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.

预扭曲和渐缩梁（例如涡轮机或直升机叶片）的行为的特征在于应力分布可能与通常的梁理论完全不同，从而在弯曲，扭曲和牵引之间产生耦合。我们提出了锥形束的物理数学模型，该模型考虑了沿中心线的横截面的预扭曲效应。梁的中心线可能会发生较大的位移，而其横截面在其平面内外均会出现较小的翘曲。假设无穷小应变，则变分方法提供了场方程，这些场方程受较小的几何比率的干扰，通常应在数值上求解。但是，在某些情况下，存在解析的封闭形式的解决方案，例如对于具有预扭曲，双锥度椭圆形截面的各向同性梁；等等。