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Abstract: This paper investigates the impact effects of the ribbed sheet with three V-grooves by the nonlinear dynamic FEM. The numerical models considered the nonlinear constitutive equation with strain rate effect, large deformation theory, and self-contact control. The full histories of deformation in simple model, complete model and adaptive model are simulated successfully. With the different groove depths of 3, 4, 7, 10, 12 and 15mm, different mesh types, and boundary conditions, the correspondent results of simulations are assessed. Detail discussions of the absorbed energy and buckling resistance of the different ribbed sheets on varying boundary conditions are presented. Furthermore, the various mesh types are examined in the simulations. And, the results of simulations are compared with the previous experimental works; the impact load of the suggested numerical model is in good agreement with the experiment. The main benefit of the proposed models will save the tremendous costs in the die designing and specimen producing while on the experimental works. The applied techniques of the numerical models are helpful for the design of ribbed sheets and correspondent impact analysis. [Copyright &y& Elsevier]

Abstract: This paper investigates the energy absorption characteristics of longitudinally grooved square tubes under axial compression by using explicit nonlinear finite element code LS-DYNA. The grooves are fabricated by stamping and the distributions of the effective plastic strain and the thickness variation from the stamping process are considered in the following crash analyses. From the simulation results, we find that when grooves are introduced on the sidewalls, the specific energy absorption of conventional tubes can be increased by up to 82.7% and the peak force can be reduced by up to 22.3%. The influences of several parameters, including the width of the tube, the length of the groove and the number of the grooves, are analyzed and the features of the deformation modes of grooved tubes are described. The introduction of groove is found to be an effective way to improve the crashworthiness of thin-walled structures. [Copyright &y& Elsevier]

Abstract: Previous experimental study has proven that rubber honeycomb claddings with thin rubber core can be used to attenuate the water blast wave impinged onto ship hull. As a theoretical extension, the dynamic crush behavior of the square honeycomb core made by thin rubber wall is investigated in this paper. As the dynamic effects play a significant role in the behavior of core, several distinct dynamic effects are analyzed including inertial resistance, nonlinear elasticity, inertial stabilization of webs against buckling, and material viscosity. The influences of the initial imperfection shape and amplitude are discussed too. These effects are illustrated and quantified with the aid of detailed numerical calculations. Some preliminary attempts are also made on the theoretical prediction on the stress wave transmission process. [Copyright &y& Elsevier]

Abstract: An experimental investigation on the behavior of an 8-storey steel staggered-truss system with a -scaled model under reversed low cyclic loading is presented in this paper. In the experiment, the hysteretic curves, skeleton curve as well as other related deformations are measured. And based on the test results, some indices of seismic behaviors of the system, such as yield load, deformation, ductility, energy dissipation, strength, and rigidity degeneration, are analyzed. However, due to the diversity of parameters of the steel staggered-truss system and the unique features of the tested model, the experimental study is not comprehensive enough. Therefore, an analytical investigation based on the finite element (FE) models using the ANSYS software is also presented. The FE models, in which both the material and geometric nonlinearity is considered, are validated using the experimental results. Then the parameters, such as the structural height and height–width ratio, truss type, arrangement of the ground floor trusses, truss span–depth ratio and open-web panel length, are varied, and their influences on seismic behaviors of the system are studied by the verified FE method. Based on the experimental and FE analytical results, some suggestions are presented for design of staggered-truss system. [Copyright &y& Elsevier]

Abstract: Steel spot-welded hat-type sections are used extensively in the automotive industry to manufacture vehicle structures. The main objective when designing a crashworthy vehicle is to protect the occupants in the event of a collision by dissipating crash energy via large plastic deformation and ensuring the survival space is not encroached. In rollover crashes, the components in the roof structure will be subjected to large deformation bending as the roof frame collapses and kinetic energy is dissipated. This paper presents a procedure whereby the energy absorbed by a spot-welded hat section under large deformation bending may be determined. The results are shown to compare well with experiments of spot-welded hat sections with seven different geometries and four different perforation sizes. The perforations were introduced into the compression flange of the sections. The range of section and perforation geometries investigated was designed to cover the full range typical to the automotive industry. The theoretical large deformation bending moment–rotation curves and energy absorbed are determined from a rigorous yet relatively simple three stage process, which includes elastic, in-plane plastic and plastic collapse mechanism components. [Copyright &y& Elsevier]

Abstract: In this paper, the nonlinear elastoplastic behavior of circular tubes with corrugated surfaces that are subjected to axial compression is studied using the finite element method. The corrugations are one of the dominant factors in influencing the deformation mode and they reduce fluctuations in the load–displacement curves for circular tubes. The numerical results show that the deformation modes corresponding to the corrugations can be classified into axisymmetric modes and asymmetric modes, and that the axisymmetric modes can be further classified into the progressive crush mode, in which the compressive force fluctuates with the formation of folds, and the simultaneous crush mode, in which the compressive force increases monotonically. These deformation modes are also observed in the crushing test of the aluminum alloy (A5052). A mode classification chart is produced for various combinations of the wavelength and the amplitude of the corrugations. [Copyright &y& Elsevier]

