Bend-twist Coupling Research Articles

A semi-analytical model for predicting the shear buckling of laminated composite honeycomb cores in sandwich panels

Laminated composite honeycomb cellular core sandwich panels are widely utilized in various industries due to their exceptional stiffness-to-weight ratio and strength characteristics. Current analytical models often simplify honeycomb cores as homogenized continua, effectively predicting stiffness but falling short in capturing crucial failure modes, particularly shear buckling of honeycomb core walls. Existing theoretical studies on shear buckling are limited to isotropic materials and specific honeycomb geometries. While numerical models can simulate cell wall buckling, their computational demands render them impractical for large structures employing sandwich panels. This paper introduces a novel, simplified semi-analytical approach that accurately predicts the shear buckling load of laminated composite honeycomb cellular cores. The model accounts for bend-twist coupling effects and rotational restraints at laminate wall boundaries. To validate the proposed approach, predictions are compared with finite element analysis results for hexagonal honeycomb cores and cores of varying shapes, incorporating diverse fibre lay-up configurations. The findings demonstrate excellent agreement between the proposed approach and finite element analysis, indicating its reliability in predicting shear buckling. This research addresses the gap in existing methodologies by offering a practical and efficient tool for predicting shear buckling in laminated composite honeycomb cores, extending applicability beyond isotropic materials and specific honeycomb geometries. The proposed approach holds promise for optimizing the design and structural integrity of sandwich panels, impacting industries relying on these lightweight and high-performance structures.

A study on interactive fiber rubber composite structures subjected to bend-twist coupling

Abstract This paper investigates the deformation behavior of shape memory alloy (SMA)-integrated fiber-reinforced composites, with an emphasis on how different fiber orientations influence bend-twist coupling. The study combines experimental analysis, finite element simulations using Ansys, and analytical modeling via Classical Laminate Theory (CLT) to assess the mechanical response of these composites. The experiments revealed that composites with higher fiber angles (60°) exhibited dominant twisting behavior, while those with lower angles (30° and 45°) showed more pronounced bending deformation. The simulations corroborated these trends, offering detailed insights into the displacement behavior. The CLT model further predicted a decrease in deflection with increasing fiber angles, which was consistent with experimental results, although some deviations in Z-deformation were attributed to material and manufacturing factors. This research highlights the critical role of fiber orientation in achieving desired deformations in SMA-integrated composites, offering valuable insights for the design of adaptive structures. The findings demonstrate the potential for optimizing fiber configurations to tailor bend-twist coupling in advanced composite applications.

Bend-twist adaptive control for flexible wind turbine blades: Principles and experimental validation

This study proposes a new methodology for optimizing the power curve of a wind turbine at low wind speeds. The principles of bend-twist coupling and the mechanism of energy exchange between the structure and inflow are analyzed. For the blade’s geometric nonlinearity, the virtual displacements and strain fields are described using the Green-Lagrange strain theorem, retaining third-order terms in the energy expressions. The equations of motion are derived using Hamilton’s principle. The bend-twist coupling effects and large deformations of the blade are analyzed using the Updated Lagrange method. Notably, the angle of attack for a single blade section is influenced by bend-twist deformation, causing variations in the rotor’s maximum power coefficient from its optimal value. Additionally, the projection length of the blade, influenced by centrifugal forces, also affects the bend-twist deformation. Based on these findings, an aero-elastic coupling control strategy, termed “Bend-twist Adaptive Control”, is proposed and validated through experiments. The results demonstrate that the proposed control strategy could increase annual power production by 2.3 %. These conclusions offer a promising outlook for future wind turbine blade design and power optimization.

