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• An accurate nonlinear buckling model is proposed for the flexoelectric cylindrical nanoshell. • The pre-buckling nonlinear deformation is employed to improve the accuracy of critical buckling stresses and buckling mode shapes. • The effects of key influencing parameters on buckling characteristics of the flexoelectric cylindrical nanoshell is investigated and reveal. In this paper, a buckling analysis for flexoelectric cylindrical nanoshells under axial compression is performed by considering the higher-order shear deformation theory and non-uniform pre-buckling deformation. Size-dependent critical buckling stresses and buckling mode shapes are obtained by the Galerkin's method with newly proposed displacement functions. Numerical results are compared with existing solutions and excellent agreements are observed. Furthermore, a comprehensive parametric study of boundary conditions, geometrical parameters and applied electric voltage is carried out to reveal the influence of flexoelectric effect on the size-dependent buckling characteristics of flexoelectric cylindrical nanoshells. [ABSTRACT FROM AUTHOR]

• Using the FG-X graphene pattern in channel section struts boosts the critical buckling temperature by 12 % for clamped and 9 % for simply-supported struts, compared to the FGO pattern. • For a shape factor of b f / b w = 0.2 , changing graphene in the flanges minimally affects strut buckling temperature. However, altering the web's graphene pattern, with consistent flange reinforcement, can alter the temperature by up to 12 %. • The study on thermal pre- and post-buckling vibrations in struts with various graphene patterns reveals FGX configurations yield the highest frequencies through the pre-buckling state, though this trend shifts in the post-buckling. • Integrating an asymmetric graphene pattern (FGV) or embedding geometric imperfections sustain the primary natural frequencies of FG-GRC channel section struts above zero as they approach the critical buckling temperature. This study explores the effect of local buckling on the compressive performance of slender structural elements, particularly those with thin-walled sections. The phenomenon of local buckling significantly reduces the axial compressive stiffness, leading to a notable decrease in the load-bearing capacity of these elements. The main goal of this research is to examine how the post-buckling characteristics of polymeric composite channel section struts can be improved under thermal loading by incorporating multi-layer graphene reinforcements. The solution methodology incorporates the von Karman geometrical nonlinearity and is based on the layerwise third-order shear deformation theory (LW-TSDT). To ascertain the precision and computational performance of the results derived from LW-TSDT, a three-dimensional (3D) finite element model is created in ABAQUS for comparative evaluation. An extensive analysis of nonlinear thermal instability in perfect and geometrically imperfect FG-GRC laminated channel section struts is undertaken to discern the graphene distribution patterns that are most and least effective in elevating the critical buckling temperature and natural frequencies through pre- and post-buckling conditions. The comparative analysis indicates that employing the FG-X graphene distribution pattern across the thickness of the web and flanges in channel section struts leads to a projected increase of 12 % in the critical buckling temperature for clamped channel section struts, in contrast to those that adopt the FGO graphene distribution pattern. For cases with simply-supported boundary conditions, this increase is noted to be approximately 9 %. Moreover, findings confirm that incorporating an asymmetric graphene distribution pattern (FGV) or introducing geometrical imperfections in the flanges and web that generate a bending moment within the structure from the beginning of thermal loading effectively prevents the primary natural frequencies of FG-GRC channel section struts from declining to zero close to the critical buckling temperature. This is significantly different from scenarios involving perfectly structured and symmetrically reinforced graphene distribution patterns such as FGX. [ABSTRACT FROM AUTHOR]

• Buckling behavior of delaminated steel-composite cylinders was experimentally explored. • Influence of delaminated parameters on the buckling behavior was numerically discussed. • Practical equations were proposed to evaluate the linear and nonlinear buckling loads. • Practical equations to evaluate the buckling loads were developed by statistical models. This study investigated the buckling behavior of steel–composite cylindrical pressure hulls with initial delamination. Hydrostatic tests were conducted on three groups of steel–composite cylindrical pressure hulls with different delamination parameters, and the study determined the relationships between the delamination parameters and buckling behavior of delaminated pressure hulls. Numerical analyses were conducted using linear subspace and nonlinear Riks methods, followed by a comprehensive comparison of the numerical and experimental results. Numerical and response surface analyses were conducted, and two sets of practical equations were proposed to evaluate the linear and nonlinear buckling loads of steel–composite cylindrical pressure hulls. The results indicated that initial delamination reduced the buckling loads by 50 %, with the ratio of delamination length to total length being the key factor determining the nonlinear buckling loads of delaminated steel–composite cylindrical pressure hulls. [ABSTRACT FROM AUTHOR]

