Analytical prediction of the cross-sectional shear flow in non-prismatic inhomogeneous beamlike solids

Abstract

Non-prismatic beamlike elements are widespread in engineering applications. Unfortunately, analytical methods commonly used for stress analyses in prismatic beams provide mispredictions in non-prismatic cases. Referring for instance to components like towers and blades of large horizontal axis wind turbines, whose main length is much larger than the dimensions of the tapered transverse cross-sections, the cross-sectional taper produces shear stress distributions that are quite different from those obtainable by formulas valid in prismatic beams, notwithstanding the slender shape of such components, the limited magnitude of their tapering slopes, and the possible Navier-like distribution of their cross-sectional normal stresses. Here, we address the analytical determination of the cross-sectional stresses in elements of this kind, which are slender, non-prismatic, inhomogeneous, and susceptible to large deflections. Recalling the results of a recent work by the author, the field equations that govern the state of stress in the considered elements are exploited to obtain a new closed-form expression of the cross-sectional shear flow, which, in turn, can be used for stress predictions. Comparisons with results of non-linear 3D-FEM analyses for elements mimicking the shape of components used in applications confirm the effectiveness of the proposed analytical approach and formulas.