The study presents deflation constraints that enable a systematic exploration of the design space during the design of composite structures. By incorporating the deflation constraints, gradient-based optimizers become able to find multiple local optima over the design space. The study presents the idea behind deflation using a simple sine function, where all roots within an interval can be systematically found. Next, the novel deflation constraints are presented: hypersphere, hypercube and hypercuboid; consisting of a combination of Gaussian and sigmoid functions. As a test case, the developed constraints are applied to the optimization of a double-cosine function, where all the 13 minima points could be found with 24 deflation constraints. It is shown that a new optimum is encountered after each deflation constraint is added, with the optimization subsequently re-started from the same initial point, or resumed from the last found minimum, being the latter the recommended approach. The new deflation constraints are then used in heuristic-based direct search methods, where a genetic algorithm optimizer is able to find new optimum individuals for straight-fiber composites. Lastly, variable-stiffness composites were designed with the deflation constraints applied to the multimodal optimization problem of recovering fiber orientations from a set of optimum lamination parameters.

An analytical model for predicting the displacement field in composite single-lap shear joints with zero-thickness interfaces is developed and verified with numerical simulations. This two-dimensional model imposes no restrictions on the composite layup or the dimensions of the adherends. It closely aligns with the displacement field predicted by numerical simulations, provided that the assumptions of small deformations and plane strain are satisfied. Small discrepancies are observed near the overlap region because the stress-free boundary condition at the overlap ends is not satisfied exactly. Consequently, the joint stiffness is slightly overestimated compared to the numerical simulations. Nonetheless, the analytical model can serve as a useful tool for providing input for more detailed analyses of single-lap shear joints, for example for determining the interlaminar stress field at the interface between the two adherends.

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 investigates 3-point bending failure of five different types of GLARE laminates (2A, 2B, 3, 4A and 4B). 73 configurations (419 specimens), with different stacking sequences and aluminum layer thicknesses are tested. Failure mechanisms, effect of stacking sequence, effect of aluminum rolling direction, effect of displacement rate and energy absorption are analyzed. Configurations with predominantly 0°glass fiber layers fail with delamination as the major failure mode, while configurations with predominantly 90°glass fiber layers fail with central cracking as the major failure mode. GLARE 3, with 1:1 ratio of 0°and 90°fibers, fail with an equal mix of delamination and central cracking. A semi-analytical framework that can be used to predict the force versus displacement curve for central cracking failure is proposed and validated.

Post-buckling of thin-walled aeronautical structures induces failure modes related to skin-stiffener separation that require three-dimensional large deformation analyses for an accurate numerical prediction. Conventional finite elements are capable of solving such analyses, but with high associated computational costs, being therefore more utilized for the simulation of smaller structural components, or even restricted to perform virtual testing at coupon-level models. In this paper, a geometrically nonlinear reduced-order method using a hybrid-stress solid-shell formulation is proposed for large deformation analysis of thin-walled structures. Current reduced-order methods are mainly applicable to buckling problems, considering only the out-of-plane deformation. Furthermore, existing displacement-based reduced models involve a computationally expensive fourth-order tensor obtained with the higher-order strain energy variations. Here, a reduced-order model with only one degree of freedom is constructed for both in-plane and out-of-plane large deformation problems. It is shown that, with the hybrid-stress formulation, the constructional efficiency of the reduced system is largely improved by zeroing the fourth-order strain energy variation using the two-field Hellinger–Reissner variational principle, followed by a condensation of the stress terms that lead to a third-order approximation of the equilibrium equation. The nonlinear predictor solved by the reduced-order model can be corrected when its numerical accuracy is not satisfactory during the path-following analysis. A simple plate, a honeycomb cell with negative Poisson ratio, and a swept-back wing structure; are used as numerical examples to verify that the proposed method enables a superior path-following capability for the three-dimensional analysis of thin-walled structures undergoing large deflection, large rotation and large strains. Furthermore, an experimental validation of the proposed method is presented using a variable-thickness plate with mixed composite-metallic materials, undergoing large out-of-plane deflection.

This study presents a Bayesian Optimisation (BO) framework for the mass minimisation of variable-stiffness (VS) composite cylinders under multiple buckling constraints, incorporating manufacturing limitations derived from filament winding processes. A computationally efficient single-curvature finite element model is used to evaluate the linear buckling response of multilayered shells. BO simultaneously optimises fibre paths, number of layers, and thickness distribution, achieving comparable or improved performance relative to a Genetic Algorithm (GA) while reducing simulation time by up to 70 %. Across most design loads, BO delivers structurally efficient solutions with smooth thickness transitions and local stiffness tailoring. Although GA outperformed BO in the highest load case in terms of weight and buckling capacity, BO retained competitive performance and demonstrated higher modal richness. Buckling mode analyses revealed that BO designs support mixed-mode instabilities with greater circumferential complexity, enhancing structural adaptability. In contrast, GA designs exhibited more uniform fibre paths and axial-dominated modes, reflecting conservative reinforcement strategies. These findings highlight the capability of BO to exploit complex design spaces more effectively, offering a scalable and data-efficient alternative to traditional optimisation methods. The proposed framework is particularly well suited for high-fidelity, simulation-driven design of advanced composite structures where computational cost and manufacturability are critical constraints.

