Brazier Effect of Thin Angle-Section Beams under Bending

Thin-walled section beams have Brazier effect to exhibit a nonlinear response to bending moments, which is a geometric nonlinearity problem and different from eigenvalue problem. This paper is aimed at investigating the Brazier effect in thin-walled angle-section beams subjected to pure bending about its weak axis. The derivation using energy method is presented to predict the maximum bending moment and section deformation. Both numerical analyses and experimental results were used to show the validity of the proposed formula. Numerical results show that the boundary condition can influence the results due to the end effect, and that the influence tends to be negligible when the length of angle beam goes up to 30 times as the length of beam side. When the collapse in experiments is governed by Brazier flattening, the moment vs. curvature curve deviates significantly from the linear beam theory, but coincides well with the proposed formula in consideration of the restraint due to limited span of experimental setup. It can be concluded that the proposed formula shows good agreement with numerical results and experimental results.

Concept for a Deployable Wing

A concept for a novel folding wing is presented, which, using the Brazier effect, can snap from a stable, extended position to a folded configuration. A wing typical of size used in an unmanned aircraft vehicle (UAV) is examined, including manufacturing aspects as well as an analytical and a finite element model (FEM) of the structure. The wing is simply made of a glass fiber reinforced plastic (GFRP) skin stiffened by ribs at regular intervals. At the mid-span location, a cut-out is made in the leading and trailing edge in order to allow the pressure and suction sides of the wing to collapse inward when folding occurs (due to Brazier effect). The analytical model draws upon work from Brazier to predict the maximum bending moment the folding section can withstand before buckling. A FEM, using a quasi-static analysis and requiring a contact definition to allow the wing surfaces to meet, reproduces with accuracy the folding pattern seen on the prototype. A bending test of the demonstrator confirmed the validity of the models in terms of bending stiffness, bending snap through and folding radius of curvature.

Suppression of Brazier Effect in Multilayered Cylinders

When a straight hollow tube having circular cross-section is bent uniformly into an arc, the cross-section tends to ovalize or flatten due to the in-plane stresses induced by bending; this ovalization phenomenon is called the Brazier effect. The present paper is aimed at theoretical formulation of the Brazier effect observed in multilayered cylinders, in which a set of thin hollow cylinders are stacked concentrically about the common axis. The results indicate that mechanical couplings between stacked cylinders are found to yield pronounced suppression of the cross-sectional ovalization. Numerical computations have been performed to measure the degree of suppression in a quantitative manner and to explore how it is affected by the variations in the bending curvature, the number of stacked cylinders, and the interlayer coupling strength.