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• A new exact buckling model based on MGE for thin-walled microbeams is proposed. • Besides the classical flexural–torsional coupling, two new coupling effects are found. • The first new coupling effect is the higher-order flexure–flexure coupling. • The second new coupling effect is the higher-order flexural–torsional coupling. More and more thin-walled micro-beams, including the I-section thin-walled micro-beams, are applied in MEMS. The buckling of a thin-walled micro-beam exhibits some different phenomena from that of a large scale thin-walled beam, such as the size effect, and the coupling effects caused by strain gradient. To investigate the influence of the coupling effects and size effect on the buckling of thin-walled micro-beams, a new buckling model is proposed. Based on modified gradient elasticity (MGE), the governing equations and boundary conditions of the new model are derived from the variational principle. The governing equations and boundary conditions can be simplified to the classical Vlasov's theory, the MGE Bernoulli–Euler beam model, MGE Bernoulli–Euler beam model considering bi-directional flexure respectively. Solved by the feature expansion method, the size effects of the thin-walled micro-beam can be captured by the new model, that is the buckling load increases with internal length scales. Besides the classical flexural–torsional coupling effect, two new coupling effects, such as the higher-order flexure–flexure coupling and the higher-order flexural–torsional coupling, are also captured by the new model. These two new high-order coupling effects of the new model reduce the critical buckling load of thin-walled micro-beams. The higher-order flexural–flexural coupling effect is far greater than the other two coupling effects, and the higher-order flexural–flexural coupling effect is on the same order of magnitude as the effect of MGE (size effect), with the former being negative and the latter positive. The size effect and higher-order coupling effect cannot be ignored and need to be considered carefully for the buckling of thin-walled micro-beams. [Display omitted] [ABSTRACT FROM AUTHOR]

This study examined the buckling of unstiffened cylindrical shells under external pressure. Six stainless steel cylindrical shell specimens were tested, with a length-to-radius ratio, L/R, ranging from 1 to 7. The wall thickness, diameter, axial length, and geometry of each specimen and the material properties of the corresponding sheets were measured. All cylindrical specimens were subjected to external pressure in a pressure chamber; the buckling load and final collapsed mode were recorded. This paper presents a comparison among theoretical calculations, finite element (FE) results, and experimental data for externally pressurized cylindrical shells. In the numerical calculations, true geometry, average wall thicknesses, and elastic–perfectly plastic modeling were considered. Deviation between theoretical and FE results was 0%to − 22%, and it increased with the length-to-radius ratio. Experimental results are consistent with FE results, with deviation of 2–9%, and final collapsed modes of all shells are consistent. [ABSTRACT FROM AUTHOR]

The Hencky bar-net model (HBM) has been shown to be a physical structural representation of the finite difference plate model (FDM). This paper extends the HBM to tackle buckling problems of rectangular plates under in-plane non-uniform loads. This class of problems requires a pre-buckling stress analysis involving plane-stress elasticity equations in order to establish the non-uniform stress distributions in the plate domain for input loads to the HBM. The converged results given by HBM compare well with existing reference solutions; thereby verifying the model. The HBM is also used to generate some new buckling solutions for rectangular plates under various point loads and partially distributed loads. [ABSTRACT FROM AUTHOR]

This paper deals with extending the domain of applicability of a recently developed Generalised Beam Theory (GBT) formulation intended to perform elastic linear buckling analyses of thin-walled members (i) exhibiting arbitrary flat-walled cross-sections (including those combining closed cells and open branches), and (ii) acted by general loadings. These loadings, which include transverse forces acting away from the member shear centre axis, are termed “general” in the sense that they may involve the presence of pre-buckling stress distributions associated with any possible combination of all the stress tensor membrane components ( σ xx , σ ss and τ xs , for a plane stress state), including cell shear flows – therefore, all the relevant geometrically non-linear effects need to be taken into consideration. After briefly presenting the main concepts and procedures involved in the development and implementation of the above GBT formulation, this same formulation is employed to analyse the buckling behaviour of beams with different types of cross-section geometry (containing closed cells) and exhibiting different loading and support conditions. In particular, they consist of (i) a RHS cantilever acted by two tip point loads, (ii) a closed-flange I-section simply supported beam subjected to a uniformly distributed load and (iii) a two-cell RHS section cantilever acted by tip transverse forces and couples. In all cases, the loads are applied both along the shear centre axis and also along axes parallel to it and located at the beam top and bottom surfaces. The results presented and discussed, which consist of pre-buckling stress fields, buckling curves and buckling mode shapes, are obtained by means of the newly released code GBTul 2.0 and validated by means of the comparison with shell finite element values obtained with the code Ansys . [ABSTRACT FROM AUTHOR]

This paper presents a method to perform generalized beam theory buckling analysis on thin-walled structural members with holes. Generalized beam theory (GBT) is an ideal tool for analyzing thin-walled structures because it can directly compute buckling mode participation in an eigen-buckling analysis. The GBT extension to members with holes is made by treating a thin-walled structural member as an assembly of prismatic sub-members, and compatibility constraints on the GBT modal amplitudes are introduced to connect these sub-members. GBT shear modes with nonlinear warping deformation are included in both first order and buckling analyses to account for the nonlinear normal stress distribution in the vicinity of a hole. GBT buckling mode shapes are verified with shell finite element analysis (SFEA) in three examples that highlight the potential for quantitatively documenting buckling modes initiated by the presence of holes. [ABSTRACT FROM AUTHOR]

The paper focuses on thermal torsional post buckling of functionally graded carbon nanotube reinforced composite cylindrical shells with sur-bonding piezoelectric layers and embedded in an elastic medium. The distribution of reinforcements through the thickness of the shells is considered to be uniform and functionally graded. The basic equations using geometrically nonlinearity in von Karman-Donnell sense within the classical thin shell theory are established. The torsional post-buckling behavior of the piezoelectric functionally graded carbon nanotubes reinforced composite (FG-CNTRC) shells is analyzed with using the Airy's stress function and the Galerkin's method, in which a three-term approximate solution of the deflection of the shell is assumed. Effects of thermal environment, CNT volume fraction, piezoelectric layers (the thickness and the constant voltage), distribution type of the reinforcement, dimensional parameters and Winkler and Pasternak foundation are investigated in this paper. Numerical and graphical results show that the carbon nanotube volume fraction and the piezoelectric layers as well as the elastic foundation and the thermal loads have significantly influenced on the torsional postbuckling behavior of nanocomposite shells. [ABSTRACT FROM AUTHOR]

