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Abstract
The geometry of wind turbine blades is characterised by the aerodynamic lift generating surface which results in lengthwise geometrical variations (LGVs), namely tapered and twisted cross sections and precurved longitudinal axis. In particular, a tapered beam presents crosssection dimensions which smoothly vary along its longitudinal span and affects the behaviour of the structure. Hence, the stress distributions in tapered structures can be at significant variance with the ones occurring in prismatic beams. The early stages of wind turbine blade design are based on simplified beam models to reduce the computational cost otherwise entailed by 3D full finite element models. The crosssection stiffness properties required for aeroelastic analysis and the prediction of the strains/stresses for structural design and optimization purposes are provided by crosssection analysis methods. Nowadays, the available crosssection analysis methods are based on prismatic hypothesis and consequently the aforementioned taper effects are ignored, notwithstanding the available scientific literature on this matter.
The first part of the thesis sheds light on the effects of taper on the stresses in thinwalled isotropic beams with circular and rectangular cross sections. Elasticity theory is employed to derive closedform analytical solutions which are compared to 3D finite element models for validation purposes. The analytical equations of the Cauchy stress components provide an insight into the role of taper in the beam behaviour. Indeed, taper evokes geometrical couplings which considerably affect the stress state of the beam. Particularly, shearaxial and shearbending contributes to the definition of the inplane shear component and significantly affect the inplane shear both qualitatively and quantitatively. For instance, neglecting taper effect in structures such as wind turbine blades could result in underestimating the shear components in the proximity of the web adhesive joints, and, therefore, to detrimental designs. In addition, the provided closedform solutions could be employed for validation of tapered crosssectional analysis tools. In addition, the provided expressions could be used for validation of tapered crosssectional analysis tools.
The second part of the thesis investigates an alternative finite element method which suits for crosssection analysis of tapered beams. It models the beam crosssection as a tapered slice consisting of onelayered of solid finite elements. The nodal forces equivalent to axial, bending and shear are derived from the assumed surface traction
acting on the two faces of the slice. In addition, constraint equations for the six rigid body modes, namely three translations and three rotations, are enforced via the Lagrange multiplier method. Parametric studies of the relation between the stresses and the magnitude of the taper angles and the thickness of the slice are conducted on a planar isotropic wedge, whose closedform solutions in terms of stresses are known. Results reveal the ability of the slice method to predict approximately the stresses in the tapered crosssections of the wedge.
The present study underlines the importance of the taper effects on the stress components of a tapered beam. Neglecting taper effects can result in a inaccurate stress prediction and accordingly lifetime calculation of tapered beams. The outcome of this project places the foundations for the development of a new advanced tapered crosssection analysis tool where a more accurate prediction of the stress components and lifetime of tapered structures is achieved without exploiting high computational tools.
The first part of the thesis sheds light on the effects of taper on the stresses in thinwalled isotropic beams with circular and rectangular cross sections. Elasticity theory is employed to derive closedform analytical solutions which are compared to 3D finite element models for validation purposes. The analytical equations of the Cauchy stress components provide an insight into the role of taper in the beam behaviour. Indeed, taper evokes geometrical couplings which considerably affect the stress state of the beam. Particularly, shearaxial and shearbending contributes to the definition of the inplane shear component and significantly affect the inplane shear both qualitatively and quantitatively. For instance, neglecting taper effect in structures such as wind turbine blades could result in underestimating the shear components in the proximity of the web adhesive joints, and, therefore, to detrimental designs. In addition, the provided closedform solutions could be employed for validation of tapered crosssectional analysis tools. In addition, the provided expressions could be used for validation of tapered crosssectional analysis tools.
The second part of the thesis investigates an alternative finite element method which suits for crosssection analysis of tapered beams. It models the beam crosssection as a tapered slice consisting of onelayered of solid finite elements. The nodal forces equivalent to axial, bending and shear are derived from the assumed surface traction
acting on the two faces of the slice. In addition, constraint equations for the six rigid body modes, namely three translations and three rotations, are enforced via the Lagrange multiplier method. Parametric studies of the relation between the stresses and the magnitude of the taper angles and the thickness of the slice are conducted on a planar isotropic wedge, whose closedform solutions in terms of stresses are known. Results reveal the ability of the slice method to predict approximately the stresses in the tapered crosssections of the wedge.
The present study underlines the importance of the taper effects on the stress components of a tapered beam. Neglecting taper effects can result in a inaccurate stress prediction and accordingly lifetime calculation of tapered beams. The outcome of this project places the foundations for the development of a new advanced tapered crosssection analysis tool where a more accurate prediction of the stress components and lifetime of tapered structures is achieved without exploiting high computational tools.
Original language  English 

Place of Publication  Roskilde, Denmark 

Publisher  DTU Wind Energy 
Number of pages  154 
DOIs  
Publication status  Published  2020 
Series  DTU Wind Energy PhD 

Number  1013(EN) 
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Dive into the research topics of 'Advanced accurate and computationally efficient numerical methods for wind turbine rotor blade design'. Together they form a unique fingerprint.Projects
 1 Finished

Advanced Accurate and Computationally Efficient Numerical Methods for Wind Turbine Rotor Blade Design
Bertolini, P., Lindby, T., Sarhadi, A., Eder, M., Jensen, J. S., Izzuddin, B. & Rolfes, R.
15/02/2017 → 12/11/2020
Project: PhD