Abstract: The Gaussian radial basis functions and first-order shear deformation theory are presented to calculate the natural frequencies of generally laminated composite plates. Several numerical examples are used to show convergence and accuracy of the present method. It is found that the natural frequencies computed with shape parameter c=1.7×NS (NS is the number of node at the each side) converge to available published results most rapidly. The results of the present paper are in good agreement with the results already reported in the literature, which demonstrate the high numerical accuracy of the Gaussian radial basis function for vibration analysis of generally laminated composite plates. [Copyright &y& Elsevier]

Abstract: Expanded metal sheeting is widely used around the world for catwalks, granting, and decorative purposes. In the literature, little information can be found regarding the behavior of structural elements made of expanded metal. This paper is aimed at studying the axial collapse of squared and round tubes made of expanded metal sheeting under compressive loading. When expanding the metal a diamond-like cell pattern is formed in the metal sheets, then these patterns are characterised by two geometrical axes. A set of experimental tests was conducted to investigate the influence of the angle formed between the major axis of the expanded metal and the compressive load. From the results, three types of collapse response were mainly observed depending on the orientation of the axes: (1) Mode 1 characterised by a plastic collapse mechanism; (2) Mode 2 local buckling of the individual cells; and (3) Mode 3 global buckling of the tube walls. [Copyright &y& Elsevier]

Abstract: This paper presents a study of the effectiveness of adding a buckling initiator which is used to reduce the initial peak force of a thin-walled circular tube under axial impact loadings. The buckling initiator is installed near the impact end of the circular tube and is composed of a pre-hit column along the axis of the tube and several pulling strips uniformly distributed around the top edge of the tube. This device functions just before the impact happens and does not affect the structural stiffness under its normal working conditions. By using two kinds of aluminum-alloy circular tubes, a series of quasi-static compression tests were conducted. The deformation mode, the initial peak force and the mean crushing force of the tubes with different number of pulling strips N, pre-hit height h and inclined angle of the pulling strips θ 0 were studied in the experiments. The results reveal that by using this buckling initiator, the large progressive deformation of the axially crushed circular tube switches from ring mode or mixed mode to diamond mode. Although specimens with N=2, 3 and 4 were tested, the stable deformation tended to diamond mode with lobe number N=3. With suitable selection of pre-hit height h, the initial peak force could be reduced by more than 30%. In addition, a simplified theoretical analysis is conducted to illustrate the reduction of the initial force as well as the energy dissipation mechanisms, leading to good agreements with the experimental results. [Copyright &y& Elsevier]

Abstract: This paper examines a composite damage constitutive model, MAT58, in LS-DYNA and its application for use in braided composite tube axial crush simulations. The constitutive response of MAT58 was investigated using single element simulations. It was found that MAT58 reproduced the softening behavior of the braided composite under monotonic compressive loading, but failed in subsequent unloading and tensile loading cycles. A deficiency in the damage law in MAT58 was identified. Unloading and reloading a volume of material that had suffered some degree of damage was a part of the process with the progressing of crush zone during the axial crush of composite tubes. Consequently, this deficiency hinders the success of MAT58 in such applications. In tri-axial braided composite tube axial crush simulations, although the predicted initial peak forces were within 20% of the experimental values, the predictions for the specific energy absorption (SEA) values were consistently low, particularly for tubes without a plug as crush initiator. These discrepancies are attributable to the deficiency in the damage law in MAT58. [Copyright &y& Elsevier]

Abstract: Circular tubes have been widely used as structural members in many engineering applications. Therefore, its collapse behavior has been studied for many decades, focusing on its energy absorption characteristics and collapse mechanism. In order to predict the collapse behavior of members, one could rely on the use of finite element codes or experiments. These tools are helpful and have high accuracy but are costly and require extensive running time. Therefore, an approximate model of tubes collapse mechanism is an alternative especially for the early step of design. This paper is also aimed to develop a closed-form solution to predict the moment–rotation response of circular tube subjected to pure bending. The model was derived based on the principle of energy rate conservation. The collapse mechanism was divided into three phases. New analytical model of ovalisation plateau in phase 2 was derived to determine the ultimate moment. In phase 3, the Elchalakani et al. model [Int. J. Mech. Sci. 2002; 44:1117–1143] was developed to include the rate of energy dissipation on rolling hinge in the circumferential direction. The 3-D geometrical collapse mechanism was analyzed by adding the oblique hinge lines along the longitudinal tube within the length of the plastically deformed zone. Then, the rates of internal energy dissipation were calculated for each of the hinge lines which were defined in terms of velocity field. Inextensional deformation and perfect plastic material behavior were assumed in the derivation of deformation energy rate. In order to compare, the experiment was conducted with a number of tubes having various D/t ratios. Good agreement was found between the theoretical prediction and experimental results. [Copyright &y& Elsevier]

