In the context of Smoothed Particle Hydrodynamics (SPH) simulations of solid structures, the initial distribution of particles is of critical importance in ensuring both numerical stability and physical accuracy. Conventional particle distributions, which are typically based on Cartesian lattices due to their inherent regularity, often introduce preferential directions that cause spurious anisotropic stress patterns. This issue is especially evident in plate-like structures that are subjected to dynamic loading, where stress waves may propagate along grid-aligned paths in an artificial manner. This work presents a novel, readily implementable approach for initializing SPH particles in three-dimensional plate geometries. The approach under consideration is inspired by the logic of lamination stacking sequences used in composite materials design. The proposed method generates quasi-isotropic particle distributions by systematically alternating local orientation angles, thereby mimicking the isotropizing effect of laminate lay-ups. This approach has been demonstrated to reduce numerical anisotropy while circumventing the complexity typically associated with advanced pre-processing tools or iterative re-meshing strategies. Indeed, the proposed approach necessitates minimal computational overhead and does not rely on external meshing code, thus facilitating seamless integration into existing commercial SPH workflows. The simulations presented herein were executed using the LS-Dyna software. The validity of the approach is established through a combination of alternative numerical simulations, analytical solutions, and experimental tests involving wave propagation and impact scenarios in plates. The findings indicate a substantial decrease in directionally biased stress and vibration fields in comparison to conventional grid-based particle arrangements while maintaining constant computational cost. The findings obtained from this study align more closely with the experimental and analytical results, thereby enhancing the overall robustness of the SPH simulations for solid mechanics applications involving thin structures, particularly in scenarios where isotropic wave behavior is critical.

A numerical and experimental investigation is carried out in this study to evaluate the crashworthiness behavior, the energy-absorbing parameters, and the failure mode of thermoplastic composite energy absorbers under axial loading. The energy absorbers are thin-walled circular tubes made of woven polyphenylene sulfide carbon composite and have a bevel trigger on the top. Finite element analysis are conducted to predict the structural behavior of the tubes. To validate the numerical model, four specimens are manufactured and tested under an axial compression load. During the tests, the load and displacement are measured by a load cell, the evolution of the longitudinal strains is captured by digital image correlation, and the progression of the failure is recorded by a high speed camera. The tubes show a progressive failure mode, with delamination between the middle plies. A stable damage propagation is observed throughout the tests, where the bevel trigger plays an important role in increasing the stability and failure progression of the thin-walled tubes. The test results are compared to the numerical prediction, with good agreement for both crashworthiness parameters and delamination behavior. The thermoplastic composite energy absorbers achieved specific energy absorption values of up to 70 kJ/kg, indicating an adequate crashworthiness performance.

Aerospace structures are thin-walled shell structures whose load-bearing capacity is often limited by buckling phenomena. The application of variable angle tow (VAT) composites allows to increase the buckling resistance by tailoring the fiber paths. Fiber placement technologies such as automated fiber placement and continuous tow shearing for VAT composites have been improved enormously in recent years. However, induced material and geometric uncertainties from the manufacturing process have a major influence on the structural performance. The paper focuses on appropriate uncertainty quantification for VAT composites, selecting various uncertainty models based on available data. Different uncertainty models are introduced to quantify the natural variability (aleatory uncertainty) and lack of knowledge (epistemic uncertainty). An uncertain fiber path definition with fuzzy variables is presented to model fiber path deviations. In addition, geometric imperfections are modeled as random fields and as Fourier series to analyze the imperfection sensitivity. Based on this, a design optimization of VAT composites is performed in presence of uncertainties. The introduced methods are demonstrated on a VAT composite panel and a cylindrical shell. Geometric imperfection measurements are provided for the VAT composite cylindrical shell to validate the approach based on experimental results. This paper contributes to a better understanding of uncertainties of tow-steered structures. The results reveal a potential conflict in optimizing the robustness measures (e.g. minimizing the variation of the buckling loads) and enhancing the performance measures (e.g. maximizing the mean value of the buckling loads) visualized by Pareto fronts. This emphasizes the need to consider uncertainties in a design process of VAT composite shells based on multi-objective optimization.

