1,721,188 research outputs found
Design of pre-twisted tapered beamlike structures via efficient yet accurate models and formulas
No full textThe influence of an initial twisting on tapered beams undergoing large displacements
Full text linkThe 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
Analytical Solutions of Partial Differential Equations Modeling the Mechanical Behavior of Non-Prismatic Slender Continua
No full textNon-prismatic slender continua are the prototypical models of many structural elements used in engineering applications, such as wind turbine blades and towers. Unfortunately, closed-form expressions for stresses and strains in such continua are much more difficult to find than in prismatic ones, e.g., the de Saint-Venant’s cylinder, for which some analytical solutions are known. Starting from a suitable mechanical model of a tapered slender continuum with one dimension much larger than the other tapered two, a variational principle is exploited to derive the field equations, i.e., the set of partial differential equations and boundary conditions that govern its state of stress and strain. The obtained equations can be solved in closed form only in a few cases. Paradigmatic examples in which analytical solutions are obtainable in terms of stresses, strains, or related mechanical quantities of interest in engineering applications are presented and discussed
Analytical evaluation of stresses and strains in inhomogeneous non-prismatic beams undergoing large deflections
No full textDamping destabilization in non-conservative mechanical systems: linear and nonlinear effects
No full text
On the inadequacy of a stepped-beam approach in predicting shear stresses in tapered slender solids
Full text link
- …