TorqTwin—An open-source reference multibody modeling framework for wind turbine structural dynamics

This paper presents an open-source multibody modeling framework for wind turbine structural dynamics, namely TorqTwin (Torque Towards wind). The multibody formulation includes both rigid and flexible bodies. For flexible bodies, such as towers and blades, the floating frame of reference formulation and modal reduction approaches are applied. The TorqTwin tool relies on Kane’s method and the symbolic Python library SymPy. The multibody formulation in TorqTwin is validated using the OpenFAST-ElastoDyn module and the commercial software Bladed. For both the fixed-bottom and floating IEA 15MW reference wind turbines, the rigid motions and flexible deflections calculated by TorqTwin are compared to those by ElastoDyn. Also, blade deflections predicted by TorqTwin are compared to those of the commercial software Bladed. The overall very good agreement between TorqTwin and other software validates the multibody formulation in TorqTwin. The strength of TorqTwin is that it contains the full functionality of the state-of-the-art open-source ElastoDyn module and includes other modeling capabilities of commercial software, such as the bend-twist coupling effect of blades and more flexible modes. TorqTwin is designed to benefit both the wind energy research community and industry, as it helps understand and verify the theory behind the ElastoDyn module, provides a reference for formulating more complicated configurations, such as multi-rotor turbines, and helps to develop aeroelastic simulation tools.

Bending and twisting rigidities of 2D materials

A novel torus-based surface parametrization is proposed and used to evaluate the bending and twisting rigidities of 2D materials of arbitrary symmetries. A generalized constitutive model is used to capture the effects of simultaneous bending and twisting curvatures on the strain energy density of a 2D material. The flexural rigidities are evaluated by subjecting the 2D material specimens to different curvature states, including simultaneous bending and twisting, evaluating the corresponding strain energy densities and curve fitting the constitutive model to the data. The proposed methodology is independent of the method used to evaluate the strain energy of the 2D materials, e.g., density functional theory or classical interatomic potentials. The flexural rigidities of graphene, molybdenum disulfide, and black phosphorus are evaluated and compared to those published in the literature. The directional dependence of the flexural rigidities is investigated. Dimensionless coefficients are presented for quantifying the bidirectional bending and bending-twisting coupling effects in 2D materials. Lastly, this study includes an analysis of the flexural anisotropy and flexure-thickness distension coefficients of black phosphorus.

Static response of wind turbine blades: Comparison of low- and high-fidelity numerical models

As wind turbine blades become longer and more flexible, the structural models employed in current aeroelastic simulation tools, usually based on beam formulations, are challenged. Effects previously considered negligible in the response of these beam-like structures might now become significant to obtain accurate predictions of their behaviour. To assess this, a test matrix covering key geometric and material characteristics of wind turbine blades is defined and three test cases are analysed as an initial stage of this study. For each case, the static deflection of the beam model from the aeroelastic tool HAWC2 is compared against higher-fidelity shell/solid finite element models. Three structures are studied: an isotropic box beam, a composite box beam and a 12.6 m wind turbine blade from DTU. A good match is observed for the box beam test cases, which study the effects of out-of-plane and distortion warping and bend-twist coupling. Important aspects of high-fidelity models (such as end effects) are highlighted. The study of the DTU 12.6 m blade shows a significant difference (15%) in the torsion natural frequencies of the beam model, though a good agreement in twist angle under torsional loading. More pronounced differences in twist angle are observed when a load distribution based on the steady state response is applied, likely resulting from challenges in modelling complex structural features and three-dimensional effects.

Towards the fast buckling load prediction of composite shells via Bloch wave based numerical vibration correlation technique