This paper presents a novel stacking sequence design framework for composite laminates, extending the recently established Double-Double (DD) laminate theory developed by Stephen Tsai. By introducing and evaluating n-Double (n-D) layouts, ranging from single-angle (D) sequences to multi-directional designs such as DD, DDD, and DDDD; this study expands the design space for laminated composite structures, enabling improved trade-offs between buckling resistance and failure strength. A genetic algorithm (GA) is used to optimise the stacking sequences of 48- and 64-layer graphite/epoxy laminates under biaxial and uniaxial compressive loading across a range of geometric aspect ratios. Results show that while GA-based free-angle designs yield the highest buckling loads, structured DDDD configurations achieve similar or superior failure performance and maintain a high level of robustness across geometric variations. The DDDD designs also approximate GA-level buckling performance, with significantly improved regularity and manufacturability. These findings highlight the benefit of generalising Tsai’s DD theory towards n-D layouts, providing a systematic, practical, and high-performing approach to laminate optimisation.

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.

Traditional aircraft crashworthiness assessments typically involve vertical drop tests on a specific fuselage segment to simulate landing impacts. However, the Flying-V’s unique geometry and mass distribution challenge the suitability of such simplified tests. Previous studies have focused solely on the wing-fuselage region, neglecting the central and outboard areas. This research aims to develop a methodology for a more elaborated crashworthiness assessment, particularly for unconventional aircraft such as the Flying-V. It proposes simplified modelling approaches to capture essential kinematics without detailing the entire aircraft. A newly introduced reduced modelling technique, leveraging moments of inertia, optimizes vertical drop tests and reduces simulation time. However, limitations arise when evaluating more intricate crash scenarios, prompting the proposal of a submodelling technique. While the submodelling technique effectively captures the engine section dynamics, comprehensive finite element modelling remains essential for addressing complex scenarios.

The present study introduces an automated multidisciplinary optimization (MDO) workflow that, for the first time, couples an explicit dynamic bird strike analysis with a post-impact static stress check. This joint problem is solved during preliminary wing sizing by integrating batch Bayesian optimization on Kriging surrogates with a variance-based variable screening procedure. The optimization problem comprises 19 thickness design variables and two highly non-linear constraints, imposing a maximum leading edge penetration and a maximum post-impact front spar stress while minimizing wing mass. The workflow is demonstrated on a five-bay metallic wing segment, yielding a 43% weight saving over the best-performing design during initial data generation while respecting CS 25.631 crashworthiness limits. Results demonstrated substantial computational savings by variable screening and highlighted the necessity of the stress constraint, as designs satisfying only the penetration depth requirement could still experience critical post-impact stress levels.

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.

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.

The study presents deflation constraints that enable a systematic exploration of the design space during the design of composite structures. By incorporating the deflation constraints, gradient-based optimizers become able to find multiple local optima over the design space. The study presents the idea behind deflation using a simple sine function, where all roots within an interval can be systematically found. Next, the novel deflation constraints are presented: hypersphere, hypercube and hypercuboid; consisting of a combination of Gaussian and sigmoid functions. As a test case, the developed constraints are applied to the optimization of a double-cosine function, where all the 13 minima points could be found with 24 deflation constraints. It is shown that a new optimum is encountered after each deflation constraint is added, with the optimization subsequently re-started from the same initial point, or resumed from the last found minimum, being the latter the recommended approach. The new deflation constraints are then used in heuristic-based direct search methods, where a genetic algorithm optimizer is able to find new optimum individuals for straight-fiber composites. Lastly, variable-stiffness composites were designed with the deflation constraints applied to the multimodal optimization problem of recovering fiber orientations from a set of optimum lamination parameters.

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.

Crashworthiness of the Flying-V Aircraft Concept with VerticalDrop Test SimulationsM. Desiderio, M.J. Schuurman, R.C. Alderliesten and S.G.P. Castro∗.Department of Aerospace Structures and Materials, Faculty of Aerospace Engineering, Delft University of Technology,Kluyverweg Street No. 1, 2629HS, Delft, The Netherlands.The following presents a preliminary assessment on the crash characteristics of the Flying-Vaircraft, an unconventional configuration consisting of a V-shaped flying wing with an oval cabincross section, currently being actively researched at TU Delft. Successively, the preliminaryassessment is carried out by means of design of experiments, where four crash structureconcepts are defined and evaluated. Virtual drop tests of the Flying-V typical fuselage sectionare performed while measuring the energy absorption of the fuselage, and the dynamic responseindex (DRI) and selected locations. The finite element modeling scheme is validated using theFokker F-28 Fellowship typical section, for which physical drop test data is available. Whilea crashworthy typical section for the Flying-V could not be designed, it has been found thata conventional crash concept with a total of four oblique floor struts is able to absorb 72%of the total kinetic energy, with a DRI reaching 18.2 units. A sensitivity analysis shows thatthe bending stiffness of the frames has a critical role in the crashworthiness of the Flying-V,due to the increase in rigidity following pressurization loads of the oval fuselage section andthat, additionally, the structural simplifications applied in the context of the research likelyrendered the results overly-conservative. A 16% frame thickness reduction resulted in a DRIof 16.2 units, just above the 16 units typically required by regulators. Recommendations forfuture work include a structural sizing optimization where requirements from crashworthinessand airworthiness can be evaluated simultaneously as design constraints, enabling design forcrashworthiness at the preliminary design.

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.

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.

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.

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.

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.