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On the post-buckling behaviour and imperfection sensitivity of regular convex polygonal columns
Published in Amin Heidarpour, Xiao-Ling Zhao, Tubular Structures XVI, 2018
R. Gonçalves, D. Camotim, André D. Martins
The most deformed configuration of the column containing the mode 1 e = 0.1 mm imperfection also exhibits local buckles at diametrically opposite walls, whereas its mode 2 counterpart has two closely spaced local buckles appearing in a single wall. The latter deformed configuration is also observed for the two columns containing a 0.2 mm imperfection (mode 1 and mode 2) – they are not shown in Figure 6. Finally, the columns containing 0.5 mm exhibit either one (mode 1) or two (mode 2) local buckles, in both cases appearing in either a single or diametrically opposite walls – these deformed configurations are also not shown in Figure 6. It should be noted that these column deformed configurations resemble that caused by the so-called Brazier effect in circular tubes subjected to bending – of course, in this case the RCPS flattening is due to compression and, thus, local buckles may appear in both sides of the flattened cross-section.
Analytical modelling of non-uniform deformation in thin-walled orthotropic tubes under pure bending
Published in J.A. Packer, S. Willibald, Tubular Structures XI, 2017
M.A. Wadee, M.K. Wadee, A.P. Bassom
The response to homogeneous bending of thin-walled tubular members with circular cross-sections has been well documented for nearly eighty years (Brazier 1927). The principal phenomenon associated with this is the so-called Brazier effect which manifests itself as an ovalization of the initially circular cross section during pure bending. However, most of the work in this field has tended to assume that the cross section ovalization is uniform along the length of the member; a good assumption for small deflections and bending to small curvatures, but practically this breaks down when deflections become large and engineer’s bending theory becomes inadequate. The Brazier effect can lead to instability, with increasing curvature the material within the zone of compression can buckle locally. In terms of the relationship between moment M and curvature κ the gradient, which is initially constant, fades away and a limiting value of M is encountered when buckling occurs; the deformation seen in the tube becomes decidedly nonuniform, a regime of negative stiffness is encountered and kinks tend to form in many cases.
Continuum modeling of nonlinear buckling behavior of CNT using variational asymptotic method and nonlinear FEA
Published in Mechanics of Advanced Materials and Structures, 2023
Renuka Sahu, Dineshkumar Harursampath, Sathiskumar A. Ponnusami
The high slenderness ratio of CNTs results in extremely large deformation under bending loads and this nonlinear deformation seen in many shell structures [54], is intensified by cross-sectional geometrical nonlinearity due to the thin-walled nature of CNT geometry and its high radius-to-thickness ratio, causing ovalisation of the initially circular cross section [55]. This nonlinear behavior decreases stiffness and increases bending deformation even under reduced loadings, potentially leading to local buckling of the CNT and poor mechanical response of the overall structure. Harursampath et al. [56] demonstrated the impact of nonlinear cross-sectional deformations in thin beams, where the thickness-to-radius ratio ≪1. They showed that nonlinear phenomena, such as the Brazier effect, first described by Brazier [57], is the nonlinear growth in the curvature of thin-walled isotropic cylindrical tubes under pure bending caused by ovalisation in the cross section, leading to collapse at a specific maximum moment. This nonlinear cross-sectional behavior becomes significant for CNTs, as they also have a small thickness-to-radius ratio, which is the main contributor to this effect. Although continuum theories successfully capture the buckling phenomena of nanoscale CNTs, they do not delve deep into the deformation shapes, geometric nonlinearity, and nonlinear effects in thin small structures, such as the Brazier effect. Atomistic models although capable of capturing exact geometry of CNTs however, are limited by the high computational time and effort requirements, which may not always be necessary to analyze continuum structures. Duan et al. [58] used a hybrid model using the classical inelastic beam and shell theory and molecular mechanics and incorporated the nature of atomic structures by fitting parameters with the MD principle. They identified the geometrical parameters for which the CNT will behave as a beam while buckling or shell upon buckling. Both these buckling modes are found to occur in CNTs and can be differentiated as: beam like buckling has that the central axis of beam deflects sideways during buckling whereas for shell like buckling the tube buckles sideways but maintains its central axis. Harik [59] established a set of geometrical conditions which define the aspect ratio and ratio of radius and thickness for CNTs to determine the applicability of the beam model based on continuum theories. It can be seen from there criteria that the model used in current work is justified.