A geometrically nonlinear Generalized Beam Theory (GBT) is formulated and its application leads to a system of equilibrium equations which are valid in the large deformation range but still retain and take advantage of the unique GBT mode decomposition feature. The proposed GBT formulation, for the elastic post-buckling analysis of isotropic thin-walled members, is able to handle various types of loading and arbitrary initial geometrical imperfections and, in particular, it can be used to perform "exact" or "approximate" (i.e., including only a few deformation modes) analyses. Concerning the solution of the system of GBT nonlinear equilibrium equations, the finite element method (FEM) constitutes the most efficient and versatile numerical technique and, thus, a beam FE is specifically developed for this purpose. The FEM implementation of the GBT post-buckling formulation is reported in some detail and then employed to obtain numerical results, which validate and illustrate the application and capabilities of the theory.
The local-plate, distortional and global vibration behaviour of thin-walled steel channel members subjected to compression and/or non-uniform bending is studied. This investigation is carried out by means of a very recently developed Generalised Beam Theory (GBT) formulation, which takes into account the geometrically nonlinear stiffness reduction caused by the presence of (i) longitudinal stress gradients and (ii) the ensuing shear stresses. Taking advantage of the GBT modal features, one analyses the effect of the applied load and bending moment gradient on the small amplitude vibration behaviour of the loaded members (beam-columns). For validation purposes, some GBT-based results are compared with values yielded by either shell finite element analyses, performed in commercial codes, or experimental results available in the literature.
This paper reports the available results of an ongoing numerical investigation aimed at providing fresh insight on the mechanics underlying the local and global post-buckling behaviour of short-to-intermediate equal-leg angle steel columns. Both pinned-ended and fixed-ended columns are analysed and the most of the results presented and discussed concern their elastic buckling and (mostly) post-buckling behaviour − moreover, the elastic-plastic load-carrying capacity of these columns is also briefly addressed, as well as the corresponding design implications. The numerical post-buckling and ultimate strength results presented were obtained by means of ABAQUS shell finite element analyses. In order to help clarifying the distinction between local and global buckling, some GBT-based critical stresses and buckling mode shapes are also displayed and interpreted.
The twist-induced anisotropic behavior of chiral carbon nanotubes (CNTs), namely the (6,3) CNT, under combined tension-twisting is presented and discussed in this paper. CNT chirality triggers anisotropic responses that depend predominantly on the direction of twisting. Both the level of axial tension and twist-induced anisotropy play a key role in the stiffness and strength of the chiral CNT. Molecular dynamics (MD) simulations of (6,3) chiral CNT under pure tension, pure twisting and combined tension-twisting are performed. The anisotropy induced by the twisting direction was shown to be remarkable: the shear modulus for direct twisting is 25% higher than that for inverse twisting whereas the buckling torque for inverse twisting is 40% higher than that for direct twisting. In the post-buckling regime, the ovalization of the CNT is higher for inverse twisting than for direct twisting and we show that ovalization leads to a decrease of post-buckling torsional stiffness. The post-buckling torsional stiffness for direct twisting was much higher than for inverse twisting. We show that the twist-induced anisotropic behavior of the chiral CNT is much more evident when it concerns stiffness than strength. For this chiral CNT under low twist-to-tension ratios, direct twisting has no impact on the failure strain (it equals the pure tensile failure strain) while inverse twisting has great influence on it (it is half the pure tensile strain). The magnitude of the twist-to-tension ratio also affects the post-buckling torsional stiffness of the chiral CNT: under combined tension-twisting, the post-failure structure of the CNT is more ductile for inverse twisting and more brittle for direct twisting. To the authors’ best knowledge, this is the first time the anisotropic behavior of chiral CNT under combined tensile-twisting loads is studied.
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Part I [1] of this two-part paper presented the formulation of a novel progressive failure model for pultruded fibre reinforced polymer (FRP) composites, allowing for the 3D simulation of quasi-orthotropic FRP plates as a homogenized material, as well as the model calibration based on a set of standardized material characterization tests. Part II presents the application of that (calibrated) model to the simulation of two case studies: (i) transverse compact tensile (CT) tests; and (ii) web-crippling tests for two load configurations, external two-flanges (ETF) and internal two-flanges (ITF). The CT test, which is often used to determine the (tensile) fracture energy of FRP materials, is especially interesting as it allows assessing the quality of the simulations for a combination of in-plane transverse tensile and shear stresses in a geometry with a sharp singularity. The web-crippling test, on the other hand, is often used to determine the strength of FRP shapes under concentrated transverse loads, a real structural problem involving combined in-plane compressive and shear stresses. In this paper these two relatively complex case studies are used to assess the quality of the simulation in the presence of combined in-plane stresses. The numerical results showed an excellent agreement with their CT test counterparts; the simulation of these experiments were also used to demonstrate the need for using a mesh regularization scheme when modelling problems with singularities. The models were also well able to simulate both web-crippling load configurations, only slightly underestimating the maximum load – this was likely due to the slight underestimation of shear strength for combined in-plane shear and moderate transverse compressive stresses, as discussed in Part I [1], and/or non-quasi-orthotropic behaviour of the web-flange junction. Overall, the numerical results showed a good agreement with the experimental data, even for relatively coarse meshes, attesting the feasibility and precision of the proposed damage progression model.
