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Over the past 25 years, interest in thermoplastic composites in aircraft has steadily increased. Combining winding and laser-assisted tape placement is a promising method to manufacture thermoplastic structures using in-situ consolidation, as shown recently by manufacturing a variable stiffness, unitized, integrated-stiffener thermoplastic wingbox at the University of Limerick. The corner regions are a critical point of the structure and require in-depth characterization studies, for example by unfolding L-shaped samples in a 4-point bend test. In this work, samples with radii varying from 2 to 10 mm were manufactured and tested. Two manufacturing parameters were varied: the rotational speed and acceleration of the tool. Test data show that decreasing the radius increases the corner strength, but an optimum radius exists to withstand a maximum unfolding force/moment. In addition, the slowest deposition rate with least acceleration of the head used during manufacturing lead to the highest corner strength for the same radius.

This article responds to increasing public and academic discourses on social innovation, which often rest on the assumption that social innovation can drive societal change and empower actors to deal with societal challenges and a retreating welfare state. In order to scrutinise this assumption, this article proposes a set of concepts to study the dynamics of transformative social innovation and underlying processes of multi-actor (dis)empowerment.First, the concept of transformative social innovation is unpacked by proposing four foundational concepts to help distinguish between different pertinent ‘shades’ of change and innovation: 1) social innovation, (2) system innovation, (3) game-changers, and (4) narratives of change. These concepts, invoking insights from transitions studies and social innovations literature, are used to construct a conceptual account of how transformative social innovation emerges as a co-evolutionary interaction between diverse shades of change andinnovation. Second, the paper critically discusses the dialectic nature of multi-actor (dis)empowerment that underlies such processes of change and innovation. The paper then demonstrates how the conceptualisations areapplied to three empirical case-studies of transformative social innovation: Impact Hub, Time Banks and Credit Unions. In the conclusion we synthesise how the concepts and the empirical examples help to understand contemporary shifts in societal power relations and the changing role of the welfare state.

Due to high specific strength and stiffness ratios, composite materials are widely used in industries where minimising structural mass is of paramount importance, such as the aerospace sector. However, designing lightweight composite laminates is challenging due to the large number of discrete design variables involved, e.g. ply numbers and fibre orientations which are usually restricted to a set of predefined values. The number of possible laminate solutions grows exponentially with increasing ply count, quickly rendering complete enumeration impossible. Current mixed-integer programming techniques for designing composite laminates with many plies either exhibit insufficient design space exploration, or demand inconceivable computational effort. As a result, laminates often have sub-optimal properties, e.g. excessive weight. We propose a novel deterministic optimiser for finding the lay-up of composite laminates with many plies. Lay-ups must match desired stiffness properties called Lamination Parameters (LPs). The design-space is explored by a procedure that uses beam search to promote fast convergence towards optimal or near-optimal solutions. Additionally, the optimality of the design solutions is improved by local searches which are performed after a first guess of the stacking sequences. The proposed optimiser is shown to retrieve symmetric laminate lay-ups with as many as 300 plies within a few minutes.

peer-reviewed Elastic boundary conditions play an important role in the buckling analysis of cylinders under compressive loading. These structures are used widely in aerospace applications and are highly sensitive to geometrical, material, loading, and boundary imperfections. In fact, the presence of these imperfections can lead to catastrophic failure. In 1968, NASA reported relations for obtaining the Knockdown Factor (KDF) based on an empirical method that is valid for isotropic and orthotropic materials; however, these relations do not consider the effect of elastic boundaries that can lead to highly conservative values of KDF. In design practice, a universal KDF of 0.65 has been used for recent designs by NASA, which may not be applicable to new types of structural configuration with different loading and boundary conditions. Therefore, there is a need for robust design factors for future designs which reduce the dependency on testing during preliminary design phases and speeds up the product development process. The availability of up‐to‐date and different KDF expressions for different structural configurations would help engineers to design lighter structures with improved load carrying capacity and reliability. The main objective of this work is to identify the buckling load sensitivity of cylindrical shells due to their boundary conditions and develop KDF relations considering elastic boundaries. To achieve this goal, the effect of axial, radial and tangential support stiffness on a quasi‐isotropic cylinder under axial compression is investigated. A data‐driven design approach is used to develop new KDF empirical relations for a quasi‐isotropic cylinder on different elastic foundations. The accuracy of these relations is within 5% for any elastic foundation considered.

The design of thin-walled cylinders in axial compression is limited by sensitivity to geometric imperfections. This paper focuses on reducing this imperfection sensitivity from a design perspective. By using variable-angle composites, the load paths are tailored to reduce the effective area over which imperfections can initiate buckling. Continuous Tow Shearing (CTS) is one such variable-angle manufacturing technique. It does not cause manufacturing defects associated with Automated Fibre Placement and entails a fibre angle-thickness coupling that results in a local thickness build-up—used as a design feature to embed stiffeners in the cylinder. Nonlinear finite element models with seeded imperfections are used to calculate knockdown factors (KDF). It was found that there is an inverse trend between embedded stiffener frequency and the KDF. The best performing CTS cylinder has a KDF 30% greater and a specific buckling load 4% greater than a QI cylinder, the optimal straight-fibre laminate for axial cylinder buckling. It was also found that, the smaller the effect of geometric imperfections on the pre-buckling strain field, the greater the KDF of the cylinder. This novel finding shows that a computationally inexpensive nonlinear analysis can provide a first-order approximation of the imperfection sensitivity of a cylinder in axial compression.