Abstract: A forced vibration analysis of laminated composite plates carrying a distributed patch mass is analyzed and presented in this paper. It deals with the determination of the transverse, dynamic response of rectangular composite plates subjected to a uniformly distributed -type excitation. The Hamilton''s Principle, using third-order shear deformation theory, is applied to simply supported rectangular plates. The displacement of the plate is postulated by a double Fourier series. The effects of size and location of the area of the patch, frequency ratio and mass ratio on the response of the plate are also presented. A thorough comparison with well-known published results is presented for the case of free vibration of unloaded plates and good agreement is observed. [Copyright &y& Elsevier]

Abstract: The paper presents the application of the new stiffener element with seven degrees of freedom per node and the subsequent application in determining frequencies, mode shapes and buckling loads of different stiffened panels. In structural modelling, the stiffener and the plate/shell are treated as separate elements where the displacement compatibility transformation between the seven and six degrees of freedom nodes of these two types of elements takes into account the torsion–flexural coupling in the stiffener and the eccentricity of internal (contact) forces between the beam–plate/shell parts. The model becomes considerably more flexible due to this coupling technique. The development of the stiffener is based on a general beam theory, which includes the constraint torsional warping effect and the second-order terms of finite rotations. Numerical tests are presented to demonstrate the importance of torsion warping. As part of the validation of the results, complete shell and the usual six degrees of freedom per node shell–beam finite element analyses were made for stiffened panels. [Copyright &y& Elsevier]

This paper proposes a procedure to calculate cross-section deformation modes for steel–concrete composite bridge cross-sections, including shear connection flexibility, within the framework of the Generalized Beam Theory (GBT). The proposed procedure is computationally efficient and makes it possible to (i) handle arbitrary (flat-walled) composite cross-sections, including complex configurations with several closed cells, (ii) consider the geometric offset between the steel and concrete mid-lines, which is essential in steel–concrete composite members, and (iii) automatically identify, separate, and hierarchize the deformation modes into physically meaningful sets, including a set of shear connection slip deformation modes. For illustrative purposes, the various deformation mode sets are determined for two representative cross-sections, namely a twin-girder and a box-girder with closed longitudinal stiffeners. These deformation modes are then employed to perform the structural analysis of simply supported decks, showing that very accurate results are obtained with a small number of deformation modes and that the modal decomposition of the solution provides in-depth insight regarding the bridge structural behavior. • A method for calculating the GBT deformation modes for steel–concrete bridges is developed. • Complex longitudinal stiffeners can be easily handled. • Shear connection stiffness is taken into account. • The resulting GBT-based finite element is very accurate and efficient. [ABSTRACT FROM AUTHOR]

A corrugated sandwich panel consists of two face-sheets and a corrugated core, which is made of sheets that are folded into a corrugated shape. In this paper, the mechanical response of aluminium corrugated sandwich panels subjected to longitudinal loading along its middle line is investigated experimentally, numerically, and theoretically. A parametric study is conducted using ABAQUS/Explicit to examine the effects of geometric configurations (i.e., corrugation angle, core height, and core web thickness) on the deformation mode, peak force, and specific energy absorption (SEA) of panels. Two major deformation modes (Mode I and Mode II) are observed. The sandwich panels that deformed in Mode I has higher peak force and energy absorption ability. When the density of core remains the same, the energy dissipated by sandwich panels can be tailored by varying the geometry of the core. Thicker core webs result in greater energy absorption. Based on the experimental and simulation observations, a theoretical analysis using energy method is carried out to predict the crushing force of panels during large deformation. • The large deformation of corrugated sandwich panels under longitudinal bending was investigated. • A parametric study was conducted using ABAQUS/Explicit. • Theoretical analysis of the crushing force based on energy method was carried out. [ABSTRACT FROM AUTHOR]

In this paper, a concave-shaped unit composed of two thin-walled beams with cantilever boundary conditions is designed and fabricated. Forces are introduced through the two cantilever ends of the beams whose constraints are hinged joints to get a bi-stable axial or lateral buckled unit. Initial buckling deformations of the concave-shaped units are analyzed theoretically and numerically. Experimental and numerical methods are used to investigate the post-buckling deformations and snap-through behaviors, when the concave-shaped units are axial buckled or lateral buckled. In the case of completing downwards and upwards snapping processes, there is a hysteresis loop in the force–displacement curve for the bi-stable lateral buckled unit, while is not for the bi-stable axial buckled unit. Finally, the influence of transverse displacements and dimension parameters on the snap-through behaviors of the bi-stable lateral buckled units is studied by the simulation method. • A bi-stable lateral buckled unit is designed and fabricated. • There are two symmetric modes for the initial buckled concave-shaped unit. • Post-buckling and snap-through behaviors of the bi-stable units are investigated. • The energy dissipation capacities are influenced by beams parameters. • The assembly bi-stable units are good candidates for energy-related applications. [ABSTRACT FROM AUTHOR]