Abstract This study aims to develop an analytical solution for the elastic buckling pressure and its corresponding equilibrium path of confined, thin-walled liners subjected to temperature variations. The admissible radial displacement function and the minimum potential energy of liners are employed to establish the equations of equilibrium. The steel liners are modelled with two-dimensional finite elements for both elastic and inelastic behaviors. The elastic buckling pressure and the equilibrium path from the computational model are in excellent agreement with the analytical predictions. The analytical solutions for elastic liners and the numerical results for inelastic liners with material and geometric nonlinearities compare well with their respective test results available in the literature. Parametric studies are performed in terms of temperature variation, out-of-roundness imperfection, non-uniform liner-pipe gap, pipe supporting medium flexibility, and steel liner yield strength. Highlights • Tightly confined liners buckle at reduced displacement under thermal effects. • The buckling pressure of tightly confined, perfect liners increases over 80% at 100 °C. • The buckling pressure of perfect liners with 1% gap changes little with temperature. • The softer the elastic medium, the lower the buckling pressure due to less confinement. • The buckling pressure of rigidly confined liners increases with yield strength of liners. [ABSTRACT FROM AUTHOR]

Emerging flexible electronics industries, such as solar cells and RFID tags manufactures, adopt the roll-to-roll (R2R) technology to improve their production efficiency. However, the flexible webs used in these fields wrinkle easily due to their tiny thickness and complex structure. Moreover, the webs are easily buckled if the rollers are misaligned. Therefore, it is desired to introduce an efficient method which can help to determine the critical buckling conditions of the webs when there is misalignment of rolls during their production. The current research presents a model based on the Kirchhoff plates buckling theory to determine the critical buckling misalignment and tension for webs transported through misaligned rollers. Webs are modeled as tensioned Timoshenko beams to obtain their stress distributions. The critical buckling conditions are calculated using the Galerkin method in the current research. Results indicate that the calculated critical conditions are close to the practical ones considering the parabolic variation of shear stress and the linear variation of bending stress. The results also indicate that the critical misalignment increases with the increase of the span ratio and tension, and critical misalignment decreases with the increase of the elastic modulus and web width. Moreover, the critical tension increases as the thickness and elastic modulus increases. The presented model provides a useful method to design and maintain R2R equipment. [ABSTRACT FROM AUTHOR]

The study presents the post-buckling behaviour of thin-walled beam of open section supported by Winkler-Pasternak foundation and it is subjected to an axial compressive load. Here, the assumptions are the strains to be small and elastic, in-plan cross-sectional deformations and the shear deformations to be negligible. The post-buckling paths are determined for clamped beam of I - cross-section which is constant. The point of bifurcation for clamped beam is calculated. It is found to be symmetric and stable for various values of Winkler-Pasternak foundation parameters and Warping parameter. [ABSTRACT FROM AUTHOR]

The effect of moment gradient on the buckling moment resistance of I-beams can be taken into account by the use of an equivalent moment-gradient factor C b . The C b factors given by the previous researchers have been derived from elastic lateral-torsional buckling (LTB) analysis of compact I-beams. However, according to the available literature it is not known whether these factors can be applied to the LTB analysis of inelastic slender-web plate girders (SWPGs). The aim of this paper is to investigate the nonlinear LTB analysis of unstiffened SWPGs subjected to central loading. To this end, a 3D finite-element model using ABAQUS is developed for the inelastic nonlinear flexural-torsional analysis of SWPGs and used to evaluate the unbraced length and load-height effects (located at center, top flange and bottom flange) on their moment-gradient factor. It was found that the C b factor given by AISC in Specification for structural steel buildings is generally unconservative for the elastic and inelastic SWPGs under the considered point load cases. Also, it was observed that the moment resistance versus unbraced length ( M – L ) relationships for the elastic SWPGs are not significantly affected by the applied load height. [ABSTRACT FROM AUTHOR]

This paper investigates the elastic buckling behavior of steel trapezoidal corrugated shear walls (STCSWs) with vertical stiffeners. On the basis of an orthotropic plate model, by utilizing the theorem of minimum potential energy and the Ritz method, the buckling loads of stiffened STCSWs can be precisely calculated using MATLAB. Then, a value of transition rigidity of stiffener is suggested and, hence formulas of elastic buckling coefficients of stiffened STCSWs are proposed. Finally, the verification of proposed formulas using a FE model shows that the formulas are validated and applicable in estimating the elastic buckling loads of stiffened STCSWs. [ABSTRACT FROM AUTHOR]

This paper presents a finite strip program CUFSM used to calculate and analyze the elastic distortional buckling of cold-formed thin-walled steel flexural members with stiffeners in the flange, which has different sectional geometric parameters. According to the classical buckling stress formula, the distortional buckling coefficient of the flange can be calculated so as to analyze the influence of changed sectional geometric parameters on it. On this basis, this study provides a simplified formula of distortional buckling stress to calculate 40 members with different sections which are selected from the Technical Code of Cold-Formed Thin-Wall Steel Structures of China but not contained in this paper. Compared with the analysis results of CUFSM, it shows that the two simplified formulas have quite high accuracy and wide applicability for general members provided by the specification. So it is suggested that they can be used for engineering design and standard revision. [ABSTRACT FROM AUTHOR]

The 2010 AISC flexural strength of I-shaped beams with slender flange was proposed based on Johnson (1985)’s experimental plate bucking coefficient ( k c ). However, our close examination revealed that most of I-beam specimens tested by Johnson to derive k c had section configuration of slender web and noncompact flange, indicating the inappropriateness of the test database itself and probable underestimation of web restraint effect in the AISC codification. In this paper, the effect of web slenderness on the elastic flange local buckling is analytically investigated using the mixed variational approach, and more accurate but still practical formula is proposed. [ABSTRACT FROM AUTHOR]

