Effect Of Bending-twisting 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.

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.

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.

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.

Optimized blade mass reduction of a 10MW-scale wind turbine via combined application of passive control techniques based on flap-edge and bend-twist coupling effects

In the present work, the possibility of reducing the mass and thereby the capital cost of a 10 MW-scale wind turbine blade is assessed by applying passive load control techniques. Two passive load control methods are combined in the analysis; the bend-twist-coupling method, aiming at reducing operational loads and the flap-edge-coupling method, aiming at alleviating stall induced vibrations in parked or idling operation. The first is materialized through rotation of the composite material plies over the caps of the spar beam, while the second is attained through displacement of the caps in opposite directions. The assessment of the material reduction capacity is performed through optimization simulations. The optimization loop combines an in-house thin lamination tool for the computation of the blade beam properties and the distribution of stresses over the cross sections of the blade and an in-house comprehensive aeroelastic analysis tool that provides the design loads of the turbine. Optimization simulations indicate that an 8.3% reduction in mass can be achieved through moderate modification of the blade inner structure, i.e. concurrent rotation of the plies of the UD material on the caps by 5.8° and displacement in opposite directions of the spar caps by 3% of the chord length.

Buckling optimization of composite rectangular plates by sequential permutation search with bending-twisting correction

Buckling problem of composite plates is of importance since it is commonly encountered in thin-walled structural components in engineering. Buckling resistance design of composite plates involves the design of laminate stacking sequence exhibiting high dimensional discrete variables owing to the combination and permutation of ply orientations of layers. In this work, a sequential permutation search (SPS) optimization algorithm is presented for the stacking sequence design of composite rectangular plates accounting for the inherent physical-mechanical behavior of composite laminates. Owing to that the governing equation for buckling of composite rectangular plates is a linear homogeneous equation on bending stiffness parameters, the convexity of flexural lamination parameters and sensitivity of bending stiffness are utilized to construct sensitive detection techniques and linear search procedures. Moreover, to increase the robustness of SPS, a sign optimization algorithm (SOA) is coupled in SPS to regulate bending-twisting coupling effects. The SPS algorithm is applied to the buckling resistance design of composite rectangular plates exhibiting various boundaries under axial compression, where the Rayleigh-Ritz method is developed to perform the buckling analysis. Optimal results of SPS are compared against layerwise optimization approach (LOA) and genetic algorithm (GA), illustrating its reliability and efficiency.

Influence of spanwise flexibility on steady and dynamic responses of airfoils vs hydrofoils.

There is growing interest in using lighter and more flexible foils with active and/or passive smart actuation mechanisms to increase efficiency and maneuverability. For efficient operations, airfoils and hydrofoils tend to have an effective aspect ratio greater than two, which permits spanwise flexibility depending on the choice of material and architectural design. The fluid density plays an important role in the steady and dynamic performance, including the governing hydroelastic instability mechanism. To understand the influence of spanwise flexibility, we examine the response of a rectangular cantilevered foil as a canonical proxy for more complex lift generating devices. This research aims to investigate the influence of key geometric, material, and flow parameters on the steady and dynamic responses of the spanwise flexible airfoils vs hydrofoils. The results are obtained using an inviscid frequency- and time-domain fluid-structure interaction model that accounts for flow-induced bend-twist coupling terms and are compared with inviscid theory results without the flow-induced bend-twist coupling terms. The results show that the flow-induced bend-twist coupling effects impact the natural frequencies and damping coefficients, and such effects grow with increasing fluid density and flow speed. Hence, the flow-induced bend-twist coupling effects are more critical for hydrofoils than airfoils, particularly for the twisting mode. Ignoring the flow-induced bend-twist coupling terms leads to an incorrect prediction of flutter speed and over-prediction of the damping, which is dangerous because the actual vibrations and dynamic load amplification may be higher than the prediction, which could lead to accelerated fatigue. The results demonstrate that flexible hydrofoils have much lower natural frequencies and higher damping coefficients than airfoils due to higher fluid inertial and damping forces, both of which are proportional to the fluid density. While all components of the fluid forces are proportional to the fluid density, the fluid damping forces grow with the velocity, and the fluid disturbing forces grow with velocity square. Therefore, divergence tends to be the governing instability mode for hydrofoils, while flutter is typically the governing instability mode for airfoils. The maximum aero/hydro-elastic bending and twisting deformations are limited by the corresponding reduced stable velocity to avoid divergence or flutter.