The buckling load revealing structural capacity bears significant value for the design of engineering composite shells, especially in the aerospace industry. Non-destructive methods are prevailing for critical buckling load prediction. However, the experimental costs and computational time for the analysis are unaffordable, especially for large-scale and complex shells. Despite the numerical vibration correlation technique (NVCT) and its modifications proposed for faster critical buckling load prediction, the efficiency requires further improvement. For composite shells with rotational periodicity, analyzing one substructure based on the Bloch wave method can be an alternate for the analysis of the entire shell. Since the NVCT comprises the linear buckling analysis and repeated frequency analyses, twofold acceleration can be performed. Thus, the Bloch wave based numerical vibration correlation technique (BW-NVCT) is proposed. Firstly, the formulations for the Bloch wave method and the NVCT are derived. As the curve of Bloch wave numbers and buckling loads is monotonous or principally comprise a single peak, the computations in the Bloch wave method to determine the minimum buckling load are further reduced. Then, the implementation of BW-NVCT is presented wherein the Bloch wave calculations are simplified compared with the Bloch wave buckling analysis method. Secondly, three types of composite shells including the Z33 composite cylindrical shell, the pressure vessel and the nozzle are analyzed by the proposed method. By applying Bloch boundary conditions to the substructure, the linear buckling loads, natural frequencies are in high accuracy with respect to results by finite element analyses directly. In addition, predicted critical buckling loads by the BW-NVCT are in excellent precision and most importantly, remarkable efficiency is achieved compared with both the NVCT and the dynamic explicit analysis. Results show that the proposed method can capture both global and local buckling modes, even when bend-twist coupling exists. It is concluded that the BW-NVCT is widely applicable for composite shells and is substantiated as an effective method for fast buckling load prediction.

Fluid-Structure Interactions Response of a Composite Hydrofoil Modelled With 1D Beam Finite Elements

_ In this paper, the hydroelastic response of a NACA0015 composite hydrofoil is studied experimentally and numerically. The foil is made of composite materials with fibers not aligned with the span of the foil, which results in the occurence of a bend-twist coupling in the material. Computations are performed using a partitioned approach. The flow problem is solved using a boundary element method. The structural response of the foil is modelled with two different finite element models. In the first one, the foil is modelled with 2D shell and 3D solid finite elements and in the second model, the foil is modelled with 1D beam finite elements. The experiments are conducted in an open circulation water channel. Hydrodynamic forces and structural displacements are measured for several angles of attack, free stream velocities and submergence depth. This paper shows that the mechanical behaviour of a composite hydrofoil submitted to hydrodynamic loads can be modelled with 1D beam finite elements. This model gives results very similar to a finite element analysis realized with 2D shell and 3D solid finite elements, which are commonly used to model composite structures. The present work also shows that the experimental results can be well predicted by numerical simulations, but it requires a precise modeling of the bend-twist coupling in the materials constituting the foil. Keywords Hydrofoil; Equivalent Beam; Fluid-Structure Interactions; Composite; Bend-Twist Coupling

Passively morphing trailing edge design for composite tidal turbine blades

Numerical simulations and lab-scale experiments are used to evaluate three passively morphing trailing edge designs for a composite tidal turbine blade. The designs include a closed trailing edge, an open trailing edge, and a corrugated trailing edge. It is shown that geometric stiffness, as well as material stiffness, play key roles in achieving the desired deformation of the trailing edge. One trailing edge design is down-selected for further investigation via full-scale numerical simulations. These simulations demonstrate how the composite lay-up influences the morphing response of the trailing edge and its likelihood of material failure. The influence of camber is also investigated in terms of both material behaviour and hydrodynamic performance. Finally, the potential for bend-twist coupling of the laminate skins is explored.

Sensitivity of cross-sectional compliance to manufacturing tolerances for wind turbine blades

Abstract. Wind turbine blades are complex structures and, despite advancements in analysis techniques, differences persist between predictions of their elastic response and experimental results. This undermines confidence in the ability to reliably design and certify novel blade designs that include self-regulating features like bend–twist coupling. To address these discrepancies, this study investigates the influence of manufacturing tolerances on the compliance properties of blade cross-sections, focusing specifically on a previously disregarded feature: the trailing edge bondline. To conduct this investigation, the validated cross-sectional modelling tools BECAS and VABS are used to demonstrate that even small geometric variations can have significant influence on cross-sectional stiffness properties. The results are further examined and substantiated through the utilisation of 3D finite element models, adopting both shell and solid elements. We reaffirm that an accurate geometric representation of the cross-section is necessary to adequately capture the shear flow within it and assure accurate predictions on cross-sectional stiffness properties, providing updated guidelines for designers in industry.