Mechanical properties of composite laminates can be tuned by either tailoring ply orientations or by using ply drops to change thickness profiles. The latter cause resin-rich pockets to form in thermoset composites that are autoclave cured after lay-down. This paper focuses on the morphology of ply drop regions with carbon fibre thermoplastic composites manufactured using in-situ consolidation with laser-assisted tape placement. Our work shows that when laying a 0° ply (parallel to the ply drop) over a ply drop then the ply readily conforms to the shape of the ply drop, eliminating voids. However, when a 90° ply covers a ply drop, the processing direction affects behaviour. When the ply ascends a ply drop, a void is created. On the other hand, when the ply descends a ply drop, the substrate changes its shape due to combined laser heat and roller pressure, leading to significantly smaller voids.

peer-reviewed This study investigates a device for in-line continuous spreading of carbon fibre/thermoplastic pre-preg tape for potential application in the Laser-Assisted Automatic Tape Placement (LATP) laminate manufacturing process.The spreading device allows variable tape width to be achieved locally during lay-up. Integration of this device in the LATP process would remove gap and overlap manufacturing defects in variable angle tow (VAT) laminates and complex curvature components. During trials different width tapes were produced using the novel spreading device. Three different width increases were investigated, viz. 15%, 30% and 45%, and were compared with as-received tape. Initial trials indicate that it is possible to achieve a tape width increase of 62%. Preliminary charac-terisation tests show that the spreading process does not adversely affect the properties of the tapes. Physical properties including cross-sectional area,fibre volume fraction and void content remain similar to as-received tape. Furthermore, differential scanning calorimetry data show that levels of crystallinity increase due to spreading, improving related mechanical properties.

The analysis of three-dimensional (3D) stress states can be complex and computationally expensive, especially when large deflections cause a nonlinear structural response. Slender structures are conventionally modelled as one-dimensional beams but even these rather simpler analyses can become complicated, e.g. for variable cross-sections and planforms (i.e. non-prismatic curved beams). In this paper, we present an alternative procedure based on the recently developed Unified Formulation in which the kinematic description of a beam builds upon two shape functions, one for the beam’s axis, the other for its cross-section. This approach predicts 3D displacement and stress fields accurately and is computationally efficient in comparison with 3D finite elements. However, current modelling capabilities are limited to the use of prismatic elements. As a means for further applicability, we propose a method to create beam elements with variable planform and variable cross-section, i.e. of general shape. This method employs an additional set of shape functions which describes the geometry of the structure exactly. These functions are different from those used for describing the kinematics and provide local curvilinear basis vectors upon which 3D Jacobian transformation matrices are produced to define non-prismatic elements. The model proposed is benchmarked against 3D finite element analyses, as well as analytical and experimental results available in the literature. Significant computational efficiency gains over 3D finite elements are observed for similar levels of accuracy, for both linear and geometrically nonlinear analyses.

Automated manufacturing of thermoplastic composites has found increased interest in aerospace applications over the past three decades because of its great potential in low-cost, high rate, repeatable production of high performance composite structures. Experimental validation is a key element in the development of structures made using this emerging technology. In this work, a $750\times640\times240$ mm variable-stiffness unitised integrated-stiffener out-of-autoclave thermoplastic composite wingbox is tested for a combined shear-bending-torsion induced buckling load. The wingbox is manufactured by in-situ consolidation using a laser-assisted automated tape placement technique. It is made and tested as a demonstrator section located at 85% of the wing semi-span of a B-737/A320 sized aircraft. A bespoke in-house test rig and two aluminium dummy wingboxes are also designed and manufactured for testing the wingbox assembly which spans more than 3m. Prior to testing, the wingbox assembly and the test rig were analysed using a high fidelity finite element method to minimise the failure risk due to the applied load case. The experimental test results of the wingbox are also compared with the predictions made by a numerical study performed by nonlinear finite element analysis showing less than 5% difference in load-displacement behaviour and buckling load and full agreement in predicting the buckling mode shape.

Nonsymmetric laminates are commonly precluded from composite design due to perceptions of reduced performance arising from in- and out-of-plane coupling. This coupling introduces warpage during cure—leading to raised stresses, together with diminished buckling and load carrying capacity. However, these reduced performance characteristics are rarely quantified and included in the design process; instead the symmetric-only paradigm remains pervasive at the cost of a significantly reduced design space. Warpage is largely driven by mismatch in the coefficients of thermal expansion between sublaminates located above and below the midplane and can be predicted by the classical laminate theory. Acknowledging that all symmetric laminates in multipart structures have build stresses from assembly, it is proposed that subsets of nonsymmetric laminates that translate tosimilar raised stress levels be considered for design. Challenging this symmetric-only design paradigm would permit greater design freedom and offer new routes to elastically tailor composite structures. Further analysis of structural performance is assessed in terms of reduced loading and buckling capacity.

The increasing reliance of aerospace structures on numerical analyses encourages the development of accurate, yet computationally efficient, models. Finite element (FE) beam models have, in particular, become widely used approximations during preliminary design stages and to investigate novel concepts, for example, aeroelastic tailoring. Over the last 50 years, developments in hp-FE methods based on elements of variable size (h) and polynomial degree (p) have helped reduce the computational cost of numerical analyses. Concurrently, many structures, including aircraft wings and wind turbine blades, have gradually increased in length, slenderness, and complexity. As a result, modern blades and wings regularly operate beyond the range of linear deformation, requiring nonlinear analyses for which hp-FE methods are often not readily applicable. The aim of this paper is, therefore, to derive a corotational FE formulation for enriched three-, four-, and five-noded beam elements, suitable for nonlinear hp-FE refinement. To this end, the mathematical formulation is derived to incorporate enriched elements within the corotational FE beam framework. The proposed formulation is then validated against multiple nonlinear benchmark problems and an experimental case study.