• The paper investigates rib-based reinforcement strategies for improving structural integrity of form-found shell structures. • The study introduces diverse stiffening patterns for shell structures, designed with geometric, biomimetic, and optimization-derived methodologies. • The paper demonstrates through mechanical testing and numerical simulations that these patterns significantly improve stiffness and buckling resistance of form-found shells. • The study validates that integrating form-finding with targeted rib-based reinforcements can lead to sustainable and structurally resilient solutions. This paper investigates innovative approaches for enhancing the structural integrity of form-found shell structures with a focus on rib-based reinforcements. It discusses the significance of ribs in enhancing stability and addressing the sensitivity of form-found structures to various loads. Traditional methods such as increasing shell thickness or introducing supports often compromise efficiency and aesthetics. A more intelligent approach involves reinforcing the shell with ribs and advanced materials. Diverse rib patterns are presented, including geometric, biomimetic, and topological optimization-inspired designs, each adhering to a 50 % volume constraint, when compared to the original shell. Physical testing and numerical simulations demonstrate that these rib patterns significantly increase stiffness and buckling resistance. The findings presented in the paper suggest that combining form-finding methodologies with well-designed rib patterns can create sustainable and resilient structures, contributing to a reduction in both the consumption of materials and the environmental impact of these structures. [ABSTRACT FROM AUTHOR]

• Deriving the strong-form of the classical sandwich plate with boundary condition under in- plane pre-loading. • Predicting the buckling load of the rectangular plate with boundary condition using vibration correlation technique for the first time. • Using meshless collocation method based on radial function in vibration correlation technique for the first time. • The use of artificial neural network and genetic algorithm in obtaining the optimal geometric parameters for elliptical cutout. • Comparison of critical load and shape of buckling and vibration modes in two numerical methods meshless and finite element with experimental method. The present research was carried out in order to estimate the buckling load of a sandwich plate with a trapezoidal corrugated core with cut-out using three vibration correlation techniques (VCT). The structure investigated in this research is a sandwich plate with a trapezoidal core and an oval cut-out, which is made of thermoplastic polymer using a 3D printer. By using artificial neural network (ANN) and genetic algorithm (GA), the specific critical buckling load (p ¯ c r) which is defined as the ratio of critical buckling load (P cr) to plate weight (gr) has been minimized and the optimal dimensions for cut-out parameters including the ratio of the large diameter of the ellipse (z = 20 m m) to the small diameter of the ellipse (b) and oval angles with the horizontal axis (a ∘) are obtained. Using the method of equivalent properties, the trapezoidal core is transformed into an equivalent orthotropic core and finally the desired structure is transformed into a three-layer sandwich plate including homogeneous upper and lower layers and an orthotropic middle layer. By using the meshless method based on radial and polynomial functions and with the help of the finite element method, the numerical simulation of buckling and free vibration of the sandwich plate has been done. The results showed that the estimation of the buckling load with the vibration correlation technique (VCT) corresponds to the actual condition of the structure, so that due to the high quality of sandwich plate construction and its integrity, the results obtained from the first, second, and third methods of the VCT show the effectiveness of this method for predicting of the buckling load of the structure. [ABSTRACT FROM AUTHOR]

• Introduced a novel formula for helical spring buckling under combined loads. • Experimental and numerical analyses confirm the formula's effectiveness. • Higher preload and prestretching enhance spring buckling torque resistance. A new formula is introduced to analytically determine the critical torsional load or angle of rotation that confers instability in a tension spring under combined tension and torsion load using the theoretical framework of Greenhill's problem applied to an elastic bar as a starting point. The formula's effectiveness is evaluated with experimental torsion tests and finite element method simulations in Abaqus. The results demonstrate the formula's accuracy in predicting instability within specific stretched operating ranges, and achieving a relative error in correlation below 10 % for most operating points. The study underscores the significance of preload and pre-stretching in enhancing the spring's resistance to buckling. [ABSTRACT FROM AUTHOR]

