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To further expand the application range of cold-formed steel (CFS) members in practical engineering, a novel fold-fastened multi-cellular steel wall (FMSW) was introduced and investigated in detail. The FMSWs were mechanically connected by the hook-shaped and groove-shaped regions at both ends of the single limb members, by which the assembly efficiency was greatly improved. In this paper, a total of 10 slender FMSW specimens were subjected to axial compressive loadings, and the failure mode, load–vertical displacement curves, load–lateral displacement curves, and bearing capacity of the specimens were obtained. According to the experimental results, the development and failure modes of the local-global interactive buckling of FMSWs were revealed. All specimens experienced local buckling initially, followed by global buckling, and ultimately interactive buckling. The load–displacement curves exhibited similar trends, being characterized by three stages: the elastic stage, the elastic-plastic stage, and the descending stage. Furthermore, the nonlinear ascending segment was short, indicating that the failure was sudden. By comparing the bearing capacities among specimens, it was recognized that the ultimate resistance of FMSWs could be obtained by the superposition of the cells, and the bearing capacity was rarely affected by the height-to-thickness ratio. Based on the experimental results, refined finite element (FE) models were established and the accuracy and effectiveness of the modeling method were verified. Valuable reference could be provided by the research achievements of this paper for the subsequent research of CFS built-up members and their application in practical engineering.

Thin-walled composite cylindrical shells are nowadays widely used as primary structures in the aerospace industry. The so-called variable stiffness (VS) composite cylindrical shells with flexible stiffness tailoring characteristics have been made possible by existing AFP techniques. Considering the inherent imperfection sensitivity property of axially compressed thin-walled cylindrical shells, the buckling behaviors of the axially compressed VS composite cylindrical shells with initial geometric imperfections and delamination imperfections are investigated respectively in this paper. The design buckling loads of the axially compressed VS composite cylindrical shells are first determined by the probing method, which is verified by comparing with the existing test data and numerical simulation results. Additionally, a parametric study is conducted to investigate the effects of delamination imperfections on the buckling loads. The constraint delamination sizes of the VS composite cylindrical shells based on the design buckling load in this paper are given. Furthermore, the effects of continuously variable fiber angles on the buckling loads are investigated considering the imperfection sensitivity. The specific VS composite cylindrical shells with both high- buckling loads and low-imperfection sensitivity are obtained. Results indicate that the effects of imperfection sensitivity need to be carefully considered in buckling design of the axially compressed VS composite cylindrical shells.

Negative stiffness (NS) structures have singular mechanical properties and potential applications in various scenarios. A corrugated tube (CT) and an NS lattice structure (NLS) composed of CTs and connection plates are proposed. The mechanical properties of CT and NLS under axial compression are investigated by experiments and simulations. The deformation modes of CT and NLS are layer-by-layer folding of structural layers. The influences of geometric parameters on the compression performance of CT and NLS have been studied. Through a reasonable design of the thickness of upper and lower conical structures, CT and NLS can exhibit periodic changes in peak and valley forces during the compression process, resulting in significant NS behavior. In addition, the increase of CT’s number does not significantly affect the NS effect, and the load-carrying capacity of NLS increases significantly as the number of CT increases. The energy absorption (EA) and peak force values of NLS-$4\times 4$, NLS and NLS-$2\times 2$ are approximately 16, 9, and 4 times those of CT-3.0-0.6-f0.5, and the EA value of an NLS model is the sum of the EA values of its all CTs. In addition, the effects of geometric parameters on the mechanical properties of NLS are systematically investigated. With reasonable parameter values, NLS exhibits strong NS effect and excellent EA capacity.

A postbuckling analysis is presented for a shear-deformable anisotropic laminated cylindrical shell of finite length subjected to axial compression. The material of each layer of the shell is assumed to be linearly elastic, anisotropic and fiber-reinforced. The governing equations are based on a higher order shear-deformable shell theory with the von Kármán–Donnell type of kinematic nonlinearity and including the extension/twist, extension/flexural and flexural/twist couplings. The nonlinear prebuckling deformations and initial geometric imperfections of the shell are both taken into account. A singular perturbation technique is employed to determine the buckling loads and postbuckling equilibrium paths. The numerical illustrations concern the postbuckling response of perfect and imperfect, moderately thick, anisotropic laminated cylindrical shells with different values of shell parameters and stacking sequence. The results confirm that there exists a compressive stress along with an associate shear stress and twisting when the anisotropic shell is subjected to axial compression. The postbuckling equilibrium path is unstable for the moderately thick cylindrical shell under axial compression and the shell structure is imperfection-sensitive.