peer-reviewed The full text of this article will not be available in ULIR until the embargo expires on the 07/01/2022 A novel strain-displacement variational formulation for the flexural behaviour of laminated composite beams is presented, which accurately predicts three-dimensional stresses, yet is computationally more efficient than 3D finite element models. A global third-order and layer-wise zigzag profile is assumed for the axial deformation field to account for the effect of both stress-channelling and stress localisation. The axial and couple stresses are evaluated from the displacement field, while the transverse shear and transverse normal stresses are computed by the interlaminar-continuous equilibrium conditions within the framework of the modified couple stress theory. Then, axial and transverse force equilibrium conditions are imposed via two Lagrange multipliers, which correspond to the axial and transverse displacements. Using this mixed variational approach, both displacements and strains are treated as unknown quantities, resulting in more functional freedom to minimise the total strain energy. The differential quadrature method is used to solve the resulting governing and boundary equations for simply-supported, clamped and cantilever laminated beams. The deflections and stresses from this variational formulation for simply supported beams agree well with those from a Hellinger-Reissner stress-displacement mixed model found in the literature and the 3D elasticity solution given by Pagano. These strain-displacement models also accurately predict the localised stresses near clamped and free boundaries, which is confirmed by the high-fidelity Abaqus models. ACCEPTED peer-reviewed

peer-reviewed An analytical solution is obtained for the 3D static deflection of variable stiffness composite beams subject to non-uniformly distributed loads. Governing differential equations with variable coefficients, reflecting the spatially variable stiffness properties, are presented in which four degrees of freedom are fully coupled. The general analytical solution in integral form is derived and closed-form expressions obtained using series expansion approximations. The static deflection of a number of variable stiffness composite beams that can be made by fibre steering are considered with various stacking sequences. The results obtained from the proposed method are validated against numerical results from the Chebyshev collocation method and excellent agreement is observed between the two. While the proposed methodology is applicable for variable stiffness composite beams with arbitrary span-wise variation of properties, it is also an efficient approach for capturing the complicated 3D static deflection of variable stiffness composite beams subject to non-uniformly distributed loads.

Multistable laminates are potential candidates for adaptive structures due to the existence of multiple stable states. Commonly, such bistable shapes are generated from the cool-down process of the unsymmetric laminates from the curing temperature. In this work, we exploit unsymmetric variable stiffness laminates with curvilinear fiber paths to generate similar bistable shapes as unsymmetric cross-ply laminates, but with the possibility to tailor the snap-through loads. Snap-through is a complex phenomenon in that is difficult to characterize using simple analytical models. An accurate yet computationally efficient semi-analytical model is proposed to compute the snap-through forces of bistable variable stiffness (VS) laminates. The differential equations resulting from the compatibility and the in-plane equilibrium equations are solved with negligible numerical error using the Differential Quadrature Method (DQM). As a result, the in-plane stress resultants and the total potential energy is written in terms of curvatures. The out-of-plane displacements are expressed in the form of Legendre polynomials where the unknown coefficients of the displacement function are found using the Rayleigh-Ritz formulation. The calculated snap-through loads are then compared with the Finite Element (FE) results. A parametric study is conducted to explore the tailoring capabilities of VS laminates for snap-through loads.

peer-reviewed Cauchy homogenisation methods are based on the assumption that materials show size independent be- haviour. For example, the effective bending modulus of a beam is constant for all cross-sectional areas and is equal to the tensile modulus. However, as demonstrated by numerous authors, the stiffness of heterogenous materials under non uniform loading (e.g. bending) can be influenced by size effects, when the microstructural size scale is comparable to the macroscopic one. In other words, an effective elastic modulus can underestimate or overestimate the bending stiffness depending on the specimen size. In this work, the effect of the thickness dimension on the effective bending modulus of composite plies is investigated. The composite is represented by cylindrical fibres uniformly distributed in a uniform matrix. The cases of fibres stiffer and more compliant than the matrix are considered. The results show that the effective bending modulus depends on fibre volume fraction ratio, mismatch of fibre/matrix material properties and the number of fibres through the thickness. The implications for the analysis of bending of thin ply composites are discussed.

peer-reviewed The full text of this article will not be available in ULIR until the embargo expires on the 30/05/2022 Laser-assisted automated tape placement (LATP) in-situ consolidation of thermoplastic composites offers an efficient solution for production of large, high performance composite structures. The present work investigates laser repass treatment as a method of enhancing surface roughness and mechanical properties of LATP processed CF/PEEK laminates. Three laminate stacking sequences were studied, viz. [0°]16, [−45°/0°/45°/90°]2s and [±45°]4s. Four repass treatments were performed, including single, double, perpendicular and tool-side repasses. The effect of these repasses on interlaminar shear strength (ILSS), open-hole compression (OHC), in-plane shear (IPS), density, fibre volume fraction, void content and surface roughness was investigated. Surface roughness tests confirmed the improvement of the surface finish due to repass treatment. However, insignificant differences in ILSS values were observed across all repass treatments, but a single laser repass did appear to improve the OHC and IPS performance. Autoclave treated samples were used as a benchmark to compare with LATP processed laminate properties.

peer-reviewed Structures used in space applications demand the highest levels of stiffness for their mass whilst also performing in a hostile environment. To partly address these requirements and so as to also pack efficiently for stowage during launch we propose a new type of compact telescopic morphing lattice space boom. This boom stows within a 1U CubeSat volume and is lightweight being only 0.4 kg. The boom has a total length of 2 m in its deployed state which is 20 times its stowed height. The device comprises two multi-stable cylindrical composite lattices that are joined telescopically. These lattices nest inside one another in the stowed configuration, with the objective of improving packaging efficiency. Notably, prestress and lamina orientation are used to smoothly change shape from being compact when stowed to being extended when deployed. The lattices in the boom have been designed to maximise deployment force and to be self-deploying by tuning manufacturing parameters. As a result, only a small, lightweight mechanism is required to regulate deployment speed of the lattice boom. By reversing its direction, this mechanism can be used to retract the lattice boom to its stowed configuration, thereby enabling two-way reconfigurability.