Modern aircraft structures consist of a multi-material mix, dominated by high-performance composites, but also including metal alloys, e.g., for load introduction parts. This experimental research investigates the static and fatigue strength of pinned hybrid titanium-composite single-lap-shear joints. The Ti6Al4V adherend is manufactured by laser powder bed fusion. The joining is done by co-curing with the carbon fiber reinforced polymer adherend. The static tests focus on damage initiation and ultimate load, and are benchmarked by identical joints without pins. The fatigue tests focus on damage initiation and propagation. Digital image correlation is used for damage monitoring. Results show, (i) a high ratio of static ultimate failure to damage initiation load, (ii) early low-cycle damage initiation but then long high-cycle fatigue life until failure, and (iii) the crack stopping effect of the interlocking pins. Furthermore, visual joint failure analysis reveals a variety of damage modes, suggesting comprehensive testing and proper pin design.

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.

Composite interfaces, particularly in joints, play a critical role in the damage resistance and durability of structures for aeronautics applications. This study investigates the use of carbon nanotube (CNT) interleaves for the co-cured joining of composite parts and its effects on fracture toughness and damage progression at the co-cured interface. CNT dispersed in a thermoset resin and partially cured into thin film interleaves at three weight concentrations (0.5% wt., 1% wt., and 2% wt.) of two discrete thicknesses (200 µ and 500 µ) were investigated. The fracture toughness of the co-cured interface with CNT interleaves in mode I and mode II loading conditions was determined through double cantilever beam and end-notched flexure tests, respectively. The results reveal that despite the occurrence of a stick–slip damage progression in mode I, the crack arrest mechanisms and forces are surprisingly predictable based on interleaf thickness. At CNT concentrations above 1% wt., there was no significant enhancement of toughening, and interleaf thickness controlled the crack arrest loads. Damage delay also occurred at the interface due to the activation of multiscale toughening mechanisms. Toughening in mode II was dominated by CNT pullout resistance and, therefore, yielded up to six-fold improvement in critical fracture toughness. These insights offer significant potential for designing joints with nanocomposites for aerospace applications, incorporating inherent toughening and damage delay mechanisms.

Composite single-lap shear joints made from virgin plies and recycled core material are manufactured via induction and conduction welding using T300/polyphenylene sulfide (T300/PPS) as well as T700/low-melt polyaryletherketone (T700/LM-PAEK). The specimens are tested in quasi-static conditions to evaluate their mechanical performance and damage growth. Digital image correlation and high-speed cameras are used to capture the specimen behavior until after failure. While joints with recycled core material show a lower load-transferring capacity than their virgin counterparts (reduction of 13.8% for T300/PPS and 41.2% for T700/LM-PAEK), they are nonetheless an appealing option for applications where sustainability is a priority. Damage in virgin thermoplastic welded single-lap shear joints grows along the weld line. Conversely, specimens containing recycled core material may also experience delaminations between the core and the virgin outer plies. This suggests that thermoplastic welding can create interfaces with higher fracture toughness properties than those achieved during the consolidation of the base laminates.

Welded omega-stiffened panels made of thermoplastic carbon composite with initial damage in the conduction welded joint are analysed and tested to investigate the damage tolerance in post-buckling. Finite element analyses are performed, using the virtual crack closure technique to investigate skin-stringer separation for both the pristine welded joint and joints with initial damage. A sensitivity study is executed for the initial damage size and location with different geometrical imperfections. Four omega-stiffened panels are tested, of which three have initial damage consisting of a foil at the welded skin-stringer interface. During the test, digital image correlation is used to measure the panels’ deformation to determine the evolution of the buckling shape and the interaction with the initial damage. A high-speed camera is placed on the stringer side of the panel to capture the final failure. The panels fail in post-buckling when skin-stringer separation occurs, starting from the initial damage. The finite element analysis is able to predict the overall structural behaviour well, with conservative failure load predictions for panels with initial damage in the middle stringer. Although the initial buckling shape is predicted well, the buckling shape evolution at higher loads is difficult to predict.