Vortex shedding from a composite hydrofoil: Experimental evidence of a novel “partial lock-in”

Lock-in is of great importance in many engineering applications due to its practical implications for structural safety. The influence of composite bend-twist coupling on the wake dynamics and vortex-induced vibration around a carbon fiber composite hydrofoil is investigated and compared to a similar stainless-steel hydrofoil. Experiments are conducted by varying linearly and slowly the upstream velocity back and forth between 5 and 15 m/s, which allows reaching lock-in conditions for both hydrofoils. Due to the blunt truncation of the trailing edge, both hydrofoils produce strong and alternate vortices in their wake, whose effect is visible on vibration spectrograms. The steel hydrofoil produces a classical lock-in onto its first torsion mode, while the composite hydrofoil exhibits two lock-in phenomena onto both torsion and second bending modes. Interestingly, for the second bending mode, the vibration spectrogram reveals the existence of two frequencies: (i) the resonance frequency, which remains almost constant during the lock-in phase, and (ii) the Strouhal frequency, which increases linearly with the upstream velocity. Using flow visualization, we found that this peculiar behavior is the result of the twist-bending coupling, which leads to the co-existence of two different vortex-shedding mechanisms. Close to the hydrofoil tip, the large vibration amplitude dictates the shedding frequency while the shedding follows the Strouhal law elsewhere. This partial lock-in gradually fades away as the velocity is increased. This result provides guidance for the safe design of composite structures.

Passive aeroelastic study of large and flexible wind turbine blades for load reduction

In this paper, passive aeroelastic coupling of wind turbine blades for load reduction is realized by introducing bending-twist coupling (BTC) and geometric sweep coupling (GSC). The BTC is implemented by composite fiber off-axis of the blade spar cap, and the GSC is achieved by defining sweep curves of the blade reference axis. To investigate the passive coupling effect and load reduction of the large and flexible blades, the IEA 15 MW blades are considered. BTC are introduced into the three-dimensional finite element (FE) models and the residual stiffness coefficient is obtained. Meanwhile, geometrically exact beam theory (GEBT) is used to build the flexible blade. Both BTC and GSC are introduced into the beam model, and the effect elastic deformation on blade load is also considered. Multi-objective optimization (MOO) process of rotating blades for load reduction is proposed under steady-state rated conditions. The results show that the highest coupling efficiency can be obtained when the fiber off-axis angle is between 12° and 15°. The BTC of the blade can reduce the load of blade root with a small fiber off-axis angle. Meanwhile, the GSC can further reduce the axis torque. Compared with the initial design of IEA 15 MW steady-state rotating blade, the maximum thrust, flapwise moment and axis torque of the blade can be reduced by 8.8 %, 13.4 % and 22.9 % respectively.

Fluid–Structure Interaction Analysis of a Wind Turbine Blade with Passive Control by Bend–Twist Coupling

The idea of improving the energy output for small wind turbines without compromising the remaining aspects of the technology, such as costs and structural integrity, is very appealing in the context of the growing concern for global warming and the goal of providing electricity to remote and isolated regions. This work aims to contribute to the development of distributed wind generation by exploring the effects of bend–twist coupling on the performance of a wind turbine with a focus on a small rotor based on the NREL Phase VI blade geometry. After defining a structure in composite materials exhibiting the coupling behavior along with a reference counterpart, a comparative numerical analysis is performed using a Fluid–Structure Interaction (FSI) analysis. The main numerical framework is based on commercial software and consists of a finite-volume solver for fluid physics, a finite-element solver for solid physics, and a coupling interface for the interaction problem. The results, complemented with the predictions from a one-way analysis based on the blade-element momentum theory are used to define the increments in rotor torque. The analysis of the annual energy yield shows a 3% increase due to the bend–twist coupling used as a passive pitch mechanism, considering a Rayleigh distribution with an 11 m/s average wind speed. Simultaneously, the coupling causes increments of 0.2% and 0.3% for the blade root flapwise moment and the rotor thrust force, respectively, when considering parked conditions and a simplified extreme wind model.