A semi-analytical method is developed for the analysis of composite stiffened panels, where stiffness variability is achieved through a combination of fiber steering and curvilinear stringers. The approach relies upon a 2D plate model for the skin and a 1D beam description for the stiffeners, according to first-order shear deformation theory. The approach is developed in the framework of a displacement-based formulation, where Legendre polynomials are used for approximating the displacement field, and the Ritz method is used for the solution strategy. The resulting tool is characterized by its excellent computational efficiency, and allows problems in free-vibrations, buckling and thermal buckling to be solved with reduced effort. The quality of the results is assessed by an extensive set of comparison against results from the literature, demonstrating the potential of the tool as a means for performing preliminary parametric studies for these variable-stiffness, variable-geometry structures.

This work illustrates a fast numerical approach for analyzing the pre-buckling and buckling response of innovative panel configurations for aerospace structures. Specifically, the approach allows composite panels with variable-stiffness skins and stiffened by curvilinear stringers to be studied in a fast yet accurate manner. The method of Ritz is applied in conjunction with first-order theories for modeling the skin and the stiffeners, the former described referring to Mindlin plate theory, the latter to Timoshenko beam model. Due to the excellent convergence properties of the approach, pre-buckling stress distributions can be captured with reduced effort. Similarly, accurate buckling predictions can be obtained with relatively few degrees of freedom, much less with respect to typical models relying upon the use of finite elements. Results are presented for a number of test cases from the literature, illustrating the potential of the proposed approach as a mean for performing preliminary studies with reduced computational effort.

Variable Angle Tow (VAT) composites offer increased freedom for tailoring material properties compared to traditional straight-fibre composites. This increased freedom leads to greater design flexibility for enhanced structural performance but comes at the cost of more complex, spatially-varying displacement, strain and stress fields. To maximise the utility of VAT composites, a computationally efficient, yet accurate, numerical framework is needed. To this end, we employ a modelling approach that builds upon the recently developed, hierarchical Serendipity Lagrange finite elements. Three-dimensional (3D) stress distribution is obtained using the present modelling technique and verified against 3D finite element solutions, as well as other formulations available in the literature. A key advantage of the present approach is the ability to predict accurate 3D stress fields efficiently, i.e. with reduced computational effort, including around local features such as geometric, kinematic or constitutive boundaries. Moreover, the present work concerns the peculiarities of commonly used mathematical expressions for describing spatially varying fibre orientations across VAT laminates. The presence of an absolute value in the function used to describe fibre orientation can lead to discontinuities in fibre angle slope and curvature. In turn, these discontinuities lead to mathematical singularities in the constitutive relations along the laminate. If this singularity is not appropriately modelled as a boundary of the continuum, but rather as an interior point of the continuum, stresses may be predicted inaccurately. Compared to other models in the literature, our method is capable of unveiling detailed 3D stresses readily and accurately also in the vicinity of this singularity.

Composite structures are extensively used in many industries, where they are subjected to a variety of loads and may undergo large deformations. Reliable utilisation of such structures requires prior knowledge of their failure response. In order to predict failure loads and modes, accurate, yet computationally efficient, evaluation of three-dimensional (3D) stress fields becomes important. In this paper, we present a modelling approach, based on the Unified Formulation, that accounts for geometric nonlinearity in laminated composites and predicts 3D stress fields for subsequent failure analysis. The approach builds upon the hierarchical Serendipity Lagrange finite elements and is able to capture high-order shear deformation, as well as local cross-sectional warping. A total Lagrangian approach is adopted and the classic Newton-Raphson method is employed to solve the nonlinear governing equations. A key novelty of the proposed formulation is its completeness and its applicability to fully anisotropic structures. In other words, using the Green-Lagrange strain components within the Unified Formulation framework, the explicit form of the tangent stiffness matrix is derived including general stiffness properties. This new model is benchmarked against 3D finite element solution, as well as other formulations available in the literature, by means of static analyses of highly nonlinear, laminated composite beam-like structures. Significant computational efficiency gains over 3D finite elements are observed for similar levels of accuracy. Furthermore, to show the enhanced capabilities of the present formulation, the postbuckling response of a composite stiffened panel is compared with experimental results from the literature. The 3D stress fields computed in the postbuckling regime are used to detect failure of the stiffened panel. The corresponding failure mode, as obtained by the new model, is shown to match with the experiment.

© 2019, American Institute of Aeronautics and Astronautics Inc, AIAA. All rights reserved. In aerospace composite material design, it is common to encounter load bearing components that vary in thickness across their length. In plate design, ply drops, tow-steering, and the addition of stiffeners, all act to change both the section geometry and the effective stiffness of the part. Often, due to aerodynamic design constraints, the geometric profile must transition non-symmetrically, i.e. thickness is built up from a reference surface, meaning the mid-surface of the plate does not remain on a constant plane. These localised changes in geometry, and associated change of position of the mid-surface, lead to inherently three-dimensional states of stress. As a consequence, and especially for composite structures, there is the potential for significant through-thickness stresses and/or stress concentrations, leading to failure—for example debonding or delamination. By investigating the effects of geometric and effective stiffness changes, we are able to gain physical insight into structural behaviour in the regions of geometric transition. This is achieved through a parametric study, whereby we compare the behaviour as predicted by Classical Laminate Theory—a commonly utilised two-dimensional approach—with a finite element analysis based on the Unified Formulation by Carrera and co-workers. Based on these investigations, we are able to illustrate how rates of profile change and/or stiffness variation are linked to variance in the predicted location of the neutral plane of the two approaches which acts as a proxy measure for predicting through-thickness behaviour. Finally, we discuss the potential opportunity to utilise laminates that possess non-standard layups to tailor the load path through geometric transitions, thus offering a potential route for elastic tailoring that minimises undesirable through-thickness stresses.