This research proposes a computationally efficient methodology using a Constrained Variational Asymptotic Method (C-VAM) for non-linear buckling analysis on a hat-stringer panel with delamination defects. Starting with the geometrically non-linear kinematics, the VAM procedure reduces the three-dimensional (3-D) strain energy functional to an analogous 2-D plate model and evaluates the closed form warping solutions. Utilising the resulting warping solutions and recovery relations for the skin and the stringer, displacement continuity at the three-dimensional level is enforced between the stringer and the skin based on the pristine and delaminated interface regions. Consequently, the constrained matrices obtained from C-VAM is incorporated into an in-house developed non-linear finite element framework. Using the developed formulation, a stiffened panel with delamination of 40 mm between the stringer and the skin is analysed under compression. The results have been validated locally and globally, employing experimental data and 3-D finite element analysis (FEA). Experiments are carried out on the co-cured panel by applying quasi-static loading with displacement-controlled conditions, and 3-D FEA is carried out in Abaqus. Load-response plots have been obtained to validate the results at the global level, and they are in excellent agreement with experiments and 3-D FEA. Subsequently, out-of-plane displacement contour plots are obtained; the number of half waves and wave intensity in 3-D FEA and C-VAM are comparable, although there are minor differences compared to the experimental findings. The proposed framework is shown to be computationally efficient by over 55% as compared to 3-D FEA for performing non-linear buckling analysis on the stiffened composite structure considered in the current work.

Two curved thermoplastic composite multi-stringer panels with roller boundary conditions are analysed and tested to investigate the buckling and failure behaviour. The panels are made of AS4D/PEKK-FC thermoplastic composite, have five stringers with an angled cap on the side and are joined to the skin with the short-fibre reinforced butt-joint technique. The panels have a roller attached to each loading edge, approximating simply-supported boundary conditions to apply compression and bending. One panel has an initial damage representing a barely visible impact damage in one of the stringer butt-joints, and one panel is in pristine condition. Finite element analyses are performed to predict the structural behaviour, and different approximations of the roller boundary conditions are compared. The analyses include material damage initiation and evolution. The out-of-plane displacement of the panels is measured by digital image correlation, and failure is captured with high-speed cameras. The panels fail in a sudden manner when the cap separates from the web, followed by web failure and skin–stringer separation in the butt-joint. The numerical analysis predicts the overall structural behaviour but cannot capture well the sudden panel collapse due to material damage.

This paper presents a numerical approach for investigating fatigue delamination propagation in composite stiffened panels loaded in compression in the post-buckling field. These components are widely utilized in aerospace structures due to their lightweight and high-strength properties. However, fatigue-induced damage, particularly delamination at the skin–stringer interface, poses a significant challenge. The proposed numerical approach, called the “Min–Max Load Approach”, allows for the calculation of the local stress ratio in a single finite element analysis. It represents the ratio between the minimum and maximum values of the stress along the delamination front, enabling accurate evaluation of the crack growth rate. The methodology is applied here in conjunction with the cohesive zone model technique to evaluate the post-buckling fatigue behavior of a composite single-stringer specimen with an initial delamination. Comparisons with experimental data validate the predictive capabilities of the proposed approach.

In this research, conduction welded C-struts, part of a thermoplastic composite fuselage designed and manufactured in the framework of the Clean Sky 2 STUNNING project, are investigated. Five specimens made of two C-section profiles are manufactured and welded using conduction welding in three different configurations with variations in the direction and distance of the two welded joints. Preliminary numerical analysis using the virtual crack closure technique are conducted to obtain an initial evaluation of the specimens behavior, in preparation of the tests. Experiments are performed under quasi-static loading conditions to measure the strength of the welds. Comparisons with the preliminary numerical analyses show a good agreement in terms of the predicted maximum load, while a clear difference is observed in the initial stiffness, due to the compliance of the support structure. The numerical model is updated, leading to results that closely match the experimental behavior. For all the analyzed specimens, the separation occurs suddenly and no signs of propagation are observed. Experimental and numerical data show no relevant difference in the joint strength among the different conduction welding configurations.

