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Highlights • A finite element is developed for beam-column distortional lateral torsional buckling. • Effects captured are pre-buckling deformation, global/local warping, and load height. • Investigated are second-order moments effects due axial forces on lateral buckling. • Assessed is the beneficial effect of transverse stiffeners on beam buckling strength. Abstract The present study develops a unified distortional lateral torsional buckling finite element formulation for the elastic analysis of beam-columns with wide flange doubly symmetric cross-sections. The solution captures several non-conventional features including the softening effect due to web distortion, the stiffening effect induced by pre-buckling deformations, the pre-buckling nonlinear interaction between strong-axis moments and axial forces, the contribution of pre-buckling shear deformation effects, the destabilizing effects due to loads being offset from the shear centre, and the presence of transverse stiffeners on web distortion. In the present theory, it is possible to evoke/suppress any combination of features and thus isolate the individual contribution of each effect or quantify the combined contributions of multiple effects. The effects of beam span-to-depth, flange width-to-thickness, web height-to-thickness, and flange width-to-web height ratios on the critical moments are investigated. Comparisons with conventional lateral torsional buckling solutions that omit distortional and pre-buckling effects quantify the influence of distortional and/or pre-buckling deformation effects. The theory is also used to investigate the influence of P-delta effects of beam-columns subjected to transverse and axial forces on their lateral torsional buckling. The solution is adopted to quantify the beneficial effects of transverse stiffeners in controlling/suppressing web distortion in beams. [ABSTRACT FROM AUTHOR]

A higher order beam model for the buckling analysis of thin-walled structures is presented in this paper.The model considers an enrichment of the displacement field so as to accurately represent the three-dimensional behaviour of thin-walled structures. The definition of an uncoupled set of deformation modes allows a meaningful definition of hierarchical higher order solutions, which are useful for the linear buckling analysis of thin-walled structures. A criterion for the definition of local and global buckling modes, as well as possible interaction between modes is put forward. A comparison between the results obtained with the higher order beam model and results obtained from a shell finite element model implemented in Abaqus allows to conclude not only the efficiency of the beam model but also its simplicity of use. [ABSTRACT FROM AUTHOR]

A high accuracy finite strip for the buckling and post-buckling analysis of moderately thick symmetric cross-ply composite plates is presented in this paper by using first order shear deformation theory (FSDT). The presented method, which is designated by the name Full-analytical Finite Strip Method (F-a FSM), provides an efficient and extremely accurate buckling solution in which the Von-Karman’s equilibrium set of equations is solved exactly, and the out-of-plane mode shapes and critical loads are obtained. In the post-buckling stage, the Von-Karman’s compatibility equation is solved exactly with the assumption that the deflected form after buckling is a combination of obtained buckling modes (single or multiple mode shapes). The principle of minimum potential energy is invoked to solve for the unknown coefficients in the assumed out-of-plane deflection and rotations functions. [ABSTRACT FROM AUTHOR]

A non-linear elastic Generalised Beam Theory (GBT) is formulated and used to investigate the buckling behaviour of aluminium and stainless steel thin-walled columns. The modifications that must be incorporated in the conventional GBT, in order to handle the material non-linearity, are addressed and particular attention is paid to the need to define the stability problem in terms of instantaneous elastic moduli. After validating the proposed GBT, by means of its application to compressed rectangular plates, the unique features and capabilities of the theory are illustrated through the presentation and discussion of results concerning C-section and RHS columns. Stress–strain laws of the Ramberg–Osgood type are used to model the uniaxial behaviour and both J2-flow and J2-deformation plasticity theories are implemented. [Copyright &y& Elsevier]