Abstract: The control of weld-induced imperfections like welding deformations and residual stresses is of critical importance in circumferentially welded thin-walled cylinders due to their wide utilization in high tech engineering applications in aerospace and aeronautical structures, pressure vessels and nuclear engineering fields. The paper presents a computational procedure for the analysis of temperature distributions and the subsequent residual stress fields during the course of arc welding of thin-walled cylinders of low carbon steel. Parametric studies based on numerical simulations are conducted to investigate the effects of critical welding process parameter on weld-induced residual stresses. Temperature-dependent thermo-mechanical behavior for low carbon steel, filler metal deposition along with double ellipsoidal heat source model is incorporated. The accuracy of the developed finite element simulation strategy is validated for transient temperature distributions and residual stress fields through full-scale shop floor welding experiments with proper instrumentation for data measurement. The aim is to present data to confirm the validity of in-process circumferential welding technology for thin-walled cylinders so that the in service failures of these structures due to process specific inherent stresses may be minimized. [Copyright &y& Elsevier]

Abstract: Experimental and analytical investigations of metal beams subjected to transverse blast loads have predominantly focused on solid metal cross-sections. In applications such as the secondary structural members used in facade structures the cross-sections consist of thin-walled aluminium hollow profiles. This paper presents an experimental study of 73 aluminium square hollow sections subjected to transverse blast loads by application of explosives. Four different section slenderness values and three different lengths were investigated, resulting in a wide range of length/depth ratios typical to facade structures. A semi-empirical analytical solution is presented whereby existing theory developed by others for solid metal sections is modified to account for local section deformations that occur in blast-loaded hollow sections. The technique considers both the energy dissipated in local deformations and the resulting reduction in the section-bending modulus, and furnishes a solution that bounds the experimental results with reasonable accuracy. A general design procedure is outlined that may be based on a final permanent deformation or a failure load, and the limitations of such a procedure are discussed. [Copyright &y& Elsevier]

Abstract: The objective of this paper is to provide an unambiguous mechanics-based prediction method for determination of initial residual stresses and effective plastic strains in cold-formed steel members. The method is founded on basic physical assumptions regarding plastic deformations and common industry practice in manufacturing. Sheet steel coiling and cross-section roll-forming are the manufacturing processes considered. The structural mechanics employed in the method are defined for each manufacturing stage and the end result is a series of closed-form algebraic equations for the prediction of residual stresses and strains. Prediction validity is evaluated with measured residual strains from existing experiments, and good agreement is shown. The primary motivation for the development of this method is to define the initial state of a cold-formed steel member for use in a subsequent nonlinear finite element analysis. The work also has impact on our present understanding of cold-work of forming effects in cold-formed steel members. [Copyright &y& Elsevier]

Abstract: The objective of this paper is to observe and quantify the relationship between elastic buckling and the tested response of cold-formed steel columns with holes. Compression tests were conducted on 24 short and intermediate length cold-formed steel columns with and without slotted web holes. For each specimen, a shell finite element eigenbuckling analysis was also conducted such that the influence of the boundary conditions and the hole on local, distortional, and global elastic buckling response could also be captured. Slotted web holes may modify the local and distortional elastic buckling half-wavelengths, and may also change the critical elastic buckling loads. Experimentally, slotted web holes are shown to have a minimal influence on the tested ultimate strength in the specimens considered, although post-peak ductility is decreased in some cases. Tangible connections are observed between elastic buckling and load–displacement response during the tests, including mode switching between local and distortional buckling. The columns are tested with friction-bearing boundary conditions where the columns ends are milled flat and parallel, and bear directly on steel platens. These boundary conditions, which greatly speed specimen preparation, are determined to be viable for evaluating the tested response of short and intermediate length columns, although the post-peak response of intermediate length specimens must be considered with care. [Copyright &y& Elsevier]

Abstract: Cold-formed steel members and structures are extremely widespread in use at the present time. The design analysis of such structures is often complex, as their behaviour can be influenced by effects, which arise due to the slenderness of members, walls and cross-sections. Prime among these effects are the various types of buckling which can occur, and which may interact with each other to promote failure at loads substantially less than those, which would be obtained in the absence of these effects. The complications induced by such effects must be taken into account in design, if the potential benefits offered by the use of such members are to be realised, and in recent design specifications this has been realised. In this paper the main types of cold-formed steel members are described, the particular characteristics affecting their design are discussed, as are the ways in which design specifications deal with these characteristics. [Copyright &y& Elsevier]

Abstract: Thin shell torispherical pressure vessel heads are known to exhibit complex elastic–plastic deformation and buckling behaviour under static pressure. In pressure vessel Design by Analysis, the designer is required to assess both of these behaviour modes when specifying the allowable static load. The EN and ASME boiler and pressure vessel codes permit the use of inelastic analysis in design by analysis, known as the direct route in the EN Code. In this paper, plastic collapse or gross plastic deformation loads are evaluated for two sample torispherical heads by 2D and 3D FEA based on an elastic-perfectly plastic material model. Small and large deformation effects are considered in the 2D analyses and the effect of geometry and load perturbation are considered in the 3D analysis. The plastic load is determined by applying the ASME twice elastic slope criterion of plastic collapse and an alternative plastic criterion, the Plastic Work Curvature criterion. The formation of the gross plastic deformation mechanism in the models is considered in relation to the elastic–plastic buckling response of the vessels. It is concluded that in both cases, design is limited by formation of an axisymmetric gross plastic deformation in the knuckle of the vessels prior to formation of non-axisymmetric buckling modes. [Copyright &y& Elsevier]

