The modeling and simulation of γ-graphyne under monotonic and hysteretic in-plane loading is presented. An atomistic finite element model of γ-graphyne was developed. Four different loading tests were conducted, including unidirectional tests in armchair and zigzag direction, bidirectional test and shear test. From monotonic analyses, the mechanical properties (elastic and strength) were obtained and validated. Hysteretic (cyclic) tests were performed to obtain stress–strain curves and the variation of dissipated energy with the number of cycles. The failure modes and the load-carrying capacity are analyzed. The proposed model simulates correctly the γ-graphyne monotonic and hysteretic mechanical behavior.
This paper presents a numerical study on the web-crippling failure of pultruded glass fibre reinforced polymer (GFRP) profiles, under external-two-flange (ETF) and internal-two-flange (ITF) configurations. The numerical study is validated through experimental tests recently conducted by the authors on four I-section profiles and one U-section profile, obtained from four different suppliers. These web-crippling tests were simulated through shell finite element (FE) models where the transverse compressive fracture toughness of each GFRP material was implemented as a damage evolution parameter. In order to quantify the influence of material damage and instability effects on the web-crippling failure, three different analyses were implemented, accounting for (i) material damage, (ii) instability, and (iii) both effects. The results obtained through the analysis accounting for both material damage and instability effects showed a good agreement with experimental results, in terms of stiffness, failure modes and ultimate loads; moreover, the transverse compressive strain distributions obtained from the numerical models also agreed well with experimental results. Finally, the transverse compressive stresses were found to influence web-crippling the most, regarding both damage initiation and ultimate load stages.
No abstract is provided for this article.
No abstract is provided for this article.
This paper reports research work concerning the use of Generalised Beam Theory (GBT) to analyse the local, distortional and global buckling behaviour of thin-walled steel frames. After a brief review of the main concepts and procedures involved in performing a GBT buckling analysis, one addresses the formulation and implementation of a GBT-based beam finite element that incorporates local, distortional and global deformation modes – in particular, one describes (i) the definition of joint elements, which involves providing a relation between the connected member GBT degrees of freedom and the joint generalised displacements, and (ii) the kinematical models adopted to simulate the torsion warping transmission. Next, one uses evidence gathered from shell finite element analyses to establish kinematical constraint conditions that ensure cross-section warping and in-plane displacement compatibility at the frame joints connecting two non-aligned plain or lipped channel members. Finally, one presents and discusses numerical results that make it possible to illustrate the application and show the capabilities of the above GBT-based finite element formulation and implementation. For validation purposes, some GBT-based results (critical buckling loads and mode shapes) are compared with values yielded by shell finite element analyses carried out in the code ANSYS.
This paper presents the numerical implementation and illustrates the application and potential of a nonlinear elastic generalised beam theory (GBT) beam finite formulation to analyze the postbuckling behavior of laminated CFRP composite thin-walled prismatic cylindrical panels. This formulation (i) is based on a novel GBT cross-section analysis approach, (ii) accounts for the presence of initial geometrical imperfections and (iii) adopts an incremental iterative solution procedure employing the Newton–Raphson method and an arclength control strategy. No stiffness degradation or ply failure is taken into consideration and the material is deemed linear elastic and orthotropic. Numerical results concerning the local buckling and postbuckling behavior of stiffened CFRP cylindrical panels are presented and discussed — one of these panels was experimentally tested and numerically investigated in the context of the COCOMAT project. Taking full advantage of the GBT unique modal features, one is able to (i) examine the nature of the panel structural response, which is expressed in terms of deformation mode participations, and (ii) perform analyses involving very few d.o.f. (by preselecting a small set of deformation modes). The panel buckling loads and deformed configurations obtained from the GBT analyses are validated through comparison with either experimental data or values yielded by shell finite element analyses carried out in the code ABAQUS. In order to assess how the curvature affects the panel buckling and initial postbuckling behavior, a stiffened plate having a width identical to the cylindrical panel is also analyzed and the results obtained are compared with those determined for the corresponding curved panels.