This paper deals with the analytical and numerical studies of elastic buckling of a three-layered beam with metal foam core. Mechanical properties of the core are variable along the z -axis. There are two schemes of displacement of the faces and core of the beam: a broken line hypothesis and a non-linear hypothesis. The mathematical models for both types of displacements are presented. The governing differential equations of the sandwich beam are derived. Numerical analysis of sandwich beams is conducted in ANSYS environment. The finite elements analysis has been performed using a linear elastic buckling model. The analysis with constant and variable Young׳s modulus of the core of the beam is carried out. The values of the critical load obtained by the analytical and numerical (FEM) methods are compared. [ABSTRACT FROM AUTHOR]

The paper is devoted to a non-typical shape of a shell of revolution with positive Gaussian curvature. The meridian of the shell is a plane curve composed of a clothoid and a circular arc. Geometrical properties of the middle surface of the shell of revolution are presented. Pre-buckling state of the shell under uniform pressure is described analytically. The critical pressure and buckling modes for the shell are calculated with the use of the FEM (the ANSYS system). Post-buckling behaviour of the shells is shown. Results of analytical and numerical investigations are presented in tables and figures. [ABSTRACT FROM AUTHOR]

In this study, a thin-walled polyhedral polymer pipe liner is proposed for the internal rehabilitation of a deteriorated/cracked underground circular metal pipe. The pipe liner is externally confined and subjected to the hydrostatic pressure of water seeped through the cracked pipe. The critical buckling pressure of the pipe liner is derived analytically based on the principle of minimum potential energy and compared with that of a cylindrical pipe liner. A finite element model of the pipe liner is established and analyzed to understand pressure-deformation equilibrium paths and the stability of post-buckling behavior. The analytical buckling pressure is in excellent agreement with the numerical results. The buckling pressure of a polyhedral liner increases with the increase of thickness-to-radius ratio and the decrease of the number of sides in polygon base shape. In comparison with the cylindrical liner, the polyhedral liner can increase buckling pressure up to 10 times but result in a less stable post-buckling behavior. [ABSTRACT FROM AUTHOR]

The elastic stability of axially compressed column related to the cross-section distortion is investigated. Two kinds of closed quadratic cross-sections are taken into consideration with internal walls and without it. The governing differential equation is derived with aid of the principle of stationary total potential energy. The critical loads for the simply supported columns are found in an analytical form and compared with the FEM solution. Sufficient accuracy of the results is worth of noticing. [ABSTRACT FROM AUTHOR]

In this work, finite element method is used to obtain elastic buckling loads and mode shapes of plates. The effect of four different in-plane boundary conditions on the elastic buckling load of simply supported plates subjected to in-plane uni-axial compressive loading is studied. Elastic buckling behavior of plates with cut-outs (circular and square with curved corners) is also studied to illustrate the effect of the size, shape and the eccentricity of the cut-out on buckling loads. Results of the study show that the in-plane boundary conditions affect the elastic buckling behavior of the plate to a significant extent. Aspect ratio influences both the mode shape and the elastic buckling load for perforated plates, whereas its influence is generally limited to mode shape only in case of a solid plate. Restraints on the in-plane movements of plate׳s unloaded edges have different influence on the elastic buckling behavior of the plate when the position of cut-out is changed along the x -axis (loading direction) and along the y -axis (normal to loading direction) of the plate. Also, results show that a large cut-out in the vicinity of edges makes the plate unstable at a much lower load compared to the plate with no cut-out. It is envisioned that the results of this study may provide insight to predict buckling loads in practical scenarios. [ABSTRACT FROM AUTHOR]

Mechanical and thermal post-buckling analysis is presented for FGM rectangular plates resting on nonlinear elastic foundations using the concept of physical neutral surface and high-order shear deformation theory, and investigations on post-buckling behavior of FGM rectangular plates with two opposite simply supported edges and other two opposite clamped edges are also new. Approximate solutions of FGM rectangular plates are given out using multi-term Ritz method, and influences played by different supported boundaries, foundation stiffnesses, thermal environmental conditions and volume fraction index are discussed in detail. It is worth noting that the effect of nonlinear elastic foundation is small at the pre-buckling and initial post-buckling state and is significant with increasing deflection at the deep post-buckling state. Especially, comparisons of post-buckling for FGM rectangular plates resting on nonlinear elastic foundations with movable simply supported edge subjected to compression acting on the geometric middle surface and the physical neutral surface are innovative, and may be helpful to clarify typical mistakes in literature. [ABSTRACT FROM AUTHOR]

The problem of elastic stability of rectangular plates with different boundary conditions under wheel and patch loading is analyzed using Ritz energy technique. Basic analytical model with two specific types of boundary conditions, designed to simulate standard experimental sample, is tested. High quality of presented analytical results, proved through comparison with data obtained by numerical methods, is due to introduction of the exact stress functions of Mathieu's theory of elasticity and adequate deflection functions. Hence, the conditions for analyzing the advanced models with different levels of complexity and for realization of comprehensive parametric study are created for these load types. [ABSTRACT FROM AUTHOR]

Steel plates may be classified as slender, moderate, and stocky based on their distinctive behavior characterized by geometrical buckling and material yielding. Slender plates undergo elastic buckling first and then yield in the post-buckling stage, while stocky plates yield first and then undergo inelastic buckling. Moderate plates, on the other hand, buckle and yield simultaneously. The development of low yield point (LYP) steel enables the application of steel plates with improved buckling and energy absorption capacities as lateral force-resisting and energy dissipating elements in structures. On this basis, buckling and yielding behavior of LYP steel plates with various support and loading conditions is studied in this paper from the point of view of their application in steel plate shear wall (SPSW) systems. The limiting thicknesses of standalone plates corresponding to concurrent geometrical buckling and material yielding are determined theoretically and verified through detailed numerical simulations. Effects of using LYP steel and plate aspect ratio parameter on the required limiting plate thickness as an effective parameter in seismic design of SPSW systems are investigated as well. In addition to the studies on the performance of plates with two and four restrained edges and also applicability of some extrapolation techniques for predicting the critical buckling load of moderate plates, detailed studies are performed on determination of the limiting plate thickness in code-designed SPSW systems. Based on the findings of this study, some practical recommendations are provided for efficient seismic design of SPSW systems with LYP steel infill plates. [ABSTRACT FROM AUTHOR]