Abstract: This paper presents some results of an extensive investigation on the failure of the pressurized double-piping system (pipe-in-pipe system) being one of the main structural elements of the thermo-conditioning installation in the sewage treatment plant. The investigation included the survey of the failed piping, checking of the design and manufacturing against the standards of various types, theoretical analysis employing the results of works carried out on buckling propagation. As an useful and highly informative element of the investigation three tests have been designed to expose the phenomena, which lead to an explanation of the cause of the failure under consideration. They also verified the results of the theoretical analysis performed. [Copyright &y& Elsevier]

Abstract: The paper presents a derivation of the stability equation and the solution method of the problem for an orthotropic elastic–plastic open conical shell. The use is made of the constitutive relations of incremental plastic flow theory, elastic compressibility of the material, and Shanley concept of increasing load are taken into account in the consideration. A variation, strain energy method is used to derive the stability equation for bilayered open conical shell with nonuniform pre-critical stress distribution. The shell is free supported at the edges and the load acting the shell, in the form of longitudinal force and lateral pressure, is active one, i.e. unloading is not considered. [Copyright &y& Elsevier]

Abstract: This paper presents results of the investigation of the stability of eccentrically compressed thin plates with one longitudinal free edge with the participation of loadings generating the variation of stresses in the direction of the length of a plate. A deflection function is proposed to enable modelling of boundary conditions on the second longitudinal edge from a simply supported, through elastically restrained, to a built-in edge. Formulas are derived for work done by external force under loading generating the variation of stress according to a linear function and according to parabola 2°. Tables and plots of buckling coefficient (k) for variously supported and variously loaded plates with a free edge, which are not found in the literature, are determined. The effect of a longitudinal stress variation on the plate buckling modes is analyzed. [Copyright &y& Elsevier]

Abstract: The aim of the paper is to present a procedure for design of a family of shells of revolution of constant mass and, as a next step, of constant volume. As a reference a cylindrical shell is taken into consideration. By decreasing the value of the meridional radius of curvature , which for cylindrical shell equals infinity, barrelled shells are created up to the spherical shell for which both meridional and circumferential radii of curvature are equal (). A numerical example of using the presented procedure is considered. Then for the family of shells of revolution of constant mass a buckling analysis using FEM method is carried out. Results of the analysis show the relationship between the radius of curvature of the shell and the critical load in the case of uniform external pressure. [Copyright &y& Elsevier]

Abstract: This paper investigates the seismic performance of steel hollow box sections. The test results obtained from the combined load tests were used to define the relationship among member performance, sectional aspect ratios and the load combinations. It was found from the comparisons that the flexural strength of members decreased when the torsion magnitude was increased. It was also observed that the reduction in flexural strength increased when the sectional aspect ratio was increased. An empirical expression for estimating member performance under three-dimensional loads is proposed for design references. [Copyright &y& Elsevier]

Abstract: Carbon fibre reinforced polymer (CFRP) strengthening of structures has been gaining increasing interest, traditionally in application with concrete structures, and more recently in application with steel structures. This paper presents experiments and plastic mechanism analysis of steel square hollow section (SHS) tubes strengthened using externally bonded CFRP, deforming in an axi-symmetric collapse mode under quasi-static large deformation axial compression. The fold formation process of the stub column was such that the flat sides formed the well-known roof mechanism. The collapse proceeded progressively by folding about concentrated hinge lines and yielding of the four corners. An expression for the plastic collapse axial load was obtained by equating the total energy absorbed in bending and yielding to the external work carried out during deformation of the composite tube. The predicted instantaneous post-buckling and mean collapse loads are shown to compare well with the experimental results. [Copyright &y& Elsevier]

Abstract: This paper deals with selected foundations of the design of perforated trapezoidal sheeting. Based on numerical analysis, graphs on effective stiffness values for perforated sheeting with different arrays of holes are provided. As an outlook on further research, the calculation of the buckling coefficient for a perforated plate under uniform in-plane compression loading and for an infinitely long perforated plate under shear loading is presented. [Copyright &y& Elsevier]

Abstract: The paper derives the differential equations for the overall bifurcation of locally buckled point-symmetric columns. It is shown that flexural buckling about the minor and major principal axes are coupled in a locally buckled point-symmetric column whereas the buckling modes are uncoupled in a non-locally buckled column. The governing equations are solved for simply supported and fixed-ended columns and applied to Z-sections. Overall bifurcation curves are obtained for five Z-sections with increasingly slender flanges. It is shown that local buckling reduces the elastic torsional buckling load more so than the flexural buckling load for Z-sections, and that local buckling can cause a mode switch from the flexural to the torsional mode in Z-sections with very slender flanges. [Copyright &y& Elsevier]