In recent years, active flap devices on wind turbine blades have been shown to both reduce peak loads at the tower and extend blade fatigue life. Associated benefits include retrofitting existing tower infrastructure with longer and greater energy-producing blades whilst also extending service life of blades. In the current work, a novel wind turbine blade control method using morphing flaps has been successfully investigated and demonstrated using a scaled demonstrator mounted on an outdoor rotating test rig. Shape adaptive structures that remain conformal to the flow are increasingly referred to as morphing devices. As part of the INNWind.eu project, a novel morphing flap device was developed for a recently designed aerofoil. The proposed morphing flap comprises a light-weight carbon fibre laminate, 3D printed honeycomb core and a flexible silicone surface. A comprehensive test campaign using an outdoor rotating test rig under atmospheric conditions was carried out to assess the potential effectiveness. As shown by experimental data, the morphing flap provides good performance in terms of aerodynamic lift control of the blade and can provide dynamic load alleviation capability.

peer-reviewed The full text of this article will not be available in ULIR until the embargo expires on the 11/11/2020 Laser-assisted Automated Tape Placement (LATP) in-situ consolidation of thermoplastic composites has significant potential to produce repeatable and accurate components more efficiently than conventional processing methods. In addition, LATP can process Variable Angle Tow (VAT) laminates, that allow modification of load paths within the laminate to result in more favourable stress distributions and improved laminate performance. Previous studies have reported dry fibre placement and thermoset pre-preg tape placement processed VAT laminates. This work investigates the processing parameters required to produce VAT laminates from carbon fibre (CF)/polyether ether ketone (PEEK) tapes using LATP. Testing was carried out to examine the effect of lay-down speed and steering radii on defect frequency and bond strength. Measurements showed that the width and thickness of the CF/PEEK tapes changed as a result of steering. In addition, bond strength, determined using a novel wedge peel rig for steered tape, was found to be a function of lay-down speed.

Simple analytical and finite element models are widely employed by practising engineers for the stress analysis of beam structures, because of their simplicity and acceptable levels of accuracy. However, the validity of these models is limited by assumptions of material heterogeneity, geometric dimensions and slenderness, and by Saint-Venant’s Principle, i.e. they are only applicable to regions remote from boundary constraints, discontinuities and points of load application. To predict accurate stress fields in these locations, computationally expensive three-dimensional (3D) finite element analyses are routinely performed. Alternatively, displacement based high-order beam models are often employed to capture localised three-dimensional stress fields analytically. Herein, a novel approach for the analysis of beam-like structures is presented. The approach is based on the Unified Formulation by Carrera and co-workers, and is able to recover complex, 3D stress fields in a computationally efficient manner. As a novelty, purposely adapted, hierarchical polynomials are used to define cross-sectional displacements. Due to the nature of their properties with respect to computational nodes, these functions are known as Serendipity Lagrange polynomials. This new cross-sectional expansion model is benchmarked against traditional finite elements and other implementations of the Unified Formulation by means of static analyses of beams with different complex cross-sections. It is shown that Serendipity Lagrange elements solve some of the shortcomings of the most commonly used Unified Formulation beam models based on Taylor and Lagrange expansion functions. Furthermore, significant computational efficiency gains over 3D finite elements are achieved for similar levels of accuracy.

International audience; Composite materials are increasingly used in high performance structural applications because of their high strength and stiffness to weight ratios together with their significant tailoring capabilities. The stiffness of a monolithic laminate can be expressed as a linear combination of material invariants, one thickness variable, and twelve lamination parameters, which is an efficient alternative to using fibre angles as design variables. However, feasibility constraints originating from the interdependency between lamination parameters must be satisfied to obtain laminates with realistic stiffness properties. Currently, enforcing these feasibility constraints is a computationally intensive task. In this paper we propose to use normalised design variables that inherently map (i.e. correspond) to feasible lamination parameters, effectively removing the need to evaluate feasibility constraints altogether. To this end, linear and B-spline maps of the feasible lamination parameter subspace are proposed and evaluated. Results of 2D and 4D benchmark analyses and optimisation studies suggest that the proposed methodology does successfully provide an efficient means of achieving feasible results at lower computational costs.

Camber morphing aerofoils have the potential to significantly improve the efficiency of fixed and rotary wing aircraft by providing significant lift control authority to a wing, at a lower drag penalty than traditional plain flaps. A rapid, mesh-independent and two-dimensional analytical model of the fish bone active camber concept is presented. Existing structural models of this concept are one-dimensional and isotropic and therefore unable to capture either material anisotropy or spanwise variations in loading/deformation. The proposed model addresses these shortcomings by being able to analyse composite laminates and solve for static two-dimensional displacement fields. Kirchhoff–Love plate theory, along with the Rayleigh–Ritz method, are used to capture the complex and variable stiffness nature of the fish bone active camber concept in a single system of linear equations. Results show errors between 0.5% and 8% for static deflections under representative uniform pressure loadings and applied actuation moments (except when transverse shear exists), compared to finite element method. The robustness, mesh-independence and analytical nature of this model, combined with a modular, parameter-driven geometry definition, facilitate a fast and automated analysis of a wide range of fish bone active camber concept configurations. This analytical model is therefore a powerful tool for use in trade studies, fluid–structure interaction and design optimisation.