Doubly symmetric steel I-section members with thin webs and stocky flanges have a tendency to buckle in a so-called distortional buckling mode, involving distortion of the web of the I-section in the plane of its cross-section. As this mode is more complicated than the local or global buckling, analytical expressions take empirical forms and vary in between different proposals. This paper has two main objectives. The first objective is to propose a complex finite strip method for distortional buckling analysis of I-section beams with slender webs and check the suitability for such analysis by comparing its accuracy with other methods and the second objective is to propose a simple method for predicting the distortional buckling loads of I-beams. The latter objective is superior to current methods with respect to the weight of the sections. [ABSTRACT FROM AUTHOR]

The elastic buckling load of an axially compressed piecewise member was derived under various ideal boundary conditions based on the differential element method; then, the result was simplified for a symmetrical member. The theoretical results were found to be consistent with existing formulas for the elastic buckling load of uniform members. Then, the elasto-plastic buckling of an axially compressed piecewise member composed of steel and elastic materials was investigated and found to be quite different from that of a pure steel member, and a theoretical analysis approach was developed. In elasto-plastic buckling analysis, the load-bearing capacity of the steel section in the ultimate state is determined considering initial imperfections and steel hardening. Furthermore, the symmetric method for obtaining the load-bearing capacity of this member was obtained based on the ultimate state of the critical section, which is simple and reparative for design. The theoretical results of the elasto-plastic buckling analysis were consistent with experimental results, therein obtaining an average error of 4%. [ABSTRACT FROM AUTHOR]

In this paper, the problem of linear elastic buckling of a simply supported rectangular plate, with a single circular cutout, subjected to uniform uniaxial edge compression is considered. The design objective is the maximization of the buckling load by determining the optimal location of the cutout. To accomplish that, a MATLAB routine coupled with finite element computation in ANSYS is employed. The study shows that the position of the center of the circular hole for the maximum buckling load remains always on the longitudinal centerline of the plate. However, the optimal center positions along this longitudinal axis for a given cutout size have great dependence on the aspect ratio of the plates. These optimal positions are reported for various values of plate aspect ratios and cutout sizes. These results are important from a design perspective and will be useful for design purposes in the future. [ABSTRACT FROM AUTHOR]

A semi analytical approach based on the trigonometric expansion and generalized differential quadrature (TE-GDQ) method is implemented to investigate the thermal buckling of a functionally graded graphene platelet reinforced composite (FG-GPLRC) conical shell. Graphene platelets distribution is assumed randomly oriented and uniformly dispersed for each ply. Variation of the volume fraction of plies is modeled according to a step functionally graded medium. Effective material properties of the shell are calculated using the Halpin-Tsai micromechanical rule. Equilibrium equations are derived by means of the first order shear deformation theory (FSDT), nonlinear geometrical relation based on the von Kármán theory, and the Donnell kinematics assumption. The pre-buckling of the shell under uniform thermal load is solved considering the linear membrane procedure. Afterward, the linearized stability equations are obtained utilizing the adjacent equilibrium criterion. Next, using the TE-GDQ method, stability equations convert to an eigenvalue problem. Finally, eigenvalue problem is solved and the critical temperature rise can be determined. After validation of the formulation and methods, several parametric studies are examined to research the effects of the volume fraction of GPLs, semi vertex angle, length-to-thickness ratio and other parameters on the critical temperature. • Thermal buckling behavior of graphene platelet reinforced composites is studies. • Halpin-Tsai method is used to obtain the elastic properties of the composite media reinforced with GPLs. • Functionally graded distribution of GPLs is considered. • Different combination of edge supports is assumed. [ABSTRACT FROM AUTHOR]

A meshfree Galerkin method is proposed for the buckling analysis of corrugated-core sandwich plates (CSP). A CSP is a composite structure composed of three parts — one corrugated sheet in the middle of the structure which can be approximated by an orthotropic plate that has different elastic properties along the two perpendicular directions. The displacement fields of the component are given with the moving-least squares (MLS) approximation and the first-order shear deformation theory (FSDT). The equations governing the elastic buckling behaviors of the three components are derived and superposed to present the meshfree governing equation of the entire CSP. A technique that was originally used to enforce essential boundary conditions in meshfree methods is developed to treat the governing equations before the superposition according to the displacement compatibility. The program is compiled on the C++ platform, and several numerical examples are employed to demonstrate the convergence and accuracy of the proposed method. The results show that the proposed method has high accuracy for the stability analysis of CSP under certain conditions. • A meshfree model for buckling analysis of CSP is proposed. • The corrugated core is approximated by an orthotropic plate. • The proposed method can be applied to buckling analysis of CSP, where the length to width ratio and span to height ratio in certain ranges. [ABSTRACT FROM AUTHOR]

To facilitate accurate but conservative design of cellular beams for resistance against lateral–torsional buckling (LTB), this study proposes rational design guidelines based on General method of EC3. The inelastic LTB resistance was the subject of parametric studies using nonlinear finite elements, covering various loading configurations and geometric parameters of practical cellular beams. End moment and shear loadings were considered. The design resistance is slightly conservative in cases with complete LTB behavior that is generally found with non-dimensional slenderness exceeding 2.50. With short beams and shear loads LTB failure may interact with the local failures web-post buckling and web distortional buckling. However, combinations of LTB and Vierendeel failure were not observed. Concentrated stresses in the flange occur with short beams and moment loads, and these can degrade the LTB resistance. Due to interactions of the local failures in short beams, the design resistance requires a correction to ensure it is conservative. The key parameters affecting resistance include load configuration, section ratio, spacing ratio, and slenderness. All these parameters reflect shear effects, but section ratio and slenderness significantly influence the accuracy of the design results. Therefore, a correction factor based on these parameters is proposed, such that improves the EC3 accuracy by minimizing overestimation. The proposed LTB resistance design approach remains mostly conservative relative to both FE simulations and experimental results. [ABSTRACT FROM AUTHOR]