Abstract: Stainless steel''s characteristic nonlinear, rounded stress–strain behaviour requires accurate recognition in numerical modelling. Its response to cold-working is far more pronounced than that of ordinary carbon steel and hence appropriate modelling of the cold-worked corner regions is very important. Despite the importance of geometrical imperfections, their measurement is not a very common practice and assumed models are generally adopted in numerical investigations—often without proper verification. This paper investigates all important aspects for modelling stainless steel cross-sections through carefully designed parametric studies. Different cross-section types have been considered and the numerically obtained load–deformation responses have been compared with selected experimental results; the findings form the basis for specific guidelines. These proposals have been verified by application to all available stainless steel stub column tests obtained from different sources. The predicted numerical results have shown excellent agreement with those obtained experimentally. [Copyright &y& Elsevier]

Abstract: The paper is devoted to investigation of stability loss of thin-walled elastic circular cylindrical pipes subjected to simultaneous action of longitudinal compressive forces and uniform corrosion from outside. The pipe is treated as a thin closed elastic circular cylindrical shell which can be described within Kirchhoff–Love approximation. The critical time of stability loss of the pipe is found, using the upper critical load value for static stability loss of the pipe, not subjected to corrosion, and the law of corrosion rate. Numerical results were obtained for pipes, made from steel and aluminum with different initial wall thickness. [Copyright &y& Elsevier]

Abstract: This paper deals with distortional buckling in monosymmetric propped cantilever I-beams under two types of load: a central point load and a uniformly distributed load. Top-flange and bottom-flange load positions are considered. ABAQUS is used for the investigation. Moment modification factors are obtained and are compared with those based on Structural Stability Research Council Guidelines, which take into account lateral–torsion buckling only. It is seen that provisions in SSRC Guidelines seriously overestimate the critical load, especially for short beams. [Copyright &y& Elsevier]

Abstract: In this paper, an energy-equivalent model is put forward for studying the mechanical properties of single-walled carbon nanotubes (SWCNTs). The equivalent Young''s modulus and shear modulus for both armchair and zigzag SWCNTs are derived by combining the methods of molecular mechanics and continuum mechanics. On the one hand, based on the principle of molecular mechanics, the total system potential energy associated with both stretching and angular variations is obtained. On the other hand, considering SWCNT as a thin cylinder subjected to an axial or torsion loading, the strain energy can be obtained based on continuum mechanics. Equating the total system potential energy to the strain energy, one derives the equivalent Young''s modulus, shear modulus and Poisson''s ratio. Finally, computations of the mechanical properties reveal that the elastic constants exhibit a strong dependence on the diameter of nanotubes. Young''s modulus and shear modulus for both armchair and zigzag nanotubes increase with increasing tube diameter, but the variation trend of Poisson''s ratios is reverse. The present results agree well with existing results and approach to those of carbon graphite when the diameter is large. Therefore, the method presented here is valid for both carbon nano-tubes and carbon graphite. [Copyright &y& Elsevier]

Abstract: The paper is devoted to a circular cylindrical panel with three edges simply supported and one edge free. This panel is axially compressed by a load uniformly distributed at both ends. The Donnell equations for linear buckling of shells are assumed and the adequate boundary conditions are defined. The deflection function and the force function–the Airy function are formulated with respect to the boundary conditions. The Donnell equations are reduced to a generalized eigenvalue problem with the use of Galerkin method. The results of numerical investigation are presented in figures. [Copyright &y& Elsevier]

Abstract: This paper studies the buckling behaviour of simply supported square plates, which have weakening or strengthening bands. The weakening/strengthening bands are equally spaced and their thickness is either decreased or increased. The analysis assumes that the stress state in the plate before and during the buckling process remains in the elastic range. Two cases of plate loading are studied, one with compressive forces and one with tangential forces. The buckling coefficients are calculated for different numbers and thicknesses of strengthening/weakening bands. The thickness of strengthening/weakening bands and the thickness of the remaining plate is varied so that the volume/weight of the plate remains constant. In one case it is found that the buckling load at constant weight of the plate can be increased by 118% if an optimal ratio of the thickness of strengthening bands and the thickness of the remaining plate is used. [Copyright &y& Elsevier]

Abstract: The static and dynamic instability characteristics of stiffened shell panels subjected to uniform in-plane harmonic edge loading are investigated in this paper. The eight-noded isoparametric degenerated shell element and a compatible three-noded curved beam element are used to model the shell panels and the stiffeners, respectively. As the usual formulation of degenerated beam element is found to overestimate the torsional rigidity, an attempt has been made to reformulate it in an efficient manner. Moreover, the new formulation for the beam element requires five degrees of freedom per node as that of shell element. The method of Hill''s infinite determinant is applied to analyze the dynamic instability regions. Numerical results are presented through convergence and comparison with the published results from the literature. The effect of various parameters like shell geometry, stiffening scheme, static and dynamic load factors, stiffener size and position, and boundary conditions are considered in buckling and dynamic instability analysis of stiffened panels subjected to uniform in-plane harmonic loads along the boundaries. [Copyright &y& Elsevier]

