The influence of an initial twisting on tapered beams undergoing large displacements

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 centre-line. 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.