This paper presents a novel way of strengthening thin-walled steel cylindrical shells against buckling during axial compression in which a small amount of fiber-reinforced polymer (FRP) composite, coated from both sides can increase the buckling strength effectively. The effects of the reinforcement and the angle of fiber orientation as well as initial geometric imperfections on the buckling load-carrying capacity have been made clear through the three kinds of analytical procedures; the conventional linear eigen value buckling analysis, the reduced stiffness (RS) buckling analysis and the fully nonlinear numerical experiments. These multiple treatments suggest obtaining valuable information for the design of FRP-based hybrid structural elements and discusses influence of FRP to increase the load-carrying capacity of the thin-walled metallic structures having complex buckling collapse behavior. This paper also discusses how the angle of fiber orientation affects on the buckling strength and the associated buckling modes of the thin-walled shells.

This paper presents the results of the experimental studies conducted on the buckling behavior of 420 MPa high strength steel, hot-rolled, equal angle columns, numbering a total of 66 specimens with a wide range of column slenderness and section sizes. Based on the test results, the buckling modes and capacities were analyzed and the nondimensional buckling strengths were obtained and compared with the design strength predicted from Eurocode 3, ANSI/AISC 360-10 and Chinese standards GB50017-2003. The experimental results in previous studies were also employed in the comparison. The effect of width to thickness ratio of legs of an angle on buckling modes and strengths were investigated. It was found that the buckling strengths from test results were much higher than the corresponding design values and current design approaches were too conservative. Based on present and previous experimental results, a new design approach is suggested for the design of angle columns with 420 MPa high strength steel.

A generalized analytical formula is developed to predict buckling of anisotropic laminated composite fixed–fixed thin columns by using the Rayleigh–Ritz displacement field approximation. Based on the generalized constitutive relationship, the effective extensional, coupling and flexural stiffness coefficients of the anisotropic layup are determined using dimensional reduction by static condensation of the 6$\times$6 composite stiffness matrix. The resulting explicit formula is expressed in terms of the flexural stiffness since the coupling and extensional stiffness coefficients drop out of the formulation for this boundary condition when following the standard Rayleigh–Ritz formulation steps. This formula is similar to the Euler buckling formula in which the flexural rigidity is expressed in terms of the flexural stiffness coefficient of laminated composites. Motivated by reducing some of the discrepancy with the finite element results, the pre-buckling solution was substituted into the bifurcation expression to yield an updated formula that includes the coupling and extensional stiffness coefficients. The analytical results are verified against finite element Eigen value solutions for a wide range of anisotropic laminated layups yielding high accuracy. A parametric study is then conducted to examine the effect of ply orientation and material properties including hybrid carbon/glass fiber composites. Relevance of the numerical and analytical results is discussed for all these cases. In addition, comparisons with an earlier buckling solution for cross-ply laminated columns are made.

This paper studies the structural stability of circular steel tubular stub columns at elevated temperatures under axial compression. Fifty-one specimens are subjected to high-temperature treatment and axial compression. The variables of the specimen are temperature, wall thickness of steel tube and duration of high temperature. The displacement–load curve, strain–load curve, ultimate load, axial compressive stiffness and failure characteristics of the specimens were analyzed. Test results show that after exposure to high temperatures, the specimens’ failure phenomenon in the axial compression loading test is consistent with that at room temperature, the bearing capacity decreases considerably, the ductility decreases slightly and the axial compressive stiffness changes irregularly. Temperature is the determining factor of the ultimate load of the specimen, and the reducing extent of ultimate load increases with the temperature. When the temperature reaches 1000^∘C, its maximum reducing extent exceeds 50%. Among the three parameters considered in this study, the duration of high temperature has the least influence on the specimen.

The geometrically nonlinear response of sandwich functionally graded cylindrical shells reinforced by orthogonal and/or spiral stiffeners and subjected to axial compressive loads is investigated in this paper. Two types of sandwich functionally graded material models are considered. The formulations are based on the Donnell shell theory considering geometrical nonlinearity and Pasternak’s elastic foundation. The improved Lekhnitskii’s smeared stiffener technique is used to account for the stiffener effects with both mechanical and thermal stresses. The results obtained indicate that the spiral stiffeners have significantly beneficial influences in comparison with orthogonal stiffeners on the nonlinear buckling behavior of shells. The relatively large effects of temperature change, geometrical and material parameters are also demonstrated in the numerical investigations.

In this paper, semi-analytical and analytical methods for the nonlinear static and dynamic buckling analyses of imperfect functionally graded porous (FGP) cylindrical shells subjected to axial compression are presented. The structure is embedded within a generalized nonlinear elastic foundation, treated as a two-parameter Winkler–Pasternak foundation augmented by a nonlinear cubic stiffness. The material property of the shell changes continuously through the thickness. Two types of FGP distributions, i.e. uniform porosity distribution (UPD) and nonuniform porosity distribution (NPD), are considered. By applying the Galerkin’s method to the von Kármán equations, the buckling of the shells was solved. The fourth-order Runge–Kutta method is utilized to obtain the responses of nonlinear dynamic buckling (NDB). The results obtained for some special cases are compared with those available elsewhere. The effects of various geometrical properties, material parameters and elastic foundation coefficients are investigated on the nonlinear static buckling (NSB) and dynamic buckling (DB) analyses of the shells. It was shown that various types of porosity, imperfection and the elastic foundation parameters have a strong effect on the buckling behaviors of the FGP cylindrical shells.