To improve the crashworthiness design of composite aircraft structures, analytical models are useful to enable engineers to have a fundamental understanding of the influence of the design variables. As such, during the preliminary design, this knowledge can be exploited, rather than needing to alter an already mature design in a later phase. Accordingly, an analytical model is derived which allows the determination of the mean crushing load and the energy absorption of composite absorbers. The analytical model allows one to accurately predict the mean crushing load of square tube absorbers while altering their side length and thickness. Moreover, the different terms in the analytical model show that the out-of-plane shearing of the material is the major energy dissipating phenomenon. The composite absorbers are then incorporated into a finite element model of the keel section of the thermoplastic composite subfloor of a fuselage demonstrator developed by the Clean Sky 2 STUNNING project. The analytical model facilitates the estimation of the energy absorption and crash load of the fuselage section augmented with the energy absorbers. In this way, during the preliminary design, the absorbers of the fuselage can be designed concurrently for the static loads and for the crash loading, leading to a more efficient design.

Traditionally, launch vehicles are constructed with a series of buckling-prone thin-walled cylindrical and conical shells, in which the buckling behavior of these shells has been well studied and buckling design guidance exists. Conical-cylindrical shell geometry is now being utilized for launch-vehicle stage adapters and payload adapters due to advances in manufacturing and numerical techniques, but there is no available buckling design guidance for this nontraditional combined geometry. In order to provide design recommendations, the buckling behavior and imperfection sensitivity of conical-cylindrical shells and how it differs from the conical and cylindrical components needs to be better understood. From this premise, it is possible to investigate whether or not the buckling knockdown factor guidelines for conical and cylindrical shells outlined in NASA SP-8019 and NASA SP-8007, respectively, are still applicable. The results in this paper will show that the current recommendations are not appropriate in some cases. In addition, it was observed that the large rotations and displacements near the transition between the cone and cylinder can have a larger effect on the buckling load than the presence of radial imperfections for conical-cylindrical shells, which is different than for conical or cylindrical shells. More interesting is the fact that design modifications to increase the buckling capability of a conical-cylindrical shell such as adding reinforcement, which may add mass, will make the shell more sensitive to imperfections. The increased imperfection sensitivity may negate the increase in buckling capability that was thought to be achievable. In the end, it may be more beneficial to design a conical-cylindrical shell in which the buckling behavior is dominated by the more predictable geometric nonlinearity, which may lead to an overall lower buckling load, but a lower knockdown factor may be possible since it will not be as sensitive to the lessknown radial imperfections.

Conical-cylindrical shells are common geometries in launch-vehicle structures as stage adapters and payload adapters, and they are susceptible to buckling due to their large radius-to-thickness ratios. Buckling design guidance is available but it is limited for conical and cylindrical shells. There is no available buckling design guidance for conical-cylindrical shells. This paper presents the validation of two finite element models used to successfully predict the buckling behavior of a composite conical-cylindrical shell with and without reinforcement tested in two separate campaigns. The laminate design for the first test campaign consisted of a quasi-isotropic layup. For the second test campaign, additional composite plies were applied to reinforce the transition region of the original laminate. The work presented demonstrates the ability to predict the buckling behavior of a composite conical-cylindrical shells with two different designs, which may aid in creating buckling design guidance for conical-cylindrical shells. Additionally, this paper shows that there is no appreciable benefit to adding reinforcement to the transition region if the intent is to increase the buckling load, due to the fact reinforcement brings increased buckling imperfection sensitivity to the shell.

This paper presents the work on six single-stringer specimens manufactured using the card-sliding technique with non-crimp fabrics and adopting a Double-Double (DD) stacking sequence. These specimens, representative of sub-structure level components, are used to investigate post-buckling and failure in aerospace structures. Two specimens maintain a constant thickness cross-section, while four are tapered, two of which incorporate a Teflon insert in the stringer flange. All specimens are tested under compression loading conditions, inducing skin buckling, skin-stringer separation, and eventual collapse. Numerical simulations are validated by experimental results and serve to analyze the specimens behavior and the failure mode. The load versus displacement curves of both experimental tests and Finite Element Method (FEM) analyses are compared, along with the out-of-plane displacement field. Subsequently, the observed failure modes are discussed, focusing on the various mechanisms that occurred and considering the impact of flanges and stiffener tapering. Both the FEM simulations and experimental tests demonstrate good agreement, with the flanges tapering revealing notable results. This offers promising evidence of a viable solution to optimize aeronautical structures and enhance resistance to skin-stringer separation.