Morphing structures that are both lightweight and conformal to the aerofoil are currently being considered as promising candidates for the next generation of aircraft high-lift systems. Utilizing spatially variable stiffness materials in morphing structures leads to a possible reduction in the actuation energy requirement and also enables geometric control over the deformed shape of the morphing structure, resulting in enhanced aerodynamic and aeroacoustic performance. In this study, a design optimization methodology has been developed to identify the required material stiffness variations of a morphing structure for target optimal deformed shapes. In the optimization scheme, a layer-wise sandwich beam model is used to predict the structural behaviour of the flap with a specific material stiffness variation. Two-dimensional fluid/structure static aeroelastic interaction analysis is performed in the design optimization. Finite element analysis and mechanical tests were also carried out for a chosen optimization result to study the actuation requirements and the capability of control over the deformed shape of the morphing trailing edge. Numerical and experimental results confirm the feasibility of the proposed optimization methodology for identifying the required stiffness variation in the core and also ways of using rapid prototyped honeycomb core to realize the honeycomb core stiffness variations are discussed.

Variable Angle Tow (VAT) laminates that generally exhibit variable stiffness properties not only provide extended design freedom, but also offer beneficial stress distributions. In this paper, the prospect of VAT composite panels with significantly reduced loss of in-plane compressive stiffness in the postbuckled state in comparison with conventional structures, is studied. Specifically, we identify that both thickness and local fiber angle variation are required to effectively define “buckle-free” panels under compression loading. In this work, the postbuckling behaviour of variable thickness VAT composite panels is analyzed using an efficient and robust semi-analytical approach. Most previous works on the postbuckling of VAT panels assume constant thickness. The additional benefits of tailoring thickness variation in the design of VAT composite panels are seldom studied. However, in the process of manufacturing VAT laminates, either by using the conventional Advanced fiber Placement (AFP) machine (tow overlap) or the newly developed Continuous Tow Shearing (CTS) process (tow shrink) thickness build-up is inevitable. The postbuckling optimization for the design of VAT layups is conducted by a two-level framework using lamination parameters as intermediate design variables. The objective is to determine optimal lamination parameters and thickness distributions for maximizing the axial compressive stiffness of VAT laminates that are loaded in the postbuckling regime. The thickness variation due to both manufacturing of VAT laminates and for where it is independent of manufacturing process are considered. In accordance with the first-level optimal postbuckling solutions in terms of lamination parameters, we investigate a practical “buckle-free” VAT panel using a blended layup configuration. This blended VAT panel consists of a piecewise combination of segmental CTS layers and constant-thickness VAT layers. The prospect of taking advantage of a benign combination of stiffness and thickness to improve the overall compressive strength of VAT panels is studied. Finally, the optimal results are analysed to provide insight into the manufacturing of VAT laminates using either the AFP or the CTS process for improved postbuckling stiffness under compression loading.

Background:Composite materials are widely used in the aerospace, marine and automotive industries. One of their main advantages is that their stacking sequence can be tailored to maximise/minimise a specific structural performance. Efficient and non-computational-expensive algorithms are always needed to find the optimum stacking sequence of a composite laminate whose thickness is either to be minimised or may be kept constant (i.e.the thickness and the plies orientation percentages are pre-determined; the problem of the optimisation is therefore permutational).Objective:A modified branch and bound algorithm is proposed here and used to determine the stacking sequence for single and multi-objective optimisation problems. Laminate thickness and orientation percentages are either variables or determined a priori (the optimisation problem is therefore permutational). Computational time is drastically reduced when compared with other meta-heuristic techniques.Methods:The proposed method is a branch and bound algorithm, modified from the original work proposed by Kim and Hwang [10]. The main novelty is the starting point of the optimisation sequence: a laminate formed by “Ideal” layers, described in this paper.Results:The modified branch and bound has been first tested with a laminate having fixed thickness and a fixed percentage of layer orientation. Three different problems have been investigated: maximisation of natural frequencies, minimisation of tip deflection and maximisation of buckling critical load. The algorithm has been also tested, secondly, for a problem of weight minimisation subjected to buckling and strength constraints.Conclusion:The MBB has been shown to give good fidelity and significant computational advantages compared with a GA. Despite the simplicity of the structures in the numerical examples, it is anticipated that the MBB can be used to determine lay-ups in multi-part structures. The method was used to determine stacking sequences for several problems. The modified branch and bound method was shown to determine good laminate designs and offer significant efficiency savings.A “Good Design” is here defined as a solution producing “Near Global Optima” fitness values by minimising the computational effort. It was shown that for a single objective without ply competition, global optima were obtained.