Abstract: Although fibre reinforced polymers exhibit several advantages over traditional materials, their widespread acceptance is being delayed by the lack of appropriate design codes. In fact, additional and comprehensive experimental data are needed to assess the accuracy of recently developed analytical and numerical design tools. This work reports an experimental study on the first-order, buckling and post-buckling behaviours of I-section beams made of GFRP pultruded profiles. Tests were first carried out on small-scale (coupon) specimens, in order to determine the most relevant material mechanical properties. Full-scale tests were then conducted on (i) simply supported beams with spans varying from 1.0m to 4.0m under 3-point bending and (ii)cantilevers with spans ranging from 2.0 m to 4.0 m subjected to a tip point load applied at the end cross-section centroid or top/bottom flange mid-point. While the first series is aimed at investigating the flexural behaviour under service and failure conditions (including the local buckling of the top flange), the objective of the second series is to study the collapse behaviour stemming from lateral-torsional buckling. The results obtained confirm that, due to the GFRP low Young’s modulus and high strength, the beam structural integrity is often governed by excessive deformation and/or local and global buckling phenomena, rather than by material strength limitations. Moreover, the low shear-to-Young’s modulus ratio implies that the role played by the shear deformation is quite relevant, particularly in stocky beams. The experimental data presented here is used to validate and assess the accuracy of numerical simulations reported in a companion paper (Part 2). [Copyright &y& Elsevier]

Abstract: The paper addresses the static stability of externally pressurised toroidal shells with closed circular and non-circular cross-sections. Results of a numerical study into bifurcation buckling and first ply failure of CFRP filament wound toroids are presented. The influence of boundary conditions, variable wall thickness, laminations stacking and initial geometric imperfections on the load carrying capacity is provided. [Copyright &y& Elsevier]

A mathematical model able to describe the buckling behaviour of moderately thick, elastic/plastic plates rigidly connected along their longitudinal edges is presented. The governing equations are derived on the basis of incremental and deformation theories of plasticity. The Ramberg–Osgood model is used to describe the elastic/plastic behaviour, whereas a Green–Lagrange strain model is adopted to measure the geometrical nonlinearities. The plate is analyzed within the framework of the Mindlin theory. comparison with results available in literature, as well as the effects of geometry, boundary conditions, loading conditions and nonlinearities on the buckling response of different stiffened plates are presented. [ABSTRACT FROM AUTHOR]

Abstract: In this paper, a new geometrically exact beam formulation is presented, aiming at calculating buckling (bifurcation) loads of Euler–Bernoulli/Vlasov thin-walled beams with deformable cross-section. The resulting finite element is particularly efficient for problems involving coupling between lateral-torsional buckling and cross-section distortion/local-plate buckling. The kinematic description of the beam is geometrically exact and employs rotation tensors associated with both cross-section rotation and the relative rotations of the cross-section walls in the cross-section plane. Moreover, arbitrary deformation modes, complying with Kirchhoff’s assumption, are also included, which makes it possible to capture local/distortional/global buckling phenomena. Load height effects associated with cross-section rotation/deformation are also included. The examples presented throughout the paper show that the proposed beam finite element leads to accurate solutions with a relatively small number of degrees-of-freedom (deformation modes and finite elements). [Copyright &y& Elsevier]

Abstract: This paper addresses, for the first time, the buckling analysis of isotropic and laminated plates that are subjected to partial inplane edge loads by a first-order shear deformation theory. The numerical approach is based on collocation with wavelets. It is shown that the present method produces highly accurate critical loads and modes. [Copyright &y& Elsevier]

Abstract: Built-up columns are often used in steel buildings and bridges providing economical solutions in cases of large spans and/or heavy loads. Two main effects should be taken into account in their design that differentiate them from other structural members. One is the significant influence of shear deformations due to their reduced shear rigidity. The second is the interaction between global and local buckling. These effects are addressed here from both a numerical and an analytical point of view for laced built-up columns. It is concluded that the largest loss of capacity occurs when the local and global Euler critical stresses and the yield stress all coincide. This reduction in capacity becomes more prominent in the presence of imperfections, reaching magnitudes in the order of 50%. Despite the detrimental effects of mode interaction many major design codes do not provide sufficient pertinent guidance. In order to address this issue, a simple analytical method is proposed for calculating the collapse load of laced built-up members taking into account the above effects as well as global imperfections, local out-of straightness and plasticity, which is then verified by means of nonlinear finite element analysis, using either beam or shell elements. The proposed method is found to provide improved accuracy in comparison to EC3 specifications in cases of global elastic failure. [Copyright &y& Elsevier]