This article presents the assessment of axial preloading impact on lateral stability capacity of a size-dependent I-section beam–column element with axially varying material properties under transverse load. Material properties of the axially/transversely loaded micro beam obey the power-law function along the longitudinal direction. Nonlocal elasticity theory, which also is identified as Eringen's theory, is employed in conjunction with Vlasov's model for non-uniform torsion to extract the governing equations for the lateral displacement and the twisting angle with the aid of energy approach. Then, the endurable buckling load is predicted using the semi-analytical power series technique. To examine the correctness of the present methodology, a comparison between the attained outcomes with those existing in the literature is made. Eventually, in the presence of a prescribed axial force, the interaction between micro beam lateral stability strength and column flexural buckling is examined and discussed. Additionally, the impact of important parameters such as nonlocal and load height ones, power-law index, and axial force is perused on the aforementioned size-dependent structure's lateral buckling resistance. • Axial preloading impact on lateral stability capacity of a size-dependent I-section beam–column have been analyzed firstly. • Material properties of the axially/transversely loaded micro beam obey the power-law function along the longitudinal direction. • Vlasov's model has been used for non-uniform torsion to extract the governing equations for the lateral displacement and the twisting angle. • The endurable buckling load is predicted using the semi-analytical power series technique. [ABSTRACT FROM AUTHOR]

This work reports the results of a numerical investigation concerning the elastic post-buckling behaviour of fixed-ended thin-walled lipped channel and zed-section columns affected by distortional-global (D-G) interaction – “unexpected” features associated with the global buckling nature are unveiled in both cases. The columns analysed (i) exhibit cross-section dimensions and lengths ensuring the simultaneous occurrence of distortional and global critical buckling, and (ii) contain critical-mode initial geometrical imperfections (linear combinations of the critical distortional and global buckling mode shapes). For comparison and clarification purposes, the post-buckling behaviour of lipped channel columns buckling in an “isolated” distortional mode and containing “pure” distortional and global (flexural-torsional) initial geometrical imperfections are also analysed. The results presented and discussed are obtained through geometrically non-linear Generalised Beam Theory (GBT) analyses and provide the evolution, along given equilibrium paths, of the column deformed configuration (expressed in GBT modal form), relevant displacement profiles and modal participation diagrams, making it possible to acquire in-depth insight on the mechanics underlying D-G interaction in columns. Finally, particular attention is paid to interpreting the differences exhibited by the various column post-buckling behaviours investigated. [ABSTRACT FROM AUTHOR]

To apply the Direct Strength Method (DSM) to web crippling of lipped channel sections, experiments were recently conducted under EOF and IOF loading conditions. In the research presented here, finite element models were first developed to predict the elastic buckling loads and the elasto-plastic behaviour, both of the experiments and an extended data set. New first- and second-order elasto-plastic theoretical models describing the plastic mechanism initiation of a 2D cross-sectional strip of the lipped channel sections were then developed. Subsequently these 2D cross-sectional models were transformed to full 3D models by using modelled yield line patterns as observed in the finite element simulations. Both the first- and second-order 3D models correlate well with the full section simulations. DSM equations were calibrated based on the results from the simulations, using several alternatives for the yield load as needed in the DSM: a first yield load from the finite element simulations; a rigid-plastic mechanism initiation load as used by other researchers; and a first-order elasto-plastic mechanism initiation load via the above theoretical models. Finally, these calibrated DSM equations were compared with the theoretical models, design codes, and a basic Merchant-Rankine approach. For the DSM, the first order rigid-plastic yield load, most appropriate for the DSM and used by other researchers also, performs best for IOF load cases. For EOF load cases, however, using the first-order elasto-plastic load in the DSM gives best results. Taking these different yield loads for the different cases then, the DSM outperforms Eurocode, AISI S100, and the basic Merchant Rankine predictions. The DSM is intuitively and relatively easy to use, and this paper shows that widening its scope to web crippling of lipped channel sections is possible. Importantly, this paper steps into the discussion for a certain type of yield load to be used in the DSM for web crippling, and gives several arguments to consider the rigid-plastic mechanism initiation load. [ABSTRACT FROM AUTHOR]

Thermal gradients often occur in fire exposed structures. This paper considers thermal gradients over the cross-section of steel columns. By means of finite element simulations, the paper demonstrates that these gradients reduce the flexural buckling resistance of the columns. This is due to the eccentricity in the column created by the temperature gradient. Design equations in modern standards provide a gross approximation of the load bearing resistance of such columns in which the eccentricity is ignored and in order to compensate for this the yield stress and modulus of elasticity are to be determined at maximum temperature. Based on an in-depth analysis of the results of the finite element simulations, this paper provides an alternative design model which much better agrees with the actual behaviour of a fire exposed column. [ABSTRACT FROM AUTHOR]

Improvement of stability of thin isotropic shell in the presence of soft elastic filler has been investigated. Critical buckling loads for empty and filled cylinder have been studied both experimentally and theoretically using FE analysis. Various percentage of cross sectional filling are examined as a parametric variation. Nonlinear analysis with proper geometric imperfection modeling is carried out to represent correct behavior of soft elastic filler. The experimental results and FE analysis corroborate well to establish this improvement in buckling strength. It is observed that critical buckling load of the cylinder subjected to external pressure improves upto an extent of five times depending upon percentage of filling. It is concluded that improved strength can be utilized for more efficient design of thin tubular shells. [ABSTRACT FROM AUTHOR]

Elastic instabilities (such as buckling) have been recognized as a promising phenomenon to design smart materials and mechanical systems. Thin-walled cylindrical shells under axial compression can attain multiple bifurcation points in their postbuckling regime due to the natural transverse deformation restraint provided by their geometry; but harnessing such behavior for smart purposes is lacking extensive study due to its notoriously high imperfection sensitivity. In this paper, the concept of seeded geometric imperfection (SGI) design is proposed to modify and control the elastic postbuckling behavior of cylindrical shells. Eigenvalue-based mode shapes were used as basic geometric forms to generate a seeded imperfection. Prototyped SGI cylindrical shells were fabricated through 3D printing and tested under loading–unloading cycles. Numerical and experimental results suggest that the SGI cylindrical shells are less sensitive to initial imperfections and load variation than uniform ones. Cylindrical shells with seeded geometry can be potentially used in the design of smart devices and mechanical systems such as energy harvesters and self-powered sensors. [ABSTRACT FROM AUTHOR]