Thin-walled prismatic metallic members as well as structures made of laminated composite materials are routinely employed in engineering branches such as civil engineering or lightweight construction and design. Due to their thin-walled nature, such structures exhibit a number of specific characteristics that need to be taken into account during analysis and design. One of these special features is the tendency to exhibit an interaction of local, global and distortional deformation patterns which has a major impact on the structural response in the framework of first-order analysis, but also concerning the buckling, postbuckling and vibration behavior of such structures. One analysis method that takes such effects into account in a natural and straightforward way is the so-called Generalized Beam Theory (GBT), and this paper aims at providing an overview of the state of the art in this specific field. In all, 460 references are cited. • Presents a state-of-the-art survey of the Generalized Beam Theory for the analysis of thin-walled structures. • Presents an encompassing literature survey sorted by working groups around the world. • Enables researchers to find their own starting point in research in this specific field. • Includes 460 references. [ABSTRACT FROM AUTHOR]

Buckling and sound radiation characteristics of curved sandwich panels subjected to combined thermo-mechanical loads are presented in the paper. The panel comprises a 3-D functionally graded graphene porous core sandwiched between FG-V Λ CNT reinforced composite face sheets (3DGrF-CF). The governing differential equations of 3DGrF-CF sandwich panels are derived using the parabolic shear deformation theory (PSDT), and the vibration responses are predicted using Navier's approach. The vibration response thus obtained is fed into the Rayleigh integral to capture the acoustic pressure. The buckling and sound radiation characteristics were found to vary significantly with the core's porosity coefficient and porosity grading pattern. However, the impact of this influence also depends on the magnitude of thermal & mechanical loading. This implies that selecting a core for acoustic comfort depends on the dominance of loading conditions and is illustrated using octave band analysis. • Buckling & vibro-acoustic analysis of 3DGrF-CF panels under thermo-mechanical loads. • Analytical prediction using Navier's & Rayleigh's approach considering PSDT. • Optimum porosity coefficient & grading pattern for different loading conditions. [Display omitted] [ABSTRACT FROM AUTHOR]

• A competitive-failure analysis framework of composite cylinder was proposed. • The material degradation model was adapted to judge the failure mode of composites. • The effectiveness and precision of the proposed framework were validated. • The effects of several design parameters on the competitive-failure were examined. When thin-walled composite cylindrical shells are subjected to combined loads, not only will they buckle, but they could fail under overstressing. Buckling-failure and stress-failure are two types of failure that compete mutually, and if one of them occurs, the structure loses its ability to carry the load. However, there is a lack of study, and very little attention was paid to the competitive-failure of the composite cylindrical shells under combined loads. To bridge this research gap, a competitive failure analysis framework of degraded composite cylindrical shells exposed to combined axial compression and external pressure loads was developed, considering the nonlinear buckling-failure interacting curve approach for buckling-failure analysis and the Tsai-Wu failure criterion for stress-failure analysis. The material degradation model was adopted to modify the properties of the failed ply based on two degrading philosophies. The proposed framework agrees well with the published results. Extensive parametric studies are accomplished and presented to detect the failure mode of composites. For material parametric study, the variation of material properties does not significantly affect the shape of the normalized buckling-failure interacting curve, while it appreciably affects the behavior of the stress-failure interacting curve. Moreover, it is found that as the proportions of the longitudinal compressive strength to longitudinal modulus and transverse tensile strength to transverse modulus of composite materials increase, the tendency for buckling-failure increases; otherwise, stress-failure happens. For a geometric parametric study, decreasing the radius-to-thickness ratio leads to an increase in the shape of the buckling-failure interacting curve and the possibility of stress-failure. [ABSTRACT FROM AUTHOR]