Functionally graded plates whose material properties vary continuously through the thickness are modelled as exactly equivalent plates composed of up to four isotropic layers. Separate models are derived for analysis using classical plate theory, first-order and higher-order shear deformation theory. For cases where Poisson’s ratio varies through the thickness, the integrations required to obtain the membrane, coupling and out-of-plane stiffness matrices are performed accurately using a series solution. The model is verified by comparison with well converged solutions from approximate models in which the plate is divided into many isotropic layers. Critical buckling loads and undamped natural frequencies are found for a range of illustrative examples. [ABSTRACT FROM AUTHOR]

Abstract: Idealized and simplified geometries are commonly used in finite element models to ease model creation and meshing. However, at smaller length-scales, the influence of geometrical imperfections and defects can significantly affect the accuracy of the model predictions. This work details the modeling techniques required to achieve an accurate prediction of the mechanical behavior of metal micro-textured thermal interface material (MMT-TIM) structures as they undergo compressive deformation. Of particular significance is the development of a novel and practical technique for accurately creating detailed micro-scale geometries for finite element modeling applications. This technique relies on an SEM stereoscopic surface reconstruction methodology and is extended here to create solid geometries amenable to direct simulation by finite element software tools. By accurately characterizing the geometry over the relevant length-scales, an improved prediction of the mechanical response of these structures is attained compared to models employing idealized geometries. Accurate mechanical models enable the subsequent heat transfer modeling of these materials to be achieved with a corresponding high degree of accuracy. The value of the geometry reconstruction technique for other applications is also discussed. [Copyright &y& Elsevier]

Abstract: In this paper, the compressive, i.e. bucking and post-buckling, behavior of composite laminates with through-the-width and embedded delaminations is investigated analytically. The analytical method is based on the first order shear deformation theory (FSDT) and its formulation is developed on the basis of the Rayleigh–Ritz approximation technique. In the case of the multiple delaminations, the contact phenomenon has significant effects on the compressional behavior of the laminates. Thus, the contact between the delaminated sublaminates is also considered in the presented FSDT analytical method. The method can handle both local buckling of the delaminated sublaminates and global buckling of the whole plate. Also, the three-dimensional finite element analysis is performed by using ANSYS5.4 general purpose commercial software, and the results are compared with those obtained by the analytical model. The agreement between the results is very good. [Copyright &y& Elsevier]

The 2-D approximation functions based on a general exact 3-D plate solution are used to derive locking-free, rectangular, 4-node Mindlin (i.e., first-order plate theory), Levinson (i.e., a third-order plate theory), and Full Interior plate finite elements. The general plate solution is defined by a biharmonic mid-surface function, which is chosen for the thick plate elements to be the same polynomial as used in the formulation of the well-known nonconforming thin Kirchhoff plate element. The displacement approximation that stems from the biharmonic polynomial satisfies the static equilibrium equations of the 2-D plate theories at hand, the 3-D Navier equations of elasticity, and the Kirchhoff constraints. Weak form Galerkin method is used for the development of the finite element model, and the matrices for linear bending, buckling and dynamic analyses are obtained through analytical integration. In linear buckling problems, the 2-D Full Interior and Levinson plates perform particularly well when compared to 3-D elasticity solutions. Natural frequencies obtained suggest that the optimal value of the shear correction factor of the Mindlin plate theory depends primarily on the boundary conditions imposed on the transverse deflection of the 3-D plate used to calibrate the shear correction factor. [ABSTRACT FROM AUTHOR]

This paper addresses a nonlinear finite element method for the crippling analysis of composite laminated stringers. For the finite element modeling, a nine-node laminated shell element based on the first order shear deformation theory is used. Failure-induced stiffness degradation is simulated by the complete unloading method. A modified arc-length algorithm is incorporated in the nonlinear finite element method to trace the post-failure equilibrium path after a local buckling. Finite element results show excellent agreement with those of previous experiment. A parametric study is performed to assess the effect of the flange-width, web-height, and stacking sequence on the buckling, local buckling, and crippling stresses of stringers. [Copyright &y& Elsevier]