Aims:A procedure to optimise the stacking sequence of a composite fan blade-like structure is proposed in this article. The aim of the optimisation is to minimise weight when respecting deformation, frequency and strain constraints. The literature often deals with stacking sequence optimisation of airplane wings or wind turbine blades whilst less attention has been dedicated to aero-engines fan blades, the objective of the present paper. The manufacturing constraints are also implemented in the optimisation process in order to obtain a manufacturable structure.Background:Stacking sequence of composite laminates can be tailored to drive the deformation towards the desired shape (potentially exploiting unbalanced laminates and their anisotropy). When optimising the stacking sequence (including blending/tapering) of an aero-engine fan blade-like structure, manufacturing constraints must be included in order to apply the results of the optimisation procedure into a “Real World” design.Objectives:To define an engineering procedure able to provide a good design point to minimise the weight of a fan blade-like structure subjected to deformation (tip extension and untwist), frequency and strain constraints.Methods:A two-level optimisation procedure is proposed. At the first level, the stacking sequence is optimised in such a way to maximise stiffness (and therefore to minimise deformation). Less stringent limits are applied to the constraints of such a level 1 optimisation. In the second step of the optimisation, the blending/tapering of each ply of the stacking sequence is searched.Results:The fan blade-like structure is loaded only with a centrifugal load (the main load acting on this kind of components). The stacking sequence obtained to minimise the weight contains 42.3% of 0 degrees fibres, 19.25% of 45 degrees fibres, 19.25% of -45 degrees fibres and 19.2% of 90 degrees fibres. Blending in terms of width and length of each layer is given in the numerical results section.Conclusions:When the fan blade-like structure is loaded with a centrifugal force only, in order to minimise weight by respecting untwist, tip extension, frequency and integrity constraints, no unbalance in the laminate has been found necessary. An “Optimum” point has been found after a two steps optimisation. This design point is claimed as a good industrial design point rather than as “optimum” in the mathematical sense. Such a “Best Solution” design point has been verified by exploring the design space near it. All the performance of the neighbour points has been found worse. A comparison between a quasi-isotropic laminate and a zero degreed dominated laminate has been also performed.

Background:Beam models have been proven effective in the preliminary analysis and design of aerospace structures. Accurate cross sectional stiffness constants are however needed, especially when dealing with bending, torsion and bend-twist coupling deformations. Several models have been proposed in the literature, even recently, but a lack of precision may be found when dealing with a high level of anisotropy and different lay-ups.Objective:A simplified analytical model is proposed to evaluate bending and torsional stiffness of a prismatic, anisotropic, thin-walled box. The proposed model is an extension of the model proposed by Lemanski and Weaver for the evaluation of the bend-twist coupling constant.Methods:Bending and torsional stiffness are derived analytically by using physical reasoning and by applying bending and torsional stiffness mathematic definition. Unitary deformations have been applied when evaluation forces and moments arising on the cross section.Results:Good accuracy has been obtained for structures with different geometries and lay-ups. The model has been validated with respect to finite element analysis. Numerical results are commented upon and compared with other models presented in literature.Conclusion:For cross sections with a high level of anisotropy, the accuracy of the proposed formulation is within 2% for bending stiffness and 6% for torsional stiffness. The percentage of error is further reduced for more realistic geometries and lay-ups.The proposed formulation gives accurate results for different dimensions and length rations of horizontal and vertical walls.

peer-reviewed The weight saving benefits of fiber-reinforced composite materials in structural applications are well established. However, there is an increasing requirement to develop processing techniques that can produce highly repeatable and accurate components more efficiently than using autoclave processing; Laser-assisted Automated Tape Placement (LATP) in-situ consolidation of thermoplastic composites has significant potential to fulfil this requirement. In addition, LATP can process layers with Variable Angle Tow (VAT), an advanced tailoring option that allows modification of load paths within the laminate to result in more favorable stress distributions and improved laminate performance. Studies of VAT laminate manufacture using dry fiber placement and thermoset pre-preg tape placement have been previously reported. This work examines the ability to produce VAT laminates from carbon fiber/PEEK pre-preg tapes using LATP. A VAT laminate was successfully manufactured which had three steering radii of 800 mm, 600 mm and 400 mm with little defects. Characterization and mechanical testing were completed on steered samples to examine the effect of lay-down speed and radius on bond strength of steered tapes. Measurements showed that the width and thickness of the carbon fiber/PEEK tapes were changed during steering. Mechanical testing showed that bond strength was a function of lay-down speed, yet the effect of steering radius was inconclusive due to undesired failures.

peer-reviewed Mechanical instabilities and elastic nonlinearities are emerging engineering means for designing shape-changing devices. In this paper, we exploit the taxonomy of post-buckling behaviours of a glass-fibre panel to design an adaptive air inlet that passively regulates the fluid flow into a connected duct. The adaptive component controls the inlet aperture by snapping open and closed depending on the velocity and pressure of the surrounding fluid. Sensing, actuation and control is entirely governed by the characteristics of the post-buckled component. Post-buckling stresses— induced in the composite panel by suitably applying compressive and bending loads—create the intrinsic characteristics of stability required for the panel to snap-through and snap-back. Furthermore, the associated post-buckled shape creates the aerodynamic pressure fields required for actuation. This design concept is explored and validated here by means of wind tunnel experiments. The passive actuation and control mechanism presented is particularly valuable for fluid control applications where simplicity and mass-minimisation are critical.

peer-reviewed The proof of an aircraft’s structural integrity and safety is typically provided by analysis and supported by structural test evidence. The experimental test of a wingbox, which is the main structural component of a wing, can provide useful data on assessment of its structural performance in an actual airplane for the design objectives. To this end, a testing fixture was designed and manufactured to introduce a prescribed shear force and bending moment at one end of a variable stiffness thermoplastic composite wingbox and react the load at the other end. We report experimental results and compare them with detailed finite element data.

