Interactive buckling in thin-walled rectangular hollow section struts

Thin-walled rectangular hollow section (RHS) struts are widely used in current structural engineering practice due to their mass efficiency and relative ease of manufacture. Owing to their optimized geometric properties, they are vulnerable to local--global interactive buckling and exhibit highly unstable post-buckling behaviour with severe imperfection sensitivity when the local buckling load is close to the global buckling load. The current work investigates the underlying mechanism of local–global interactive buckling of RHS struts using both analytical and finite element (FE) approaches. Variational models formulated using analytical techniques, describing the nonlinear local–global mode interaction in thin-walled RHS struts with varying flange–web joint rigidity, different strut lengths and geometric imperfections under pure compression, are presented. A system of nonlinear differential and integral equations subject to boundary conditions is formulated and solved using numerical continuation techniques. For the first time, the equilibrium behaviour of such struts with different cross-section joint rigidities is highlighted with characteristically unstable interactive buckling paths and a progressive change in the local buckling wavelength. Studies on the effects of strut length identify the boundaries for the four distinct length-dependent zones, where different characteristic post-buckling behaviour are exhibited. The most unstable zone is demonstrated to have a considerably narrower range than previously determined owing to the consideration of more realistic corner boundary conditions within the cross-section. Imperfection sensitivity studies identify the high degree of sensitivity of struts exhibiting mode interaction. They also reveal that local and global imperfections are relatively more significant where global and local buckling are critical respectively. Moreover, a unified local geometric imperfection measurement based on equal local bending energy is proposed to determine the most severe local imperfection profile. It reveals that the most severe profile is modulated rather than periodically distributed along the strut length for purely elastic case. For verification and extensive parametric study purposes, a nonlinear FE model, which considers material nonlinearity, geometric imperfections, and residual stresses, is developed within the commercial package Abaqus. The classical solutions and experimental results from two independent studies are used to verify and validate the FE model, both of which show excellent comparisons. The validated FE model is then used to verify the variational model, which also shows excellent comparisons in local buckling wavelengths, cross-section deformation profile, ultimate load and the mechanical behaviour. Finally, parametric studies on geometric properties, material nonlinearity and residual stresses are conducted using the developed FE model to understand the behaviour of RHS struts exhibiting mode interaction in more practically realistic scenarios. Based on the numerical results and existing experimental results from the literature, the current design rules for thin-walled welded RHS struts are assessed by means of reliability analysis in accordance with Annex D of EN1990. A modified Direct Strength Method (DSM) equation has been proposed and it is shown to provide a better ultimate load prediction than it does presently.Open Acces

Manufacturing of complex 3D surfaces inspired by biological growth mechanics

Traditionally, engineers avoid residual stresses in manufacturing because residual stresses can lead to undesired geometric distortions and a loss of strength and stiffness. On the other hand, nature astutely exploits residual stresses to create complex morphologies. For example, residual stresses induced from in-plane differential growth have been identified as a key mechanism in fractal rippling at the edges of leaves [2] and the blooming of flowers [1]. Here, we demonstrate the feasibility of creating complex 3D geometries (non-developable surfaces) from 2D developable surfaces by tailoring residual stresses during manufacturing, with a focus on tow-steered fibre-reinforced composite materials. Fibre-reinforced composite materials have orthotropic properties (thermal expansion factors and Young’s modulus) and by smoothly blending the fibre direction along curvilinear trajectories, tailored in-plane residual stress distributions can be induced during post-cure cooling that then lead to a target shape through a loss of stability of the developable metric. An in-house nonlinear FE solver with extended stability capabilities (bifurcation pinpointing and branch switching) is adopted to simulate the manufacturing process of three benchmark structures, i.e. a rectangular strip (to mimic the rippling at the edge of a leaf), a cylindrical shell (to mimic the edge wrinkling pattern in a daffodil), and a doubly curved thin elastic shell (to mimic the curvature reversal in a blooming lily). We also demonstrate the multi-stability of the manufactured morphologies, which can potentially be exploited for shape-shifting purposes. The present work sheds light on manufacturing complex geometries by precisely tailoring in-plane residual stress distributions.References[1] H. Liang and L. Mahadevan. “Growth, geometry, and mechanics of a bloom- ing lily”. In: Proceedings of the National Academy of Sciences of the United States of America 108.14 (2011), pp. 5516–5521. issn: 10916490.[2] H. Liang and L. Mahadevan. “The shape of a long leaf”. In: Proceedings of the National Academy of Sciences of the United States of America 106.14 (2009), pp. 5516–5521. issn: 10916490