The design of glass fibre reinforced polymer (GFRP) pultruded members is often governed by deformability and buckling phenomena, preventing the full exploitation of the material potential. Hybridization – the partial replacement of the glass reinforcement with (stiffer) carbon fibres – is a possible approach to improve the performance of GFRP thin-walled profiles. This paper presents an experimental study on the structural behaviour of I-section hybrid fibre reinforced polymer (FRP) pultruded columns made of glass and carbon fibres (GF and CF) embedded in a polyester resin. A bare GFRP reference profile and four series of hybrid C-GFRP profiles, with different types and architectures of CF reinforcement, were designed, manufactured and tested under compression in three different lengths – short, intermediate and long. Particular attention was given to the buckling behaviour of the columns and to the delamination at the interface between GFRP and CFRP layers. In terms of serviceability performance, results obtained confirm the hybridization’s effectiveness in increasing the axial stiffness of GFRP compressive members. In terms of ultimate limit states behaviour, hybridization increased the load carrying capacity of the long columns, which exhibited global buckling. In opposition, for the short and intermediate columns, which failed respectively due to local buckling and a combination of global and local buckling, the load carrying capacity of the hybrid columns was lower than that of the reference profile; such worse performance seems to have been caused by the delamination of the CF layers, owing to the relatively high axial strains that developed in those columns. In a companion paper (Part 2), the experimental data presented and discussed herein is compared with predictions from numerical models and analytical formulae, which also provide further information about the delamination and progressive failure of the hybrid columns.
This paper is concerned with the development and application of a Generalized Beam Theory (GBT) formulation to analyse the local and global buckling behavior of thin-walled steel plane and space frames with arbitrary loadings and various support conditions. This formulation takes into account the geometrical effects stemming from the presence of longitudinal normal stress gradients and also the ensuing pre-buckling shear stresses. Following a description of the main concepts and procedures involved in determining the finite element and frame linear and geometric stiffness matrices (incorporating the influence of joints, applied loading and support conditions), one presents and discusses some numerical results concerning the local and global buckling behavior of (i) simple "L-shaped" frames and (ii) space frames formed by two symmetrical portal frames joined through a transverse beam. For validation purposes, the GBT-based results are compared with those obtained by rigorous shell finite element analyses using ANSYS. An excellent correlation, for both the critical buckling loads and mode shapes, is found in all cases.
This paper reports an ongoing investigation intended to assess the performance of the Direct Strength Method (DSM) to estimate the ultimate strength of lipped channel columns affected by local-plate/distortional mode interaction.First, the DSM approaches to safety check columns against local-plate and distortional failures are briefly reviewed, with special attention devoted to a recently proposed extension that takes into account the above buckling mode interaction.Next, one presents and discusses the results of a parametric study, carried out by means of the code ABAQUS and involving the evaluation of the "exact" ultimate loads of 63 lipped channel columns with various geometries, all exhibiting local-plate/distortional interaction.Then, these ultimate strength data are compared with the estimates provided by the available DSM formulae and, on the basis of this comparison, one identifies several features that a DSM approach successfully accounting for local-plate/distortional interaction must incorporate.
When compared with carbon steel, stainless steel exhibits a more pronounced non-linearity and no well-defined yield plateau, as well as appealing features such as aesthetics, higher corrosion resistance and lower life cycle cost. Due to its considerably high ductility/strength and cost, stainless steel structural solutions tend to be adopted mostly for slender/light structures, thus rendering the assessment of their structural behaviour rather complex, chiefly because of the high susceptibility to instability phenomena. The first objective of this paper is to present the main concepts and procedures involved in the development of a geometrically and materially non-linear Generalised Beam Theory (GBT) formulation and numerical implementation (code), intended to analyse the behaviour and collapse of thin-walled members made of materials with a highly non-linear stress–strain curve (e.g., stainless steel or aluminium). The second objective is to validate and illustrate the application of the proposed GBT formulation, by comparing its results (equilibrium paths, ultimate loads, deformed configurations, displacement profiles and stress distributions) with those provided by shell finite element analyses of two lean duplex square hollow section (SHS) columns previously investigated, both experimentally and numerically, by Theofanous and Gardner (Eng Struct 2009; 31(12): 3047–3058.). The stainless steel material behaviour is modelled as non-linear isotropic and the GBT analysis includes initial geometrical imperfections, but neglects corner strength enhancements and membrane residual stresses. It is shown that the GBT unique modal nature makes it possible to acquire in-depth knowledge concerning the mechanics of the column behaviour, by providing “structural x-rays” of the (elastic or elastic–plastic) equilibrium configurations: modal participation diagrams showing the quantitative contributions of the global, local, warping shear and transverse extension deformation modes - moreover, this feature makes it possible to exclude, from future similar GBT analyses, those deformation modes found to play a negligible role in the mechanics of the behaviour under scrutiny, thus further reducing the number of degrees of freedom involved in a GBT analysis, i.e., increasing its computational efficiency.
