for new wing concepts.@en

In this paper, an innovative design methodology is proposed to simultaneously optimize the size, layout, and number of stiffeners of a stiffened panel using a gradient-based optimizer. In the proposed method, CAD-based parameterization is used to parameterize the layout of the stiffeners. The location and orientation of each stiffener are controlled with only two layout variables. The geometric constraints to avoid overlapping and crossing of stiffeners are implicitly applied through the layout parameterization scheme, therefore no additional constraints on the grid point coordinates are required. Moreover, the CAD model is maintained throughout the optimization process, therefore the additional step of converting the optimal design back to CAD is eliminated. The layout changes are accommodated in the finite element mesh through the re-meshing technique. The number of stiffeners is controlled by allowing an optimizer to transform an existing stiffener into a ghost stiffener. Every stiffener is assigned a topology variable that can be optimized to a value of either 0 or 1 using a penalization constraint. In case the optimal value is 0 then the contribution of that stiffener in determining the mass and the stiffness of the panel is lost, and it is considered an inactive or ghost stiffener. The stiffener is considered fully active when the optimal value is 1. The sensitivities of grid point coordinates relative to layout variables are calculated analytically. The sensitivities of the structural responses relative to size, layout, and topology variables are achieved through Nastran. The effectiveness of the proposed methodology is evident from the obtained results.@en

Material properties, geometrical dimensions, and environmental conditions can greatly influence the characteristics of bistable composite laminates. In the current work, to understand how each input feature contributes to the curvatures of the stable equilibrium shapes of bistable laminates and the snap-through force to change these configurations, the correlation between these inputs and outputs is studied using a novel explainable artificial intelligence (XAI) approach called SHapley Additive exPlanations (SHAP). SHAP is employed to explain the contribution and importance of the features influencing the curvatures and the snap-through force since XAI models change the data into a form that is more convenient for users to understand and interpret. The principle of minimum energy and the Rayleigh–Ritz method is applied to obtain the responses of the bistable laminates used as the input datasets in SHAP. SHAP effectively evaluates the importance of the input variables to the parameters. The results show that the transverse thermal expansion coefficient and moisture variation have the most impact on the model’s output for the transverse curvatures and snap-through force. The eXtreme Gradient Boosting (XGBoost) and Finite Element (FM) methods are also employed to identify the feature importance and validate the theoretical approach, respectively.@en

This paper reviews analytical models proposed by Abramowicz et al.[1, 2] and Stefan et al.[3] for the axial crushing of metallic tubular structures with square and circular cross-sections. First, a database of experiments for square and circular tubes was created based on the literature. Subsequently, the predictions obtained using these analytical models were compared against the database of experiments to determine the accuracy of these analytical models. The database of experiments was also compared against some results generated using Finite-Element Method (FEM). Furthermore, the sensitivity of the analytical models to various material and geometrical parameters was studied to determine the influence of these parameters on the mean crushing force. Both models were found to be highly sensitive to the thickness of the tubular structures. It was observed that the models proposed by Abramowicz et al.[1, 2] showed better agreement with experimental results, although an over-prediction was observed for square tubular structures made of materials with a significant difference between the values of yield and ultimate stress. The model proposed by Stefan et al.[3] slightly over-predicted for square tubes and showed reasonable accuracy for circular tubes.

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In thermoplastic composite joints with a circular ultrasonic spot weld, the damage growth is located at the interface between the joined components. This means that any damage in these joints is invisible from the outside. This experimental study compares three different in-situ methods to measure the damage growth indirectly. The motivation lies in the potential benefits of using multi-spot welded joints for increased damage tolerance and the need to prove the damage arresting and damage progression behaviour for certification. The current study focused on measuring the damage in single-spot welded Single Lap Shear (SLS) joints during fatigue test with the global specimen compliance, the local out-of-plane displacement and the local strain on the surface. Digital Image Correlation (DIC) measurements were used to obtain the local quantities. The results showed that the local quantities are better suited to obtain detailed information on the damage state. The local surface strain showed more distinct features that facilitate the recognition of damage locations. The benefits and challenges of all methods are discussed as well as the difference in the level of detail, generalization and the prior knowledge necessary to obtain the damage state.

