The behaviour of pre-twisted and tapered beams (such as turbine or helicopter blades) is characterized by stress distributions that may be quite different from those of the usual beam theory, yielding couplings among bending, twisting and traction. We propose a physical-mathematical model for tapered beams that accounts for the effects of the pre-twist of the cross-sections along the centreline. The beam centre-line may undergo large displacements, while its cross-sections see small warping both in-and out of their plane. Supposing infinitesimal strain, a variational approach provides the field equations, which are perturbed in terms of a small geometric ratio and shall be solved numerically in general. However, analytical closed-form solutions exist in some cases, such as for isotropic beams with pre-twisted, bi-tapered elliptic cross-sections; they are presented and compared with the results of nonlinear 3D-FEM simulations.
Abstract. Continuous ongoing efforts to better predict the mechanical behaviour of complex beamlike structures, such as wind turbine blades, are motivated by the need to improve their performance and reduce the costs. However, new design approaches and the increasing flexibility of such structures make their aeroelastic modelling ever more challenging. For the structural part of this modelling, the best compromise between computational efficiency and accuracy can be obtained via schematizations based on suitable beamlike elements. This paper addresses the modelling of the mechanical behaviour of beamlike structures which are curved, twisted and tapered in their unstressed state and undergo large displacements, in- and out-of-plane cross-sectional warping, and small strains. A suitable model for the problem at hand is proposed. Analytical and numerical results obtained by its application are presented and compared with results from 3D FEM analyses.
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