Stacking sequence optimization of doubly-curved laminated composite shallow shells for maximum fundamental frequency by sequential permutation search algorithm

A sequential permutation search (SPS) optimization algorithm is proposed for the stacking sequence design of doubly-curved laminated composite shallow shells. The SPS algorithm takes advantages of the inherent physical–mechanical features of composite laminates that the outer layers contribute more than the inner layers to bending rigidity and the convexity of lamination parameters. In SPS, the linear and nonlinear sensitive detection techniques are introduced, which detect the sensitive ply orientation at a proper stacking position. By assigning identical ply orientation at respective stacking position, and designing the stacking sequence from the inner to the outer positions sequentially and iteratively using the sensitive ply orientation, the solution will converge to the optimum when no sensitive ply orientation can be detected at any stacking position. In addition, the bending-twisting coupling effects of the laminates are regulated by means of a sign optimization algorithm (SOA) coupled in SPS. The stacking sequences of doubly-curved laminated composite shallow shells exhibit various boundaries and geometries are optimized to maximize the fundamental frequency, and the Rayleigh-Ritz method is developed for vibration analysis. The optimal results are compared with those of layerwise optimization approach and genetic algorithm, demonstrating the robustness and efficiency of the SPS algorithm.

Stacking sequence optimization of composite cylindrical panels by sequential permutation search and Rayleigh-Ritz method

A novel sequential permutation search (SPS) optimization algorithm is proposed for the stacking sequence design of composite cylindrical panels to maximize the fundamental frequency. The SPS exploits the sensitive information of bending stiffness, the convex property of lamination parameters, and the bending-twisting coupling feature of composite laminates. By assigning identical ply orientation at respective stacking positions and designing the sign configuration independently, a good initial point is identified. Subsequently, sensitive ply orientation is detected at the innermost position or a specific stacking position, and this sensitive ply orientation is adopted to replace other existing ply orientations from the inner to the outer position to seek the optimum. Such procedures are repeated till no sensitive ply orientation is available at any stacking position. In addition, the sign optimization algorithm (SOA) is coupled in the SPS to regulate the bending-twisting coupling effects. The Rayleigh-Ritz method is developed to assess the vibration frequencies which can accommodate arbitrary boundaries. The optimal results of the SPS are compared with those of layerwise optimization approach (LOA) and genetic algorithm (GA), demonstrating the robustness and efficiency of SPS.

Stacking sequence optimization for maximum buckling load of simply supported orthotropic plates by enhanced permutation search algorithm

An enhanced permutation search (EPS) algorithm is proposed for stacking sequence optimization of simply supported orthotropic plates to maximize the buckling load. By taking advantage of the approximate linear superposition regular of buckling load factor and accounting for the nonlinear effects of buckling mode as well as the non-dimensional anisotropic coefficients, the stacking sequence design is decomposed to three phases. First, the best ply orientations are identified using the sequential permutation table with multiple buckling modes. Secondly, the stacking sequence is designed from the mid-plane to the outermost position sequentially within a nested-loop search accounting for the buckling mode. Thirdly, the signs of the ply orientations are designed independently to control the bending–twisting coupling effects. Numerical examples are presented to verify the robustness and efficiency of the EPS, and the results are compared with those of heuristic algorithms. Better optimal solutions are obtained by EPS, with higher efficiency.

Semi-analytical optimal solution for maximum buckling load of simply supported orthotropic plates

The buckling characteristic of rectangular orthotropic plates under axial compression with simply supported boundary has been extensively studied. To enhance the structural efficiency, the stacking sequence of laminate should be optimized to maximize the critical buckling load. In this study, the discrete stiffness parameters are employed to yield the theoretical optimal ply orientation corresponding to the maximum critical buckling load at a layer level, and the buckling mode shapes are calculated analytically. Subsequently, the derivation is performed based on optimal ply orientation to derive the optimal stacking sequence of the laminate, in which a sign vector is adopted to minimize the bending-twisting coupling effects. As a result, two laminate optimal design problems are solved: maximizing critical buckling load with fixed thickness, as well as minimizing the thickness with buckling constraint. Two numerical examples are adopted to verify the yielded optimal solutions. Lastly, the theoretical optimal ply orientations exhibiting different load ratios and aspect ratios are presented.