Abstract: The presence of in-plane loading may cause buckling of stiffened panels. An accurate knowledge of critical buckling load and mode shapes are essential for reliable and lightweight structural design. This paper presents some parametric studies on simply supported laminated composite blade-stiffened panels subjected to in-plane shear loading. A total of 450 models were analyzed using ANSYS 7.1 and a database is prepared for different plate and stiffener combinations. Studies are carried out by changing the panel orthotropy ratio, stiffener depth, pitch length (number of stiffeners), smeared extensional stiffness ratio of stiffener to that of the plate and extensional stiffness to shear stiffness ratio of the plate. Based on the studies, few important parameters influencing the buckling behaviour are identified and guidelines for better stiffener proportioning are developed, which will be helpful for the designer. [Copyright &y& Elsevier]

Abstract: The analysis of submarine pressure hull assumes great importance among structural engineers due to the complexity involved in the collapse mechanism of stiffened shell structures. In most of the cases, the failure of stiffened shell structures occurs due to elastic buckling. But for some combinations of shell-stiffener geometry and material characteristics, the structure can fail by inelastic buckling, for which the methods of analysis are meagre. In this paper, the analysis of submarine pressure hull structure in which the failure gets governed by inelastic buckling is demonstrated. Three different approaches have been employed to investigate the ultimate strength of the ring stiffened submarine pressure hull structure with inelastic buckling modes of failure. The methods used are ‘Johnson–Ostenfeld inelastic correction’, ‘imperfection method’ and ‘finite element approach’. A typical submarine shell structure has been analysed for the inelastic buckling failure using these three approaches and the results are discussed. [Copyright &y& Elsevier]

Abstract: In this paper, the problem of optimal design of shells against instability is considered. A thin-walled shell is loaded, in general, by an external pressure and lateral forces causing overall bending moment (which varies along the axis of a shell) and the appropriate shearing force. We look for the shape of meridian as well as the thickness of a shell, which ensure the maximal critical value of the loading parameter. As the equality constraints, the volume of material and the capacity of a shell are considered. The concept of a shell of uniform stability is applied. [Copyright &y& Elsevier]

Abstract: This paper deals with the post-buckling deformation characteristics of aluminum alloy extruded polygonal section tubes subjected to dynamic axial impacts. The explicit finite element code LS-DYNA is the primary analytical tool used in this investigation. The study focuses on investigating a post-buckling deformation phenomenon that is primarily manifested by an axial crumpling action that generates material folds as the impact energy is dissipated. The research is conducted in two phases. The first phase consists of validating the LS-DYNA model parameters and numerical results pertaining to thin-walled aluminum extruded square tubes with actual published experimental data. The post-buckling deformation characteristics of the specimens such as the overall final configuration and the various folding deformation modes (extensional, symmetric and asymmetric) resulting from the axial collapse of the member is also investigated in a subsequent phase. Based on the numerical simulation results, it is apparent that the increase in the number of walls (flanges) has a direct impact on the mean axial crushing force and permanent displacement parameters. In particular, the adoption of a hexagonal tube section as an axially loaded energy absorbing column yields an average increase of 11% in the mean axial crushing force and an average decrease of 10% in the permanent displacement. The greatest benefits are obtained in the specimens with the thinnest nominal wall thickness, where the upper bound results show an average increase of 27% in the mean axial crushing force and average decrease of 20% in the permanent displacement. [Copyright &y& Elsevier]

Abstract: A geometrically non-linear theory for thin-walled composite beams is developed for both open and closed cross-sections and taking into account shear flexibility (bending and warping shear). This non-linear formulation is used for analyzing the static stability of beams made of composite materials subjected to concentrated end moments, concentrated forces, or uniformly distributed loads. Composite is assumed to be made of symmetric balanced laminates or especially orthotropic laminates. In order to solve the non-linear differential system, Ritz''s method is first applied. Then, the resulting algebraic equilibrium equations are solved by means of an incremental Newton–Rapshon method. This paper investigates numerically the flexural–torsional and lateral buckling and post-buckling behavior of simply supported beams, pointing out the influence of shear–deformation for different laminate stacking sequence and the pre-buckling deflections effect on buckling loads. The numerical results show that the classical predictions of lateral buckling are conservative when the pre-buckling displacements are not negligible, and a non-linear buckling analysis may be required for reliable solutions. [Copyright &y& Elsevier]

Abstract: Fuselage panels are commonly fabricated as skin-stringer constructions, which are permitted to locally buckle under normal flight loads. The current analysis methodologies used to determine the post-buckling response behaviour of stiffened panels relies on applying simplifying assumptions with semi-empirical/empirical data. Using the Finite Element method and employing non-linear material and geometric analysis procedures it is possible to model the post-buckling behaviour of stiffened panels without having to place the same emphases on simplifying assumptions or empirical data. Previous work has demonstrated that using a commercial implicit code, the Finite Element method can be used successfully to model the post-buckling behaviour of flat riveted panels subjected to uniform axial compression. This paper expands the compression modelling procedures to flat riveted panels subjected to uniform shear loading, investigating element, mesh, idealisation and material modelling selection, with results validated against mechanical tests. The work has generated a series of guidelines for the non-linear computational analysis of flat riveted panels subjected to uniform shear loading, highlighting subtle but important differences between shear and compression modelling requirements. [Copyright &y& Elsevier]