Industrial steel storage pallet racks are quite similar to the framed steelworks traditionally used for civil and commercial buildings: great differences are due to both the presence of boltless beam-to-column connections and to the very extensive use of thin-walled cold-formed members. Serviceability response as well as ultimate limit conditions are quite complex to predict; high engineering competences are required to guarantee significant load carrying capacities with structural systems of extremely limited weight, and, as a consequence, of very modest costs to be competitive on the market. Design standards have been recently updated worldwide; with reference to the European practice, different alternatives are now offered to designers: from the selection of the method of analysis to the approaches for the serviceability, resistance and buckling checks of the whole racks as well as of its main components. The design paths admitted by the Codes correspond to different values of the structural performances guaranteed by racks, or equivalently, to significantly different costs. A two-parts paper has been written to summarize the first research outcomes of a study on the static design rules currently adopted in Europe for steel storage pallet racks. In particular, a parametric numerical analysis has been developed on medium-rise racks of different configurations, member geometries and rotational stiffness of both beam-to-column and base-plate connections. A wide range of cases of practical interest, comprising of mono- and bi-symmetric cross-sections used for uprights, has been analyzed by means of an open source finite element program for academic use, improved by authors with a suitable beam formulation accounting for main warping effects. The present part 1 deals with the selection of the method of analysis, i.e. 1st or 2nd order elastic analysis, depending on the rack deformability to horizontal loads. Internal forces and moments on members are significantly influenced by the effects of lateral displacements as well as by the type of the beam formulation adopted in the finite element analysis program. In the following, different design alternatives are discussed: the use of the overall buckling analysis, a classical approximate method and few theoretical approaches. The rules for the resistance and stability checks of beam-column members under static loading are discussed in part 2 (“Essential Verification Checks”) of this two-parts paper, together with a critical analysis of the influence of warping effects on the serviceability limit state for lateral deflection of the whole racks. [ABSTRACT FROM AUTHOR]

In the paper the buckling of simply supported plates under combined bending, shear and patch loading is studied in this paper with ANSYS, such a stress state occurs in girder supporting over-head crane. The effect of the width-to-height ratio of the plate and the width of patch loading on the interactive curves are analyzed in detail. And, it is found that the effect of the width of patch loading on the nondimensional interaction curves of bending and patch loading and the interactive curves of shear and patch loading is small. Through detailed FEM analysis, the interaction curves between any two among three stress components are obtained, and then through a designed numerical strategy the nondimensional 3D interactive surfaces of bending, shear and patching loading is found. An approximate equation for the 3D surface is proposed, comparison with the FE results shows that the proposed formula has excellent accuracy. [ABSTRACT FROM AUTHOR]

So far, the equations for buckling capacity of web panels focus on thin-walled beams with very strong flanges. In this paper, elastic buckling behavior of web panels of thin-walled beams with weak flanges is further studied, aiming at a buckling coefficient formula unifying the effect of both weak and strong flanges. A new parameter, the flange-to-web ratio of moment of inertia, is proposed to characterize the effect of flanges. Then, a semi-analytical method is applied to investigate the buckling behavior of simply supported web panels, in two cases, inclusive or exclusive of effect of the moment of inertia of flanges. It is revealed that elastic buckling load, in particular, the buckling coefficient of web panel is a function of two key parameters, web aspect ratio and flange-to-web ratio of moment of inertia. Meanwhile, a finite element analysis (FEA) model allowing for the sensitivity of boundary conditions is validated by comparing with the semi-analytical solution to the case exclusive of effect of the moments of inertia of flanges. Next, numerical results are utilized to illustrate the influence of the previous parameters, which verify the increase of buckling coefficient with flange-to-web ratio of moment of inertia or the decrease of buckling coefficient with web aspect ratio. Besides, it also verifies that for the same flange-to-web ratio of moment of inertia, the buckling behavior of square web panels is closer to the uniform shear buckling than other rectangular web panels. Finally, an accurate design formula is proposed to calculate buckling coefficient of web panel. [ABSTRACT FROM AUTHOR]

The lateral-torsional buckling behavior of functionally graded (FG) non-local beams with a tapered I-section is here investigated using an innovative methodology. The material properties are supposed to vary continuously along the longitudinal direction according to a homogenization procedure, based on a power-law function, whereas the nanobeam is modeled within the framework of a Vlasov thin-walled beam theory. The flexural-torsional governing equations of the problem are derived based on the Eringen's nonlocal elasticity theory and the energy method. The system of lateral stability equations is, thus, reduced to a fourth-order differential equation in terms of the twist angle by uncoupling the equilibrium differential equations. The buckling loads are finally determined using the differential quadrature method (DQM), which is here applied as numerical tool to solve directly the differential equations of the problem in a strong form. A systematic investigation checks for the influence of some parameters such as the power-law index, tapering ratios, loading height parameter, boundary conditions and non-local parameter, on the lateral stability resistance of the tapered I-nanobeams. The numerical outcomes of this paper can be used as benchmarks for further studies on nanoscale tapered thin-walled beams. • The lateral-torsional buckling behavior of axially functionally graded non-local beams with a tapered I-section. • Eringen's nonlocal elasticity theory and the energy method. • The buckling loads are determined using the Differential Quadrature Method (DQM). • The influence of various parameters on lateral stability resistance of the tapered I-nanobeams is considered. [ABSTRACT FROM AUTHOR]