Numerical analysis on propulsive efficiency and pre-deformated optimization of a composite marine propeller

The objectives of this paper are to numerically investigate the performance of a composite propeller through bidirectional FSI algorithm combining CFD and FEM, and to improve its propulsive efficiency by a pre-deformated method. Numerical results are presented for the composite propeller which has been modeled by unidirectionally stacking with glass-fiber reinforced composites. The propulsive efficiency of the composite and rigid propellers with different advance coefficients J has been compared. The results show that the efficiency of the composite propeller is obviously higher than that of the rigid propeller when J≤0.8, which is attributed to the decrease of pitch angle caused by the bend-twist coupling effects. But for the design condition J=0.851 and the cases with J 0.851, the efficiency of the composite propeller is significantly lower than that of the rigid propeller, which is because the angle of attack αcomposite is deviated from the optimal angle of attack αdesign more than that for the rigid case αrigid. Based on the optimization by the proposed pre-deformated method, the efficiency improvement of the composite propeller at the conditions with J≥0.851 could be obtained, and the composite material used in this work can meet the strength requirement of the designed propellers.

Compression and shear buckling performance of finite length plates with bending-twisting coupling

This article investigates the compression and shear buckling performance of finite length Bending-Twisting coupled laminated plates with simply supported edges. New contour maps are developed, representing non-dimensional buckling factors, which are superimposed on the lamination parameter design spaces for laminates with standard ply orientations. Changes in buckling mode for finite length plates complicate the contour maps, which are shown to be continuous only within discrete regions of the lamination parameter design space and are strongly influenced by plate aspect ratio. The contour maps also serve to demonstrate the degrading effect of Bending-Twisting coupling on compression buckling performance as well as providing new insights into shear buckling performance improvements, including optima that are non-intuitive. The adoption of two recently developed laminate databases, to which common design rules are now applied, including ply percentages and ply contiguity constraints, ensure that the conclusions drawn are based on practical rather than hypothetical designs.

An investigation on design of signs in composite laminates to control bending-twisting coupling effects using sign optimization algorithm

A sign optimization algorithm (SOA) is proposed to design the “±” signs in composite laminates to control the bending-twisting coupling effects. Owing to that the bending-twisting coupling stiffness are cubic on thickness, the innovation is to design the signs of ply orientations from the mid-plane to the outermost sequentially and iteratively. In this manner, the nondimensional anisotropic coefficients are controlled to the target values. Numerical examples are adopted to verify the effectiveness and efficiency of SOA. First, the signs of symmetric laminates [θ32]s are optimized with various boundaries, load ratios, and aspect ratios to show the bending-twisting coupling effects on bending, buckling, and vibration responses of composite plates. Second, the bending-twisting coupling effects are minimized since they may cause large errors in buckling load prediction when using closed-form solution after neglecting them. Third, the optimal sequences obtained from heuristic algorithms are employed for sign optimization. Results show that the bending-twisting coupling effects cannot be neglected; moreover, the buckling and vibration performances can be further improved by redesigning “±” signs in composite laminates. This research aims to provide a design technique to minimize the error induced by bending-twisting coupling and increase the probability to find the global optimum.

Load-dependent bend-twist coupling effects on the steady-state hydroelastic response of composite hydrofoils

The objective of this work is to present combined experimental and numerical studies of load-dependent bend-twist coupling effects on the steady-state hydroelastic response of composite hydrofoils. Experimental studies are presented for three composite and one stainless steel hydrofoils, all with the same unloaded geometry and mounted in the same cantilevered configuration. The stainless steel hydrofoil serves as the rigid baseline. The three composite hydrofoils are all made of epoxy resin reinforced with the same nominal layup of carbon fiber reinforced polymers and glass fiber reinforced polymers, with the primary difference being the orientation of the structural carbon layers relative to the spanwise axis of the hydrofoils. To compliment the experimental studies, a simple two-degrees of freedom fluid-structure interaction model is presented. The results show that material bend-twist coupling that leads to nose-up twist will experience higher hydrodynamic load coefficients, accelerated stall and static divergence, while the opposite is true for material bend-twist coupling that leads to nose-down twist. The non-dimensional hydrodynamic load coefficients for all four hydrofoils can be collapsed into the same trend line using the effective incidence, which is the geometric incidence plus the generalized tip twist angle. The results show good agreement between the experimental measurements and numerical predictions.

Effect of bending-twisting coupling on the compression and shear buckling strength of infinitely long plates

This article describes the development of closed form polynomial equations for compression and shear buckling to assess the effect of Bending-Twisting coupling on infinitely long laminated plates with simply supported edges. The equations are used to generate contour maps, representing non-dimensional buckling factors, which are superimposed on the lamination parameter design spaces for laminates with standard ply orientations. The contour maps are applicable to two recently developed databases containing symmetric and non-symmetric laminates with either Bending-Twisting or Extension-Shearing Bending-Twisting coupling. The contour maps provide new insights into buckling performance improvements that are non-intuitive and facilitate comparison between hypothetical and practical designs. The databases are illustrated through point clouds of lamination parameter coordinates, which demonstrate the effect of applying common design heuristics, including ply angle, ply percentage and ply contiguity constraints.