peer-reviewed Compliance-based morphing structures have the potential to offer large shape adaptation, high stiffness and low weight, while reducing complexity, friction, and scalability problems of mechanism based systems. A promising class of structure that enables these characteristics are multi-stable structures given their ability to exhibit large deflections and rotations without the expensive need for continuous actuation, with the latter only required intermittently. Furthermore, multi-stable structures exhibit inherently fast response due to the snap-through instability governing changes between stable states, enabling rapid configuration switching between the discrete number of programmed shapes of the structure. In this paper, the design and utilisation of the inherent nonlinear dynamics of bi-stable twisting I-beam structures for actuation with low strain piezoelectric materials is presented. The I-beam structure consists of three compliant components assembled into a monolithic single element, free of moving parts, and showing large deflections between two stable states. Finite element analysis is utilised to uncover the distribution of strain across the width of the flange, guiding the choice of positioning for piezoelectric actuators. In addition, the actuation authority is maximised by calculating the generalised coupling coefficient for different positions of the piezoelectric actuators. The results obtained are employed to tailor and test I-beam designs exhibiting desired large deflection between stable states, while still enabling the activation of snap-through with the low strain piezoelectric actuators. To this end, the dynamic response of the I-beams to piezoelectric excitation is investigated, revealing that resonant excitations are insufficient to dynamically trigger snap-through. A novel bang–bang control strategy, which exploits the nonlinear dynamics of the structure successfully triggers both single and constant snap-through between the stable states of the bi-stable twisting I-beam structures. The obtained optimal piezoelectric actuator positioning is not necessarily intuitive and when used with the proposed dynamic actuation strategy serve as a blueprint for the actuation of such multi-stable compliant structures to produce fast and large deflections with highly embeddable actuators. This class of structures has potential applications in aerospace systems and soft/compliant robotics.

The principle of control signal amplification is found in all actuation systems, from engineered devices through to the operation of biological muscles. However, current engineering approaches require the use of hard and bulky external switches or valves, incompatible with both the properties of emerging soft artificial muscle technology and those of the bioinspired robotic systems they enable. To address this deficiency a biomimetic molecular-level approach is developed that employs light, with its excellent spatial and temporal control properties, to actuate soft, pH-responsive hydrogel artificial muscles. Although this actuation is triggered by light, it is largely powered by the resulting excitation and runaway chemical reaction of a light-sensitive acid autocatalytic solution in which the actuator is immersed. This process produces actuation strains of up to 45% and a three-fold chemical amplification of the controlling light-trigger, realising a new strategy for the creation of highly functional soft actuating systems.

peer-reviewed It is well known that the macroscopic behaviour of many engineering materials is strongly affected by the role of underlying microstructure. Currently though, mathematical expressions linking behaviour of large scale structures to the geometry of their microscopic structure are largely lacking. In this respect, establishing quantitative links across different material lengthscales may offer new pathways for engineering design. In the present work an analogy between cross sectional geometrical properties, representing macrostructure, and a material length parameter, representing microstructure, is presented. The analogy is established through the study of a thin plate subject to axial loading undergoing finite displacements from two alternative perspectives. First, we consider a thin elastic plate with a pretwist about the loading axis where a warping term is introduced accounting for the out-of-plane deformation of the cross section. The coupled governing differential equations and the corresponding coupled boundary conditions are explicitly derived employing a classical structural mechanics approach utilising an energy variational statement. Secondly, an axially loaded thin flat plate (i.e. with no pretwist) is studied with strain gradient elasticity theory incorporating only one material length parameter representing the microstructure, in addition to the two classical Lamé stiffness constants. The ensuing analogy emerges by comparison of the governing equations of the two formulations which shows a mathematical expression can be identified, which incorporates both geometric and material length variables, that formalises the link between microscale and macroscale. This mathematical expression, which constitutes the kernel of the proposed multiscale approach, admits a twofold interpretation depending on the assumed independent variable. On the one hand, the proposed multiscale modelling approach suggests that a plate with complex global geometry can be substituted by a structurally - equivalent, flat plate with constitutive relations given by a non - local, strain gradient theory. On the other hand, the material length parameter can be interpreted on a physical basis because for the first time it has been identified as a known function of geometrical features of the structure through simple algebraic relationships for various cross sectional profiles.

Aeroelastic performance controls wing shape in flight and its behaviour under manoeuvre and gust loads. Controlling the wing’s aeroelastic performance can therefore offer weight and fuel savings. In this paper, the rib orientation and the crenellated skin concept are used to control wing deformation under aerodynamic load. The impact of varying the rib/crenellation orientation, the crenellation width and thickness on the tip twist, tip displacement, natural frequencies, flutter speed and gust response are investigated. Various wind-off and wind-on loads are considered through Finite Element modelling and experiments, using wings manufactured through polyamide laser sintering. It is shown that it is possible to influence the aeroelastic behaviour using the rib and crenellation orientation, e.g. flutter speed increased by up to 14.2% and gust loads alleviated by up to 6.4%. A reasonable comparison between numerical and experimental results was found.

The aeroelastic performance of a wing, including static aeroelastic shape, flutter/divergence speed and gust load response, has a significant influence on aircraft design. The tailoring of aeroelastic responses therefore offers potential weight savings. In this paper, the spars and stringers planform geometry (i.e. shape and root/tip chord wise location) on a representative wind tunnel model aircraft wing are used to modify the wing aeroelastic performance. Several optimisations are performed to illustrate the ability of the spars and stringers planform geometrical features to change the wing vibrational mode natural frequencies, deformation under a static tip load and aerodynamic load, gust response and aeroelastic instability speed. Changing the stringers planform geometry is shown to offer minor variation in the wing deformation and loads. Changing the spars planform geometry is shown to enable a reduction in root bending moment under static aerodynamic loading greater than 10%, a reduction in maximum root bending moment encounter during a worst case scenario gust event greater than 10% and a 25% increase in flutter speed. The improvements due to a change in the spar planform geometry are compared to the effect of changing the wing sweep angle. A framework to characterise Euler-Bernoulli beam properties on wings with geometric coupling is then developed and validated to relate the stiffness and bend/twist coupling parameter to the full 3D FE models.