Thermoplastic composite welding is a key technology that can help to make the aviation industry more sustainable, while at the same time enable high-volume production and cost-efficient manufacturing. In this work, characterization, testing and analysis of thermoplastic composite conduction welded joints is performed while accounting for the influence of the manufacturing process. Test specimens are designed from welds of a half a meter long welding tool that is developed to weld the stiffened structures of the next-generation thermoplastic composite fuselage. In the design, special attention is paid to the weldability of the laminates, while ensuring fracture occurs only at the welded interface. Two specimen configurations are evaluated for the Double Cantilever Beam and End-Notched Flexure characterization tests. Moreover, Single Lap-Shear specimens are tested in tension and in three-point-bending. Finally, the characterized material properties are introduced in finite element analyses to demonstrate that the cohesive zone modeling approach can be used to conservatively predict the strength of these welded joints. New insights are obtained in the relation between the manufacturing process, the quality of the weld and the mechanical properties of the joints, which are significantly different compared to autoclave consolidated composites.

Thermoplastic composite three-stringer panels with omega stiffeners and conduction welded joints are designed, analysed and tested until final failure to investigate the performance of the welded joint in post-buckling. The three-stringer panels are designed to be structurally representative of the fuselage demonstrator of the Clean Sky 2 project STUNNING. A simplified model of the fuselage keel section is analysed by finite element analysis, using the virtual crack closure technique to model skin-stringer separation of the welded joint. The post-buckling and skin-stringer separation behaviour of the fuselage section is then adopted as the reference for the design of the three-stringer panels. Two panels are then tested. The test setup utilises digital image correlation to measure the deformation of the panels, and a high-speed camera to capture the final failure mode. The panels failed in post-buckling due to the separation of the middle stringer, with unstable separation growth followed by separation of the outer stringers and then stringer fracture. The numerical analysis of the panels, with geometrical imperfections included, is able to predict the structural behaviour accurately, with only minor differences in buckling shape and separation behaviour.

This study aims at better understanding the damage tolerance of stiffened composite panels subjected to fatigue loads in the post-buckling regime. Ten single-stringer hat-stiffened specimens with an initial delamination between the skin and the stringer foot were manufactured, and then tested under quasi-static and fatigue loads in post-buckling conditions, with different load levels and load ratios. The tests were monitored with digital image correlation and an ultrasonic system, providing data on the displacements, strains, and extension of the delamination length. The quasi-static results showed that the delamination onset, when the initial delamination begins propagating, occurred at loads over twice the buckling load, while collapse occurred for values almost 20% higher than the delamination onset. During fatigue testing at load levels below the delamination onset, the specimens were able to sustain 150000 cycles and then, when tested statically after fatigue, the average load at collapse was reduced by less than 10% with respect to the quasi-static benchmark. When the maximum load during fatigue was increased to 5% over the delamination onset load, the specimens still withstood between 8000 and 16500 cycles before collapse, depending on the load ratio. It was also seen that for tests at the same load level, the specimens with high load ratio had a slower damage propagation.

Launch vehicle structures, such as payload adapters and interstages, are increasingly designed and constructed using composite materials due to their high stiffness- and strength-to-weight ratios. Therefore, it is important to develop a validated finite element modeling methodology for designing and analyzing composite launch-vehicle shell structures. This can be achieved, in part, by correlating high-fidelity numerical models with test data. Buckling is often an important failure mode for cylindrical shells, and the buckling response of such structures is also often quite sensitive to imperfections in geometry and loading. Hence, it is crucial to understand the model parameters and details required to accurately predict the buckling load and behavior of composite cylindrical shells, especially if the shell is buckling critical. The inclusion of as-built features, such as radial imperfections, thickness variations, and loading imperfections can help improve the correlation between test and analysis. To demonstrate such an approach, a validated modeling methodology that was used to predict the buckling behavior of a scaled component for a launch-vehicle-like structure is presented, and results from the model are compared with experimental results. The modeling approach presented herein was used to successfully predict the buckling behavior.