Influence of flow-induced bend–twist coupling on the natural vibration responses of flexible hydrofoils

For flexible hydrofoils, the natural flow-induced bending and twisting deformations are coupled if the center of lift is away from the elastic axis; this coupling may be influenced by viscous effects due to movement in the center of lift. The objective of this work is to investigate the role of flow-induced bend–twist coupling effects, as well as their dependence on the reduced velocity and solid-to-fluid added mass ratio. A secondary objective is to compare inviscid and viscous fluid–structure interaction (FSI) simulations of the natural flow-induced vibration responses of flexible cantilevered hydrofoils in water. The focus is on attached flow conditions in fully turbulent regimes at low angles of attack, where inviscid FSI method should be relatively accurate, and the foil response should be dominated by the foil's natural frequencies. The viscous FSI model is formulated by coupling a two-dimensional (2D) unsteady Reynolds-averaged Navier–Stokes (URANS) model with a two-degrees-of-freedom (2-DOF) model representing the spanwise tip bending and twisting deformations. The results show that the flow-induced bend–twist coupling terms are important for accurate prediction of the natural vibration frequencies and damping characteristics, particularly for the twisting motion, and their relative importance grows when the relative velocity increases and the solid-to-fluid added mass ratio decreases.

On Bending-Twisting coupled laminates

The definitive list of stacking sequences is presented for Bending-Twisting coupled (ASB0DF) laminates, with up to 21 plies. This class of laminate arises from the ubiquitous balanced and symmetric design rule, but symmetry is shown to be a sufficient rather than a necessary constraint. Each stacking sequence configuration is derived in symbolic form together with dimensionless parameters from which the extensional and bending stiffness terms are readily calculated for any fibre/matrix system and angle-ply orientation. Expressions for ply orientation dependent lamination parameters are also given, together with graphical representations, which demonstrate the extent of the design space. Pseudo Quasi-Homogeneous (ASB0DF) laminates are introduced as an important laminate sub-set, since such laminates have concomitant orthotropic properties, i.e. matching orthotropic or isotropic stiffnesses in extension and bending, from which the isolated effects of Bending-Twisting coupling can be studied. These coupling effects are quantified for compression buckling of Angle-ply and Quasi-Isotropic laminated plates with simply supported and clamped edges.

Investigation of the effect of bending twisting coupling on the loads in wind turbines with superelement blade definition

Bending-twisting coupling in the composite blades is exploited for load alleviation in the whole turbine system. For the purpose of the study, inverse design of a reference blade is performed such that sectional beam properties of the 3D blade design approximately match the sectional beam properties of NREL's 5MW turbine blade. In order to appropriately account for the bending-twisting coupling effect, dynamic superelement of the blade is created and introduced into the multi-body dynamic model of the wind turbine system. Initially, a comparative study is conducted on the performance of wind turbines which have blades defined as superelements and geometrically nonlinear beams, and conclusions are inferred with regard to the appropriateness of the use of superelement blade definition in the transient analysis of the 5MW wind turbine system that is set up in the present study. Multi-body dynamic simulations of the wind turbine system are performed for the power production load case with the constant wind and the normal turbulence model as external wind loadings. For the internal loads, fatigue damage equivalent load is used as the metric to assess the effect of bending-twisting coupling on the load alleviation in the whole wind turbine system. Results show that in the overall, through the bending-twisting coupling induced with the use of off-axis plies in the main spar caps of the blade, damage equivalent loads associated with the critical load components can be reduced in the wind turbine system.

Bend-twist coupling potential of wind turbine blades

In the present study an evaluation of the potential for bend-twist coupling effects in wind turbine blades is addressed. A method for evaluation of the coupling magnitude based on the results of finite element modeling and full-field displacement measurements obtained by experiments is developed and tested on small-scale coupled composite beams. In the proposed method the coupling coefficient for a generic beam is introduced based on the Euler-Bernoulli beam formulation. By applying the developed method for analysis of a commercial wind turbine blade structure it is demonstrated that a bend-twist coupling magnitude of up to 0.2 is feasible to achieve in the baseline blade structure made of glass-fiber reinforced plastics. Further, by substituting the glass-fibers with carbon-fibers the coupling effect can be increased to 0.4. Additionally, the effect of introduction of bend-twist coupling into a blade on such important blade structural properties as bending and torsional stiffness is demonstrated.