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The Flying-V aircraft concept promises better fuel-burn performance over conventional tube-and-wing configurations, integrating the passenger cabin and cargo volume into the lifting surface. However, the wing-fuselage and cockpit windows of the Flying-V are exposed to the flight direction, posing a new challenge to the design and certification of structures in terms of bird strikes. This study is a first step towards understanding the dynamic load path and contribution of each structural element on the bird strike resistance of the Flying-V leading-edge structures. The objective is to propose a building block approach to design the Flying-V's leading edge bird strike crashworthiness that complies with the EASA's certification CS25.631 using a 4lb bird impacted at a sea level cruising speed of 70 m/s. An additional requirement by the authors is to keep the structure within the elastic deformation during the impact of a 4lb bird to avoid the need for repairs in the Flying-V fuselage. Plasticity generated in the structure is regarded as damage and is used as a comparative parameter. At the highest building block level, a sensitivity analysis is performed to identify the effect of the thickness of each structural element on the plasticity and weight of the leading-edge structures. The trends are used to modify the baseline design and achieve a reduction of 80% of the plastic energy. The critical case of a 133 m/s impact of a 4lb bird at the cruise altitude of 37000 ft is also evaluated, and the results show penetration.

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Variable-angle filament-wound (VAFW) cylinders are herein optimized for minimum mass under manufacturing constraints, and for various design loads. A design parameterization based on a second-order polynomial variation of the tow winding angle along the axial direction of the cylinders is utilized to explore the nonlinear steering-thickness dependency in VAFW structures, whereby the thickness becomes a function of the filament steering angle. Particle swarm optimization coupled with three Kriging-based metamodels is used to find the optimum designs. A single-curvature Bogner–Fox–Schmit–Castro finite element is formulated to accurately and efficiently represent the variable stiffness properties of the shells, and verifications are performed using a general purpose plate element. Alongside the main optimization studies, a vast analysis of the design space is performed using the metamodels, showing a gap in the design space for the buckling strength that is confirmed by genetic algorithm optimizations. Extreme lightweight while buckling-resistant designs are reached, along with non-conventional optimum layouts thanks to the high degree of thickness build-up tailoring.

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Ultrasonic spot welding is a joining technique for thermoplastic composites with great potential regarding processing speed and cost. To investigate the damage tolerance and possible inherent damage arresting behavior of multi-spot welded joints, a technique is necessary to measure damage growth in the joints under cyclic loading. Visual inspection is not possible because the damage is not located on the outside surface and conventional techniques such as C-scan are not practical during a fatigue test because the specimen would have to be removed from the setup. This paper details a methodology for quantifying damage growth rates in singlespot welded joints using surface strain measurements made by Digital Image Correlation. This represents the first step towards developing a methodology for quantifying damage progression behavior in complex multi-spot welded joints. @en

The electric aircraft industry is starting to gain traction mainly due to the growing specific energy capacity of new batteries. Within this industry electric vertical takeoff and landing (eVTOL) aircraft serve the urban and regional air mobility market, requiring less infrastructure investments such as large airports, due to their vertical takeoff and landing capabilities. The present study investigates the preliminary performance evaluation of a tandem wing long-rage eVTOL concept. First, the power and energy consumption of a typical mission with a range of 300 km is estimated, consisting of: vertical takeoff, climb, cruise, loiter, descent, and vertical landing. The takeoff, climb, descend and landing phases are simulated numerically. The climb performance is evaluated in vertical and horizontal configuration. The flight paths were optimized aiming at a minimum energy consumption, showing very high climb rates due to the large power needed for vertical takeoff. To quantify the effect of different payloads on the aircraft range, a payload range diagram is constructed. Next, a sensitivity analysis is performed with respect to some operational parameters, relating the range and mission block speed to cruising altitude, cruise speed and wind speed. Finding the sensitivity of the flight range to these input parameters allows one to adequately select the safety margins for a given battery capacity. Finally, a conclusion and recommendation for next studies is given.@en