Buckling design of axially compressed cylindrical shells is still a challenging subject considering the high imperfection-sensitive characteristic in this kind of structure. With the development of various design methods, the energy barrier concept dealing with buckling of imperfection-sensitive cylindrical shells exhibits a promising prospect in recent years. In this study, buckling design of imperfection-sensitive cylindrical shells under axial compression based on the energy barrier approach is systematically investigated. The methodology about buckling design based on the energy barrier approach is described in detail first taking advantage of the cylindrical shells whose buckling loads have been extensively tested. Then, validation and discussion about this buckling design method have been carried out by the numerical and experimental analyses on the cylindrical shells with different geometrical and boundary imperfections. Results in this study together with the available experimental data have verified the reliability and advantage of the buckling design method based on energy barrier approach. A design criterion based on the energy barrier approach is therefore established and compared with the other criteria. Results indicate that buckling design based on energy barrier approach can be used as an efficient way in the lightweight design of thin-shell structures.

Circular steel-tube members are extensively used in various large-scale steel structures. The detrimental effects of corrosion on the ultimate bearing capacities of these structures require urgent attention. This study designed six circular steel tube specimens to explore the degradation pattern of the ultimate bearing capacity of corroded circular steel tubes under axial compression; three were subjected to accelerated corrosion by electrification, and the other three were used as the control group. Following the accelerated corrosion test, both groups of specimens were subjected to material-property and axial-compression tests. These tests provided data on the bearing capacity and midspan displacement of the corroded circular steel tubes, allowing for the construction of load–displacement relationship curves. The test results demonstrate that corrosion significantly affects the bearing capacity of circular steel tubes. As the severity of the corrosion increased, the bearing capacity and stiffness of the corroded circular steel tubes progressively weakened. To simulate the behavior of circular steel tubes, a numerical model was established that provided the ultimate bearing capacity under axial compression and generated load–displacement curves. The simulation results closely aligned with the test results. This study introduced a novel approach for accurately computing the stability-bearing capacity of circular steel tubes subjected to corrosion and axial compression. Comparative analyzes with test results validated the superior performance of the proposed method in accurately predicting the ultimate bearing capacity.

Surgery of nucleus pulposus removal is one of the methods used for the treatment of lumbar disc herniation in the clinic. In order to understand the strain states of the lumbar intervertebral disc (IVD) after nucleotomy, the axial compression experiments of porcine lumbar IVD were implemented using digital image correlation (DIC) technology. The normal IVDs are named as control group; the IVDs treated with trypsin by removing the nucleus pulposus are named as experimental group. The distributions and the change rules of both axial and radial strains in different regions of the IVD with load were studied, and the experimental results of two groups were compared. The results show that both axial and radial strains of different regions increased with stress in two groups, and the variation had non-uniformity. The axial strain in the posterior region of the annulus fibrosus (AF) was larger than that in the anterior region, and the inner AF was larger than that of the outer AF. The axial strain increase of the experimental group was larger than that of the control group obviously. In the posterior region, the radial strain increase was larger than that in the anterior region, and the outer AF was significantly larger than that of the inner AF. The radial strain direction of the experimental group in the inner AF was towards the center of the nucleus pulposus, which was opposite to that of the control group, and the radial strain increase was evidently smaller than that of the control group. In the outer AF, the radial strain direction of the experimental group was the same as that of the control group and the radial strain increase was significantly larger than that.

This paper studies the instability behavior of stringer-stiffened cone–cylinder shells under axial compressive load via computational finite element (FE) code, ABAQUS. First, the FE model was validated using past experiments on four cone–cylinder specimens (two unstiffened and two stringer-stiffened) fabricated in pairs using mild steel. Results show that the comparison between numerical and experimental collapse loads was less than 10%. Second, parametric study was conducted using the validated FE model to investigate the effects of the location and number of stringers on the buckling behavior of axially compressed cone–cylinder structures. It has been found that reinforcing the cone–cylinder structures tends to produce higher buckling load when compared to the unstiffened ones. The presence of stringers changes the failure mode of the structure, and the initial post-buckling curves show a less steep negative slope when compared to that of the unstiffened counterpart. Externally stiffened structures were able to sustain more load as compared to the internally stiffened counterpart. Introducing longitudinal reinforcement on the conical section and ring reinforcement on the cone–cylinder junction produces a much higher buckling load compared to having stringer-stiffeners on the conical part only.