A qualitative analytical investigation of geometrically nonlinear effects in wind turbine blade cross sections

Abstract

This article analytically investigates the Brazier effect on asymmetric thinwalled sections subject to biaxial bending. In the latter case a torsional moment -in this paper referred to as Brazier torsion -is induced, which proved to be a vital part of the solution. By means of a generic cross section, that was inspired by a wind turbine blade it is demonstrated that geometric nonlinear effects can induce an in-plane opening deformation in re-entrant corners that may decrease the fatigue life. The opening effect induces Mode-I stress intensity factors which exceed the threshold for fatigue crack growth at loads well below the load-carrying capacity of the beam. The findings in this paper are twofold: Firstly, the investigated analysis procedure can be integrated into the design process of wind turbine blade cross sections. Secondly, the proposed approach serves as a basis for computationally efficient numerical analysis approaches of structures that comprise complex geometry and anisotropic material behaviour -such as wind turbine rotor blades.

Effects of geometric non-linearity on energy release rates in a realistic wind turbine blade cross section

“…An analytical investigation of geometrically non-linear effects on a simple cross-section as discussed in [12] supports this suspicion. These investigations suggest that of all six cross-section forces, bi-axial bending (i.e.…”

“…1 are typical for the multi-directional plies. 12 5.047 × 10 9 1.150 × 10 10 9.413 × 10 9 1.667 × 10 7 1.287 × 10 9 N m −2 Shear modulus G 13 5.047 × 10 9 4.539 × 10 9 4.538 × 10 9 1.500 × 10 8 1.287 × 10 9 N m −2 Shear modulus G 23 5.047 × 10 9 4.539 × 10 9 4.538 × 10 9 1.500 × 10 8 1.287 × 10 9 N m −2 Mass density ρ 1.916 × 10 3 1.845 × 10 3 1.845 × 10 3 1.100 × 10 2 1.350 × 10 3 kg m −3…”

“…A torsional moment M t B per unit-length -in this paper referred to as Brazier torsion -is introduced into the cross section if the bending axis is not aligned with one of the principal bending axes as discussed in [12]. Equation 1 expresses the magnitude of the Brazier torsion as a function of bending moment for a force-controlled analysis.…”

An advanced structural trailing edge modelling method for wind turbine blades

“…Moreover, stability analyses are an essential part of the ultimate strength assessment of wind turbine blades, since buckling can be a failure mode [8,6]. The ultimate limit state of wind turbine rotor blades depends heavily on local cross-sectional deformation, which is a highly nonlinear phenomenon and varies depending on the load congurations [9,8,6,10,11]. Crosssection deformations are often provoked by combined load situations, where, for example, bending moments and torsional moments act simultaneously and need detailed and accurate prediction models able to handle these challenges.…”

Accuracy of an efficient framework for structural analysis of wind turbine blades

“…Future work will focus on the study of nonlinear effects like, e.g., geometrically nonlinear deformation of the trailing edge panels can be observed at relatively low loads (e.g., in the literature). 16 The paper is divided as follows. The theoretical methodology underlying the BECAS framework is described in the next section.…”