The various assessment methods of ultimate strength for hull girder of ships or offshore structures might lead to different results and computation time. The nonlinear finite element (FE) analyses include the implicit static analysis and explicit dynamic analysis, which both can consider the large deflection and material nonlinearity during the process of progressive collapse. Comparing with the implicit static analysis, the explicit dynamic analysis can consider the transient influence of time and avoid the convergence issue in iterative procedure. The object of the present paper is to figure out a reliable and suitable FE modelling in the explicit dynamic method, which could keep the balance of the acceptable accurate results and computation resources. Several influential factors on the collapse behaviours of hull girder are discussed including boundary conditions, geometric ranges of finite element model, element types, loading methods and loading time. The results of a Suezmax oil tanker and Reckling models assessed by the explicit dynamic method are compared with that by the other analytical methods or in the experiment. [ABSTRACT FROM AUTHOR]

This article studies the influence of the bimoment on the buckling of thin-walled beams with open cross section subjected to axial loading. In the case of torsional and torsional-flexural buckling of thin-walled Z-section beam, it is shown that influence of the bimoment could be of importance in the assessment of buckling loads. In order to verify the accuracy and validity of this analysis, the obtained results are compared with those calculated by ANSYS software. [ABSTRACT FROM AUTHOR]

The objective of this paper is to provide benchmark test results, explanatory shell finite element models, and preliminary Direct Strength Method prediction for cold-formed steel lipped channels undergoing torsion dominated by warping response. Although the elastic theory for the torsional response of a thin-walled cold-formed steel lipped channel member is well-developed, the extent to which warping torsion dominates the response of cold-formed steel members is not widely appreciated. Further, for cold-formed steel members in torsion little exists in terms of experimental benchmarks and even less on situations beyond the classic elastic theory, including geometric nonlinearity and post-buckling, and/or material nonlinearity from partial to full plastification of the section. Here, a typical cold-formed steel lipped channel member loaded experimentally in torsion exhibits significant strength beyond first yield. Shell finite element models of the testing correlate well with the experiments and indicate the extent of plastification as the thin-walled member undergoes torsion dominated by warping response. Idealized end boundary conditions are developed for the shell finite element model that is conservative with respect to the response, and in agreement with classical expressions in the elastic regime. The shell finite element model with idealized end boundary conditions is used to develop a parametric study on ultimate torsional capacity for members dominated by warping torsion. The results indicate that torsional slenderness may be used to predict torsional capacity and indicate that Direct Strength Method predictions for torsion for members dominated by warping torsion are possible. Preliminary design expressions for warping torsion strength prediction are provided. [ABSTRACT FROM AUTHOR]

In thin-walled bars with open cross-section, built from flat walls, cases are found in which, the cantilever wall, elastically restrained in the web, is compressed, and at the same time, longitudinal variation in stresses along its length occurs. Such a wall can be analyzed as a cantilever thin plate, elastically restrained against rotation on the longitudinal supported edge. The paper presents the results of investigations into the stability of elastically restrained cantilever plates for varied stress intensity in the longitudinal direction. Graphs of plate buckling coefficients ( k ) were determined and approximation formulas were derived for technically crucial stress distributions and different degrees of the plate edge elastic restraint. The impact of longitudinal stress variation and of the degree of elastic restraint on the plate buckling modes was analyzed. [ABSTRACT FROM AUTHOR]

In this paper, the effect of growth on the stability of elastic materials is examined through a numerical approach. Growth and resorption are considered to have two main effects from the stability standpoint. Corresponding to the change in mass, the geometry of a system changes, and the critical length of the system can be modified. In addition, the growth of the material may be affected by the stress, yet it may also impose residual stresses. As a result, the material is either stabilized or destabilized by these stresses. As a general framework for the description of elastic properties, the theory of finite elasticity is employed to investigate the growth of elastic materials. Growth is taken into account through matrix multiplication of the deformation gradient. The formalism of incremental deformation is adopted to consider growth effects. Using this formalism, the stability of growing neo-Hookean incompressible cylindrical and spherical shells under external pressure is considered. Firstly, the incremental equilibrium equations and the corresponding boundary conditions for the incompressible growing shells are summarized and afterward employed in order to analyze the behavior of spherical and cylindrical shells subjected to external pressure. The generalized differential quadrature method (GDQ) is utilized to solve the eigenvalue problem that results from a linear bifurcation analysis. It is shown that this numerical method can be efficiently utilized to solve the considered problem. The results are in full agreement with the previously obtained results. In the presence of external radial pressure, an elastic shell will buckle circumferentially to a noncircular cross-section. A change in thickness due to the growth can significantly affect buckling, both in terms of the critical pressure and the buckling pattern. Finally, the effects of the thickness ratio A 1 / A 2 , mode number n , and the growth parameter γ are studied on the shell's stability. • Incremental equilibrium equations for hyperelastic growing shells are summarized. • The GDQ method is utilized to solve the eigenvalue problem. • The results are in full agreement with the previously obtained results. [ABSTRACT FROM AUTHOR]

In this paper, the dynamic buckling of axisymmetric circular cylindrical shells subjected to axial impact is investigated theoretically and experimentally. The von Mises yield criterion is used for the elastic–plastic cylindrical shell made of linear strain hardening material in order to derive the constitutive relations between stress and strain increments. Nonlinear dynamic circular cylindrical shell equations are solved with using finite difference method for two types of loading which are stationary cylindrical shells impacted axially and traveling cylindrical shells impacted against a rigid wall. Experimental tests for two types of loading are performed by gas gun. Theoretical and experimental results for cylindrical shells under axial impact for different loading conditions are reported and it is found that there is a good agreement between them. [ABSTRACT FROM AUTHOR]

The present paper deals with an influence of the longitudinal-transverse mode on interactive buckling of the thin-walled composite girder with imperfections subjected to bending moment when the shear lag phenomenon and distortional deformations are taken into account. A plate model (2D) is adopted for the girder. The structure is assumed to be simply supported at the ends. A method of the modal solution to the coupled buckling problem within the first order approximation of Koiter's asymptotic theory, using the transition matrix method and Godunov's orthogonalization, has been used. The calculations have been carried out for square girders. [ABSTRACT FROM AUTHOR]