Abstract: The aims of this paper are to investigate the ultimate shear strength reduction characteristics of steel plates due to local impacts, and also to develop the ultimate shear strength design formulae of dented steel plates. The ANSYS nonlinear finite element code is used to investigate the effects of shape, size (depth, diameter), and location of the denting on the ultimate strength behavior of simply supported steel plates under edge shear loads. A closed-form expression for predicting the ultimate shear strength of dented steel plates is derived by the regression analysis based on the computed results. The results and insights developed from the present study will be very useful for damage tolerant design of steel plated structures with local denting. [Copyright &y& Elsevier]

Abstract: Despite of the intensive research effort of the last decades there are considerable gaps of knowledge concerning the imperfection sensitivity of steel shell structures, even with regard to the basic buckling cases. It is explained in the presented paper why the most unfavourable imperfection pattern does not exist for shell structures but only different unfavourable patterns depending on the imperfection amplitude. This amplitude-depending pattern cannot be determined with certainty because of the substantial influence of the material non-linearity and because of the numerous post-buckling paths which cross each other. However, the method of quasi-collapse-affine imperfections allows a reasonable approximation to the most unfavourable imperfection pattern. The basic thoughts of this concept are presented. The application of the concept to slender wind-loaded shells illustrates its capability. [Copyright &y& Elsevier]

Abstract: This paper derives the similitude invariants and scaling laws for buckling of polar orthotropic annular plates subjected to radial compressive load and torsional load. The similitude transformation is applied to the governing differential equation directly resulting in a scaling law for buckling load of annular plates and the similarity conditions between a model and a prototype. The scaling law is verified by a series of numerical tests using the solutions from the Ritz method as the theoretical solutions. For complete similitude cases, the buckling loads obtained from the scaling laws are identical to those of the theoretical solution. Since the derived scaling law is independent of the boundary conditions, it is valid for any pairs of model and prototype on the condition that they have identical boundary condition. Therefore, buckling behaviors of the prototype with complicated boundary conditions, of which a theoretical solution is not available, can be predicted from the experimental result on the model. Partial similitude model or scaling law for a pair of model and prototype without complete similarity is also investigated. The partial similarity model is not recommended for polar orthotropic materials, however it demonstrated good estimations for isotropic materials. [Copyright &y& Elsevier]

Abstract: Buckling behavior of rectangular functionally graded plates with geometrical imperfections is studied in this paper. The equilibrium, stability, and compatibility equations of an imperfect functionally graded plate are derived using the classical plate theory. It is assumed that the nonhomogeneous mechanical properties of the plate, graded through thickness, are described by a power function of the thickness variable. The plate is assumed to be under in-plane compressive loading. Simultaneous solving of the stability and compatibility equations in conjunction with the equilibrium equations leads to the buckling relation of the plate. The critical buckling load of a sample plate is obtained and compared for different geometrical ratios. The results are reduced and compared with the results of perfect functionally graded and imperfect isotropic plates. [Copyright &y& Elsevier]

Abstract: Slender section columns can carry additional loads up to failure after local buckling has happened in its elements. This post-local buckling capacity depends mainly on the width–thickness ratios of elements forming the section as well as the state of stresses within it. This paper presents tests to examine the influence of these factors on this additional capacity. The experimental local buckling and ultimate loads of two series of specimens are presented. Each series contains a group of slender I-sections varying in their flange and web width–thickness ratios. In the first series the loads are applied axially through the CG. of the sections, while in the other one they are applied eccentrically about the major and minor axis. Additionally, the tested specimens are simulated numerically by a non-linear finite element model considering different values of overall geometric imperfections. Generally, the post-local buckling strength gained by the sections is higher for axially loaded columns than that of bi-axially loaded ones, and it decreases with increasing eccentricity for the same web and flange width–thickness ratios. [Copyright &y& Elsevier]

Abstract: This paper presents the Finite Element (FE) analysis based mode interaction analysis of thin-walled steel box columns under axial compression. Earlier theoretical results on the optimum design of axially compressed box columns were validated through FE analysis. The study was then extended to cover factors that were previously omitted. These factors included column out-of-straightness, residual stresses and plasticity. Emphasis was given on imperfection sensitivity and its effect on optimum design. [Copyright &y& Elsevier]

Abstract: The design of cylindrical metal silos and tanks is often controlled by considerations of buckling under axial compression. Whilst the effects of geometric imperfections on the buckling strength have been extensively explored, few studies have explored the effects of defects in the boundary conditions and the effects of residual stresses have received even less attention. This paper investigates the initiation and development of imperfections caused by local differential settlement at the supported base and their effect on the elastic buckling of a thin cylindrical shell under axial compression. The shells were treated as initially perfect with perfect support, but developing geometric imperfections and residual stresses as a consequence of local displacement at the supported edge and with residual stresses consistent with the induced geometric imperfections. The results raise interesting questions concerning the criteria of failure and appropriate tolerance measurements for constructed cylindrical shells. [Copyright &y& Elsevier]