The Impact of Bend–Twist Coupling on Structural Characteristics and Flutter Limit of Ultra-Long Flexible Wind Turbine Composite Blades

Flutter is an instability phenomenon that can occur in wind turbine blades due to fluid–structure interaction, particularly for longer and more flexible blades. Aeroelastic tailoring through bend–twist coupling is an effective method to enhance the aeroelastic performance of blades. In this study, we investigate the impact of bend–twist coupling on the structural performance and flutter limit of the IEA 15 MW blade, which is currently the longest reference wind turbine blade, and determine the optimal layup configuration that maximizes the flutter speed. The blade is modeled by NuMAD and iVABS, and the cross-section properties are obtained by PreComb and VABS. The accuracy of the blade model is verified in terms of stiffness and frequency. The bend–twist coupling is implemented by changing the fiber angle of the skin and spar cap considering symmetric and asymmetric layups. The flutter limits of both the baseline and the bend–twist coupled blade are evaluated based on HAWC2. The results show that the angle of spar cap carbon fiber has a greater effect on the blade’s structural properties and flutter speed than the skin fiber. Varying the spar cap carbon fiber angle increases the flutter speed, with the effect being more significant for the symmetric layup, up to 9.66% at a fiber angle of 25 degrees. In contrast, the variation in skin fiber angle has a relatively small impact on flutter speed—within ±3%.

Mode decomposition and simulation of cloud cavity behaviors around a composite hydrofoil

Numerical investigation of the cavity dynamics around a composite hydrofoil with a blunt trailing edge in the cloud cavitating flow is carried out using a tightly coupled fluid–structure interaction method. The hydrofoil is made of a carbon-fiber-reinforced polymers with a ply angle of −45∘(CFRP −45). The results of a stainless-steel hydrofoil with the same geometry and conditions are used as a reference. Simulation results have been validated carefully against experimental data. Several fundamental mechanisms are dictated through simulation results and mode decomposition, including the multistage shedding process, the influence of the bend–twist coupling effect on cavity behaviors, cavitation–vortex interaction, and kinematics of coherent structures. The main reason for the generation of a secondary re-entrant jet is that the primary cloud cavity collapse leads to high pressure, which spreads to the residual sheet cavity closure and then induces a high-pressure gradient. The negative bend–twist coupling effect causes the CFRP −45 hydrofoil to exhibit a smaller cloud cavity scale and non-uniform re-entrant jet strength in the spanwise direction compared to the stainless-steel hydrofoil. Modal decomposition via proper orthogonal decomposition and dynamic mode decomposition indicates that the dominant coherent structures in the cloud cavitating flow include the large-scale cloud cavity, rotating structures due to the re-entrant jet, attached cavity, and small-scale vortex in the wake. The results obtained in this study provide physical insight into the understanding of the mechanisms relevant to complex cloud cavitating flow around a composite hydrofoil.

Computationally efficient optimal design of hygrothermally stable laminate with bend–twist coupling by analytical and numerical strategy

Computationally efficient optimal design of hygrothermally stable laminate with bend–twist coupling by analytical and numerical strategy

Mechanism of the reciprocal effects for bending and twisting during spatial tube forming

The process of bending and twisting has always been employed for spatial tubular product forming. To reveal the mechanism of the reciprocal effects during the forming process, a quadratic model considering both bending and torsion in the frame of the total plasticity theory is proposed. This model presents an important relationship among the moment for pure bending Mo, the torque for pure torsion To, as well as the corresponding bending moment and torque M∗ and T∗ in the case of bending-twisting coupling. Particularly, for the above relationship, the proportion between the bending radius and twisting angle is pointed out. The calculation methods of the bending moment and torque for spatial tubes with non-linear hardening materials are provided. In addition, a finite element model based on the properties of pure aluminum is established for validation. Results show that the quadratic model could address the issue of bending and twisting coupling forming under simple loading effectively and the relative errors are all less than 10 %. The loading ratio of the bending moment to the torque is deduced by the maximum work principle. Its function is verified as well.