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This paper presents a new modal theory for the wrinkling analysis of membranes and discusses the stretch-induced wrinkling behaviour of fixed-ended thin sheets. This modal theory corresponds to an extension of Generalised Beam Theory (GBT) to analyse the wrinkling behaviour of highly stretched sheets. The inherent GBT modal nature adopted in this investigation enables the acquisition of an in-depth knowledge (when compared with the traditional shell finite element analysis) of the behaviour underlying this peculiar buckling phenomena. In order to conduct this study, the work begins by presenting the formulation, describing its main steps and concepts involved in the determination of the “deformation modes” (cross-section analysis), followed by the description of the procedures involved in the development and implementation of the aforementioned formulation that accounts for pre-wrinkling and wrinkling analysis (member analysis). Then, an illustrative example is presented and discussed in detail, which involves the characterisation of the sheet “signature curve” (tensile critical stress vs. length), respective critical wrinkling modes, modal participation diagrams and pre-wrinkling stress distribution patterns. For comparison and validation purposes, refined ABAQUS shell finite element wrinkling results are also reported. Finally, several conclusions are drawn regarding the wrinkling behaviour of stretched sheets, mostly based on the modal nature of this formulation.
An original analytical model to study the non-linear flange curling in wide single-flange panels is presented in this paper. Flange curling phenomenon is the tendency of the wide thin flanges (in compression or tension) to move towards the neutral axis, when thin-walled members are subjected to bending. Despite the simplicity of the formula developed in earlier works of Winter to account for the flange curling effects, which is used in current steel codes, recent work has showed that this expression is rather restrictive and does not apply for all cases. The analytical expressions reported here are rather general since they (i) consider the restraining effect provided by the web, (ii) account for the shift of the neutral axis due to curling, (iii) incorporate the decrement of the second moment of area due to curling, and (iv) are fully analytical, thus avoiding iterative techniques. The analytical model is applied to study the curling behaviour of profiled steel decks and cassette-wall panels and is validated by means of comparisons with experimental results available in the literature. Since the EC3 rules state that the tensioned wide flange in liner trays should be reduced if the curling displacement is higher than 5% of the web height, approximate expressions to evaluate the reduced width of the wide thin flange under curling are proposed.
This paper reports the results of an investigation on the use of Generalised Beam Theory (GBT) to assess the buckling behaviour of steel cylindrical shells (pipes, tubes and pressure vessels) acted by combinations of axial compression and external lateral pressure. Initially, the derivation of an adequate GBT formulation is addressed − it (i) incorporates all the effects stemming from the presence of longitudinal and/or hoop stresses (the latter act in the circumferential direction), and (ii) takes into account the destabilising influence associated with the follower nature of the external pressure, which remains normal to the shell wall along the deformation process. Then, after numerically implementing the above formulation, by means of GBT-based beam finite elements, its application and capabilities are illustrated through the presentation and discussion of numerical results concerning the buckling behaviour of (i) pressure vessels and pipes acted by external pressure and (ii) tubes subjected to combinations of compression and external pressure. For validation purposes, most GBT results are compared with values either available in the literature or yielded by Ansys shell finite element analyses.
This paper presents the incorporation of shear deformation effects into a Generalized Beam Theory (GBT) developed to analyze the structural behavior of composite thin-walled columns made of laminated plates and displaying arbitrary orthotropy. Unlike other existing beam theories, the present GBT formulation incorporates in a unified fashion (i) elastic coupling effects, (ii) warping effects, (iii) cross-section in-plane deformation and (iv) shear deformation. The main concepts and procedures involved in the available GBT are adapted/modified to account for the specific aspects related to the member shear deformation. In particular, the GBT fundamental equilibrium equations are presented and their terms are physically interpreted. An I-section is used to illustrate the performance of GBT cross-section analysis and the mechanical properties are explained in detail. With the purpose of solving the GBT system of differential equilibrium equations, a finite element formulation is briefly presented. Finally, in order to clarify the concepts involved in the formulated GBT and illustrate its application and capabilities, the linear (first-order) and stability behavior of three composite I-section members displaying non-aligned orthotropy are analyzed and the results obtained are thoroughly discussed and compared with estimates available in the literature.
This paper presents a numerical investigation on the fire resistance of pultruded GFRP columns with tubular cross-section, both unprotected and protected with a passive fire protection. Three-dimensional finite element models were developed and they considered the thermo-mechanical behaviour of GFRP material (temperature-dependent mechanical properties) and the temperature distributions previously obtained through heat transfer analyses and fluid dynamics inside the tube cavity. The numerical results presented include the time evolution of axial and flexural deformations of the GFRP columns, as well as the stress distributions in both longitudinal and transversal directions of the unprotected column under one-side fire exposure and axially compressed (designated as reference column). In comparison with this reference column, the paper focuses on the evaluation of the several effects, such as the use of fire protection system, the imposition of different fire exposure conditions and the application of distinct load levels. The Tsai-Hill criterion is used to identify the initial failure of GFRP columns and assess the evolution of failure index with fire exposure time, while the Hashin criterion is used to obtain an estimate of column strength and collapse mode. It is concluded that the proposed models are able to qualitatively capture the general trend of the experimental results, despite the quantitative differences not yet overcome. With the consideration of creep, delamination effects and fracture, the authors are confident that these models will soon correctly predict the complex mechanical behaviour and the fire resistance of GFRP columns.
