Cross-sectional Stiffness Properties Research Articles

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.

Integrated Design of Aerodynamic Performance and Structural Characteristics for Medium Thickness Wind Turbine Airfoil

The currently geometric and aerodynamic characteristics for wind turbine airfoils with the medium thickness are studied to pursue maximum aerodynamic performance, while the interaction between blade stiffness and aerodynamic performance is neglected. Combining the airfoil functional integration theory and the mathematical model of the blade cross-section stiffness matrix, an integrated design method of aerodynamic performance and structural stiffness characteristics for the medium thickness airfoils is presented. The aerodynamic and structural comparison of the optimized WQ-A300 airfoil, WQ-B300 airfoil, and the classic DU97-W-300 airfoil were analyzed. The results show that the aerodynamic performance of the WQ-A300 and WQ-B300 airfoils are better than that of the DU97-W-300 airfoil. Though the aerodynamic performance of the WQ-B300 airfoil is slightly reduced compared to the WQ-A300 airfoil, its blade cross-sectional stiffness properties are improved as the flapwise and edgewise stiffness are increased by 6.2% and 8.4%, respectively. This study verifies the feasibility for the novel design method. Moreover, it also provides a good design idea for the wind turbine airfoils and blade structural properties with medium or large thickness.

Stability Analysis of Columns with Imperfection

In this paper, geometrically exact fully intrinsic equations and variational asymptotic beam sections are used to study the buckling and postbuckling of a column under self-weight. Initial curvature effects both generalized one-dimensional beam equations and the cross-sectional stiffness properties. The effects of initial curvature have been studied on buckling and postbuckling in this paper. This problem is a valuable test case for the utility of the fully intrinsic equations and variational asymptotic beam sections.

Wind Turbine Cross-Sectional Stiffness Analysis Using Internally Layered Solid Elements

An efficient finite element modeling approach is presented for analyzing the general cross-sectional stiffness properties and stress distribution of thin- and thick-walled sections with isotropic and general anisotropic materials. The procedure is based on discretizing the walls of the section using a single layer of displacement-based elements whereby the element’s stiffness is obtained using Gaussian quadrature through each layer. The interlaminar stresses are recovered at points of interest via a three-dimensional equilibrium-based postprocessing scheme that uses the distribution of in-plane stress gradients derived in the local laminate coordinate system. The theory is illustrated by application to three composite sections of various shapes and material layups.

On the behavior of thin walled composite beams with stochastic properties under matrix cracking damage

Thin walled composite beam structures are prone to damage which results in change in the performance of these structures. The change in the performance due to damage may get confused with the variation in the performance due uncertainties in the properties of these structures. Here, the performances of the thin walled composite beam under matrix cracking damage having material uncertainties are studied. The cross-sectional stiffness properties are obtained using thin walled beam formulation, which is based on a mixed force and displacement method. The stochastic behaviors of material properties are obtained from previous experimental and analytical studies. The effects of matrix cracking are introduced through the changes in the extension, extension–bending and bending matrices of composites. The effects of matrix cracking on out-of-plane bending, inplane bending and torsion cross-sectional properties are studied at different crack densities for stochastic material properties. Further, the effects of matrix cracking and uncertainties on measurable properties such as deflections and frequencies are studied. Results show that the beam responses at different crack densities get mixed due to the material uncertainties. The estimates of variance obtained for observable system properties due to uncertainty can be used for developing more robust damage detection algorithms.

Aeroelastic Response of Composite Helicopter Rotor with Random Material Properties

This study investigates the effect of uncertainty in composite material properties on the cross-sectional stiffness properties, natural frequencies, and aeroelastic responses of a composite helicopter rotor blade. The elastic moduli and Poisson’s ratio of the composite material are considered as random variables with a coefficient of variation of around 4%, which was taken from published experimental work. An analytical box beam model is used for evaluating blade cross-sectional properties. Aeroelastic analysis based on finite elements in space and time is used to evaluate the helicopter rotor blade response in forward flight. The stochastic cross-sectional and aeroelastic analyses are carried out with Monte Carlo simulations. It is found that the blade cross-sectional stiffness matrix elements show a coefficient of variation of about 6%. The nonrotating rotor blade natural frequencies show a coefficient of variation of around 3%. The impact of material uncertainty on rotating natural frequencies varies from that on nonrotating blade frequencies because of centrifugal stiffening. The propagation of material uncertainty into aeroelastic response causes large deviations, particularly in the higher-harmonic components that are critical for the accurate prediction of helicopter blade loads and vibration. The numerical results clearly show the need to consider randomness of composite material properties in the helicopter aeroelastic analysis.

Flap–torsion coupling in sandwich beams and filled box sections

Slender aerodynamic structures such as helicopter rotor blades are routinely idealised as 1D beams with associated cross-sectional stiffness properties, and often exhibit structural couplings. A strength of materials based analytical model is presented for determining the cross-sectional stiffness that couples flap bending and torsion (a coupling that is of particular interest in helicopter rotor blade design), by considering strains of individual substructures of the cross-section. The section may be square or rectangular in nature and be foam-filled or hollow. The top and bottom skins may exhibit anisotropic elastic behaviour through non-symmetry and both membrane and flexural anisotropy. This allows a more detailed parametric investigation of this cross-sectional property than is possible with existing analytical models. The analytical model is validated by comparison with a finite element model of the cross-section.

Optimisation of a 4-layer laminated cylindrical shell to meet given cross-sectional stiffness properties

The design of a 4-layer laminated cylindrical shell is considered as an optimisation problem in which the objective is determined as the N-dimensional Euclidean distance between current and target value of various cross-sectional stiffness properties (where N is the number of cross-sectional stiffness properties to be matched). The optimisation problem is made convex by appropriate choice of design variables, allowing a deterministic solution method to be employed. Although such deterministic methods are usually based on linear approximations of the objective function with respect to the design variables, it is found that the optimisation efficiency can be significantly improved by making a linear approximation with respect to each of the cross-sectional properties in turn (rather than the single objective function). The resulting simultaneous linear equations may be easily solved via matrix methods, and a solution to the linearised problem may be obtained directly. Successive iterations remove any discrepancy between the linearised and actual behaviours of the problem.

Obliqueness effects in asymptotic cross-sectional analysis of composite beams

Cross-sectional stiffness properties for general composite beams, along with the interior solution for warping, are derived in such a way as to provide the extra freedom to choose a cross-sectional plane that is not perpendicular to the local beam reference line. The present development treats prismatic as well as initially twisted and curved beams. The main purpose of allowing such a choice of coordinate systems is for the convenience of the analyst; one, of course, should not expect the final 3D results to change. The 3D strain field is derived for the corresponding nonorthogonal curvilinear set of coordinates which describe the undeformed and the deformed geometry of the beam. The analysis is carried out based on the variational-asymptotic method which is used to determine the warping field. For the development of the solution, it is shown that there is a fundamental difference between the solutions for a prismatic beam and a beam with initial twist and curvature, which in turn produces a limitation of the angle of obliqueness: the effect of obliqueness is treated exactly for a prismatic beam, while for the initially twisted and curved beam the obliqueness is regarded as a small parameter. The ultimate goal of the analysis is the determination of the cross-sectional stiffness matrix, which can then be used as input for the 1D problem. Then, using the recovering relations, one can recover the strain field over the entire cross section, once the previous problem has been solved. The validity of the method is demonstrated by recovery of accurate cross-sectional stiffnesses associated with a normal cross-sectional plane from those associated with an oblique cross-sectional plane, using a simple rotation-of-axes transformation.