Abstract This work deals with the structural behaviour, ultimate strength and design of fixed-ended cold-formed steel (CFS) lipped channel columns experiencing various levels of local-distortional-global buckling mode interaction (more or less close critical local, distortional and global loads). First, a comparison between experimental results, obtained from three tests carried out at The University of Hong Kong (UHK), and the corresponding A baqus shell numerical simulations are presented and discussed – the UHK test campaign is reported in Part I of this two-part paper. The comparison (i) involves equilibrium paths, deformed configurations, failure loads and collapse mechanisms, and (ii) provides enough evidence to ensure that the numerical model developed may be deemed validated. Then, this numerical model is employed to perform a parametric study, aimed at obtaining numerical failure load data concerning lipped channel columns experiencing different levels of local-distortional-global interaction – 368 fixed-ended columns, exhibiting different geometries (cross-section dimensions and lengths) and various yield stresses, thus covering a wide slenderness range. Finally, the present (Part II) paper also assesses the quality of the failure load estimates provided by various design approaches, based on the Direct Strength Method (DSM), for CFS columns affected by the triple coupling phenomenon under consideration. This assessment is based on the comparison with both (i) experimental failure loads, namely those reported in Part I and others collected from the literature, and (ii) numerical failure loads, obtained from A baqus shell finite element analyses (SFEA) and either reported in this work or gathered from previous publications by the authors. [ABSTRACT FROM AUTHOR]

Cold-formed steel purlins are commonly used in the construction of industrial buildings. The roof sheeting increases the strength of the attached purlin to a considerable extent by providing lateral and rotational restraints. Further, the rotational restraint plays an important role on the buckling behaviour of the attached purlin. There is a need for a design method that accurately predicts the rotational restraint without experimental tests. Addressing this problem, in this research work, a non-linear finite element model is developed to estimate the rotational restraint provided by the first and second generation trapezoidal sheeting to the attached purlin. This model is applicable to trough-fixed and crest-fixed single skin purlin-sheeting systems commonly employed in steel roofs. The performance of the finite element model is validated by conducting experimental tests and found to be in good agreement. The factors influencing the rotational restraint can be investigated by using this validated finite element model. It opens the way to the development of a design method for estimating the rotational restraint provided by the sheeting to cold-formed steel purlins. [Copyright &y& Elsevier]

Abstract: We present in this paper MITC shell elements for large strain solutions of shell structures. While we focus on the 4-node element, the same formulation is also applicable to the 3-node element. Since the elements are formulated using three-dimensional continuum theory with the full three-dimensional constitutive behavior, they are referred to as 3D-shell elements. Specific contributions in this paper are that the elements are formulated using two control vectors at each node to describe the large deformations, MITC tying and volume preserving conditions acting directly on the material fiber vectors to avoid shear locking, and a pressure interpolation to circumvent volumetric locking. Also, we present solutions to some large strain shell problems that represent valuable benchmark tests for any large strain shell analysis capability. [Copyright &y& Elsevier]

This paper presents an analysis model for cold-formed purlin-sheeting systems subjected to wind uplift loading in which the restraint of the sheeting to the purlin is taken into account by using two springs representing the translational and rotational restraints provided by the sheeting. The model yields a set of three differential equations corresponding to one torsion and two bending equations. The set of equations is solved by means of trigonometric series. The influence of spring stiffness and fixing position of the purlin and sheeting on the stresses resulted in the cross-section of the purlin is discussed. The results obtained from this study not only highlight the influence of the sheeting restraints on the results of stresses but also can be used as an input to the finite strip code for carrying out the linear elastic buckling analysis of the sections. [Copyright &y& Elsevier]

This paper presents a displacement based finite element model for predicting the constraint torsion effect of stiffeners. In structural modelling, the plate/shell and the stiffeners are treated as separate elements where the displacement compatibility transformation between these two types of elements takes into account the constraint torsional warping effect in the stiffeners. The development is based on a general beam theory which includes flexural-torsion coupling, constrained torsion warping, and shear-centre location. The virtual work principle includes the second order terms of finite beam rotations. For finite element analysis, cubic Hermitian polynomials are used as shape functions of the straight space frame element with two nodes. Elastic stiffness and geometric stiffness matrices for an arbitrary cross-section are evaluated in a closed form, and load correction stiffness for eccentric stiffener loads are considered. To demonstrate the importance of torsion warping constraints and to illustrate the accuracy of this formulation, finite element solutions are presented and compared with available solutions. [Copyright &y& Elsevier]