Design of bend-twist coupled rectangular composite beams based on extension-twist multicoupled laminates

Wind turbine blades are easily damaged and fractured and power output is unstable under strong wind conditions, which are urgent problems to be solved. In this paper, the box structure of wind turbine blade is designed based on the extension-twist multicoupled laminates, which has the self-adaptive characteristics of bend-twist coupled deformation. The stiffness equation of the box structure is obtained by decoupling the deformation caused by the bending moment and torsion moment of the box structure, and the accuracy deviation of the torsional coupled stiffness is solved. The AOC 15/50 wind turbine blade is taken as an example, the paving optimization design is realized for the 80-ply hygrothermal stable extension-twist multicoupled laminates and their bend-twist coupled box structures. The results show that compared with the single-coupled laminates, the multicoupled laminates can not only increase the extension-twist coupling of the laminate (reaching more than 25%), but also greatly increase the bend-twist coupling of the box structure (reaching more than 40%). Finally, the robustness analysis is realized for the extension-twist coupling of laminates and the bend-twist coupling of blade, and the hygrothermal effect and coupling of the blade box structure are verified by numerical simulation.

Automated manufacture of optimised shape-adaptive composite hydrofoils with curvilinear fibre paths for improved bend-twist performance

Composite marine propellers improve hydrodynamic efficiency by inducing bend-twist coupling and allowing for passive pitch changes. One critical limitation, however, is the extent to which a composite propeller blade can deform and cause a pitch change without incurring structural failure. Recent numerical studies showed that curvilinear tows could improve the structural response of a composite blade by lowering its deflection or stress and strain required to induce a pitch change, but no experimental validation has been carried out before. The current study, thus, presents the manufacture of composite sandwich hydrofoils made with steered tows using automated fibre placement and validates the curvilinear tow benefits. Two hydrofoils were optimised with straight and curved fibre path layups, respectively and were manufactured for mechanical testing. The manufacturing complications arising from steering curvilinear tows in a three-dimensional convex mould are also discussed in the paper. The study found that significant tow buckling occurred near the tool cavity edge due to excessive steering radius during manufacture. The follow-up structural cantilevered tests showed that the experimental results were consistent with the FE predictions despite the presence of some manufacturing defects. The experiment agreed that the hydrofoil manufactured with curved tows achieved a similar tip twist but a significant reduction in deflection and critical principal strains compared to the hydrofoil made with straight tows. The use of a foam core reduced the overall weight of the sandwich hydrofoils by about 25% compared to that of a fully-carbon composite hydrofoil, and the numerical analysis showed that the core shear failure induced by transverse shear stresses was unlikely to occur.

Bend-twist coupling effects on the cavitation behavior and hydroelastic response of composite hydrofoils

The objective of this work is to investigate the influence of bend-twist coupling effects on the cavitation behavior and hydroelastic response of four hydrofoils with identical geometry: one rigid hydrofoil and three composite hydrofoils of carbon-fiber reinforced plastic (CFRP) with the ply angles of 45°, 0°, and -45°, respectively. A synchronized measurement system consisting of a high-speed camera, a hydrodynamic load cell, and a Laser Doppler Vibrometer is applied to obtain the cavity dynamics and hydroelastic response simultaneously. The theoretical cross-sectional effective bending stiffness, twisting stiffness, and bend-twist coupling stiffness are calculated based on a chordwise-rigid laminated plate model. In addition to the primary cavity shedding frequency and natural frequencies, additional modulated frequencies are excited for all the hydrofoils due to time-varying added mass effects, which broadens the frequency response of the hydrofoil. Re-entrant jet and shockwave mechanisms are identified as instabilities causing periodic cloud cavity shedding. The cloud cavity shedding frequency is found to be independent of cavitation number in certain conditions induced by the shockwave mechanism. Bubbly shock induces a secondary shedding of cloud cavities, causing the reduction of the cavity shedding frequency. The CFRP 45 hydrofoil with a positive bend-twist coupling effect promotes the bending and twisting deformations of the hydrofoil, increasing lift and moment, decreasing the cloud cavity shedding frequency due to the increase in cavity length, and accelerating the cavitation regime transition by reducing cavitation number. And the opposite is true for the CFRP -45 hydrofoil with a negative bend-twist coupling effect.