No abstract is provided for this article.
This paper proposes a new approach to predict the web crippling failure load of cold-formed steel beams under External Two Flange (ETF) loading using the Direct Strength Method (DSM). After the description of the existing test data, Eurocode 3 (Comité Européen de Normalisation (CEN), 2006) [1] and the North-American Specification (American Iron and Steel Institute (AISI), 2012) [2] are used to predict the corresponding web crippling failure loads and the accuracy of such predictions is briefly assessed. In order to obtain additional information on the web crippling behaviour of each test specimen, non-linear numerical simulations are performed. Since the calibration of the DSM-based design expressions requires the previous calculation of (i) elastic buckling loads and (ii) plastic strengths/loads, two procedures are presented to achieve these goals. While the buckling loads are determined using the GBTWEB software, specifically developed for this purpose, the plastic loads are calculated by means of analytical expressions based on yield-line models. By adopting a non-linear regression procedure, the coefficients of a DSM-based formula are determined on the basis of the set of 128 experimental results available and the corresponding buckling and plastic load values. In spite of the different cross-sections, fastening conditions and test set ups considered in the calibration procedure, it is possible to establish a clear relationship between the web crippling slenderness and the nominal-to-plastic load ratio. Finally, it is shown that the developed/proposed DSM-based formula for ETF web crippling design yields reliable predictions, since they are associated with a LRFD (Load and Resistance Factor Design) resistance factor ϕ=0.81, which is located within the range of values currently adopted in the 2012 NAS (American Iron and Steel Institute (AISI), 2012) [2].
The optimal design of cold-formed steel columns is addressed in this paper, with two objectives: maximize the local-global buckling strength and maximize the distortional buckling strength. The design variables of the problem are the angles of orientation of cross-section wall elements—the thickness and width of the steel sheet that forms the cross-section are fixed. The elastic local, distortional and global buckling loads are determined using Finite Strip Method (CUFSM) and the strength of cold-formed steel columns (with given length) is calculated using the Direct Strength Method (DSM). The bi-objective optimization problem is solved using the Direct MultiSearch (DMS) method, which does not use any derivatives of the objective functions. Trade-off Pareto optimal fronts are obtained separately for symmetric and anti-symmetric cross-section shapes. The results are analyzed and further discussed, and some interesting conclusions about the individual strengths (local-global and distortional) are found.
No abstract is provided for this article.
An extension of the Generalised Beam Theory (GBT) is employed to investigate the buckling behaviour of thin-walled lipped channel FRP columns, beams and beam-columns, fabricated by pultrusion and displaying a special kind of orthotropy. The GBT equations are used to identify the relevant (local and global) buckling modes and determine the corresponding bifurcation stress values. The influence of loading, material and geometrical parameters on the member buckling behaviour is assessed by means of a number of parametric studies. Special attention is paid to aspects related to the occurrence of local plate, distortional and flexural-distortional buckling modes.
Neste artigo apresenta-se uma formulacao da Teoria Generalizada de Vigas (GBT) para a analise elasto-plastica de 1a ordem de barras com seccao de parede fina, submetidas a um carregamento e condicoes de fronteira arbitrarios. Depois de apresentar a derivacao das equacoes de equilibrio e o desenvolvimento de um elemento finito de barra, aplica-se e ilustra-se a formulacao para um conjunto de exemplos (casos 1 a 5). Nestes exemplos ilustrativos, consideram-se cinco vigas com seccao em I ou tubular quadrada, utiliza-se uma lei constitutiva elastica-perfeitamente plastica, e considera-se unicamente fenomenos de deformacao global da seccao, nomeadamente flexao uniforme, flexao nao uniforme, flexao composta com compressao, e torcao nao uniforme. Finalmente, validam-se os resultados da GBT por comparacao com os resultados do programa Abaqus, utilizando elementos finitos de barra e de casca. Geralmente, obtem-se uma excelente correlacao entre os resultados da GBT e do Abaqus, no que diz respeito a trajectorias nao-lineares de equilibrio, configuracoes deformadas e diagramas de tensoes. Nos casos em que tal correlacao nao e tao boa, apontam-se possiveis causas para as diferencas observadas.