This work presents a multi-scale design methodology for the deterministic optimisation of thin-walled composite structures integrating a global–local approach for the assessment of the buckling strength and a dedicated strategy to recover blended stacking sequences. The methodology is based on the multi-scale two-level optimisation strategy for anisotropic materials and structures. In the first step, focused on the macroscopic scale, several design requirements are included in the problem formulation: lightness, feasibility, manufacturing, blending, buckling failure, static failure and stiffness. The second step, which focuses on the laminate mesoscopic scale, deals with the recovery of blended stacking sequences, for the structure at hand, matching the optimal geometric and elastic properties determined in the first step. As a case study, the unconventional PrandtlPlane box-wing system is used to show the effectiveness of the proposed design methodology. • Least-weight design of the PrandtlPlane aircraft wing-box composite structure. • A general deterministic multi-scale two-level optimisation approach is presented. • Static, buckling, failure, feasibility and blending requirements are considered. • The scale transition is ensured through a global-local modelling approach. • An efficient strategy to recover blended stacking sequences is developed. [ABSTRACT FROM AUTHOR]

In recent years, mechanical characteristics including vibration, bending, buckling and postbuckling, stability and instability, etc. of small-scaled structures (such as micro/nanowires, micro and nano plates, micro and nano tubes, micro and nano beams, carbon micro/nano-tubes, micro and nano shells, micro and nano probes, etc.) have been broadly investigated, because of recent advances in nanotechnologies and due to their astonishing characteristics. Also, these small-scaled structures are extensively applied in several areas. However, comprehending the mechanical characteristics of these small-scaled structures is of great prominence and yet a daunting task. To understand the mechanical behaviors and capture the effects (including small-scale effect) of these different advanced small-scaled structures (at micro and nano levels), it is very essential to implement them into classical/nonclassical continuum elasticity based on a suitable classical/nonclassical elasticity formulation or theory. Thus, this work searches the literature and hereby presents an ample literature review study with a special focus primarily on the novel progress of vibration analyses of microplates and nanoplates using nonlocal/nonclassical continuum theories of elasticity. Scopus and web of science databases were used as the primary scholarly-databases to acquire the documents reviewed in the current research. Furthermore, several perspectives of classifications are considered while reviewing and grouping these acquired documents. The main purpose was to illustrate existing research trends in the vibrational analysis of small-scaled plate-based structures utilizing nonlocal plate-based theories and nonclassical continuum elasticity theories, and to provide a foundation and guidance for future research on the mechanics of small-scaled plate-based structures. • Small-sized structures are applied in several application because of their extremely properties. • Vibrational analyses of micro/nanoplates using nonclassical continuum theories are reviewed. • Presented the current research trends considering several perspectives of classifications. • Further efforts could be devoted to the implementations of machine/deep learning techniques. [ABSTRACT FROM AUTHOR]

The continuous strength method (CSM) is a recently developed deformation-based design method for metallic structures. In this method, cross-section classification is replaced by a normalized deformation capacity, which defines the maximum strain that a cross-section can endure prior to failure. This limiting strain is used in conjunction with an elastic, linear-hardening material stress-strain model to determine cross-section capacity allowing for the influence of strain hardening. To date, the CSM has been developed for the determination of cross-section capacity under normal stresses (i.e. compression, bending and combined loading), where it has been shown to offer more accurate predictions than current codified methods. In this paper, extension of the CSM to the determination of shear resistance is described. The relationship between the normalized shear deformation capacity, referred to as the shear strain ratio, and the web slenderness is first established on the basis of experimental and numerical data. The material model and proposed resistance functions are then described. Comparisons of the developed method with the ultimate shear capacity of a series of tested stainless steel plate girders show that improved resistance predictions of test capacity over current design methods are achieved. [ABSTRACT FROM AUTHOR]

The geometric imperfections in honeycomb cells inevitably arise during the manufacturing process and can affect the honeycomb's mechanical performance. Hence, it is critical to identify and quantify the geometric imperfections and characterize the effects of these imperfections on the effective mechanical properties of honeycomb. In this study, the geometric imperfections inside the honeycomb were identified from micro-CT scan data. Using the obtained geometric topology, a Fast Fourier Transform (FFT) based method was employed in combination with the composite pixel method to predict the effective in-plane elastic properties of honeycomb at large elastic deformations. The results of the nonlinear homogenized prediction were compared with the experimental data and the prediction values from analytical models to investigate the effects of geometric imperfections. It was found that the predictions from the FFT-based method agreed well with the experimental results. However, the predictions from the analytical models significantly overestimated or underestimated the elastic properties, indicating that the geometric imperfections inside the honeycomb significantly influence its in-plane elastic properties. • The geometric imperfections inside the honeycomb were identified and quantified. • An FFT-based method with a composite pixel technique was proposed to predict the in-plane elastic properties of honeycombs. • The effects of geometric imperfections on the in-plane elastic properties of the honeycomb were evaluated quantitatively. • It is necessary to introduce the effect of geometric imperfections to guarantee calculation precision. [ABSTRACT FROM AUTHOR]

The component method is widely used nowadays for the analytical prediction of the mechanical properties (rotational elastic stiffness, design resistance and ductility/deformation capacity) of steel and composite beam-to-column joints. The Part 1-8 of Eurocode 3 (EN 1993-1-8) provides expressions for the evaluation of the properties of many different joint components. However, a quick examination of EN 1993-1-8 highlights a glaring disproportion between the quantity of information related to rotational stiffness and plastic resistance, and that related to ductility and deformation capacity. For the latter, only few recommendations are provided, sometimes in line, and sometimes even not with the component approach itself. Present paper concerns one of these components, the "column web in transverse compression" (CWC), for which no information is basically available in terms of ductility. An original procedure for the prediction of the plastic deformation capacity is presented. It relies on a preliminary evaluation of the four main component properties: elastic stiffness, plastic resistance, post-plastic stiffness and ultimate resistance. Through this study, more accurate analytical formulae than those provided by EN 1993-1-8 for the evaluation of the plastic resistance are also suggested. All the developments are validated through extensive comparisons with already available experimental tests performed in various countries. • Characterization of the full-range behaviour of the column webs in transverse compression. • Improved analytical formula for the characterization of the plastic resistance. • New analytical formula for the characterization of the ultimate resistance. • New analytical formula for the characterization of the deformation capacity. • Validation of the model against a wide range of experimental results. [ABSTRACT FROM AUTHOR]