• Higher order FEMs are proposed for bio-inspired laminated composites plates using a quasi-3D theory for the first time. • Three different FEMs are derived based on non-conforming elements with different number of nodes and degree of freedom. • No shear locking phenomenon was observed in the analyses conducted using these FEMs. • Effects of lamination scheme, orthotropy ratio and aspect ratio on the mechanical response of the bio-inspired helicoidal composite plates are examined. A comprehensive study is carried out by employing various finite element models (FEMs) for the bending, buckling stability and free vibration analyses of bio-inspired helicoidal composite plates with various lamination schemes. A higher order quasi-3D kinematic plate theory is developed to include a shear deformation effect. The variational formulation of the problem is exploited to derive the equations of motion, element stiffness, geometrical stiffness, and mass matrices based on a non-conforming rectangular element. Three different finite elements models are derived based on non-conforming elements with different number of nodes and degree of freedom. The developed finite element model has been validated with those found in the open literature. The effects of boundary condition, lamination scheme, orthotropy ratio and aspect ratio on the mechanical response of the bio-inspired helicoidal composite plates are examined. Notably, for the lamination schemes investigated in this study, no shear locking phenomenon was observed in the analyses conducted using these FEMs. Dimensionless centre deflections, critical buckling loads and fundamental frequencies of bio-inspired helicoidal composite plates vary depending on the type of lamination scheme, boundary condition and aspect ratio. The new orientation schemes can replace the traditional ones to overcome the shear singularity and overcome the delamination defects. [ABSTRACT FROM AUTHOR]

• A new non-uniform rectangular honeycomb sandwich panel is designed based on Bezier curves to enhance material utilization. • The effective elastic constants of non-periodic honeycombs are obtained through the geometric equivalent method and the strain energy-based homogenization method. • The analytical solutions of bending and buckling responses of the non-uniform rectangular honeycomb sandwich panel are derived by using parabolic shear deformation theory. • The weight/performance multi-objective optimization design of the non-uniform rectangular honeycomb sandwich panel is conducted. Honeycomb sandwich panels have a wide range of applications in aerospace, marine and energy industry due to their high stiffness-to-weight ratio. In this study, a new non-uniform rectangular honeycomb core is presented to promote its material utilization ratio. The non-uniform wall of honeycomb core is described using Bezier curves, and the effective elastic constants are obtained by both the geometric equivalent method and the strain energy-based homogenization method. To analyze the bending and buckling behaviors of the sandwich panel, the parabolic shear deformation theory is adopted, and the governing equations are derived by employing Hamilton's principle. Then, the closed-form solutions of bending and buckling responses of the non-uniform rectangular honeycomb sandwich panel are derived. Furthermore, multi-objective design formulations are established, with the objectives of minimizing the weight and deflection, and maximizing the critical buckling load. Illustrative examples demonstrate that the non-uniform design of the honeycomb core can remarkably increase the material utilization rate and improve the mechanical performance of sandwich panels. [ABSTRACT FROM AUTHOR]

• Frameless CFSCWs can work as lateral systems in low rise long span structures. • Tension field action increases the shear strength in the post-buckling region. • Finite element models can simulate the CFSCWs under combined shear and axial loads. • Frameless CFSCWs can be designed under varying axial loads by obtained equations. This paper presents a comprehensive evaluation of a novel Cold Form Steel Corrugated Walls (CFSCWs), named Frameless CFSCWs, under combined axial and lateral loads. A series of experimental investigations were carried out on full-scale specimens. The influence of different axial loads on the buckling-failure mode, the peak force capacity, the post-buckling stiffness, and the residual force capacity are presented. Subsequently, robust finite element models were developed to simulate the complex bucking behavior of these Frameless CFSCWs. The results of the experimental and numerical investigations revealed that the lateral force-deformation response of Frameless CFSCW is highly influenced by the axial loads. A linearized backbone curve of the Frameless CFSCWs with different axial loads is proposed. Key design parameters such as overstrength and ductility ratios of the Frameless CFSCW panels are identified. The linearized backbone curve can be used by engineer to design Frameless CFSCWs under different axial loads. [ABSTRACT FROM AUTHOR]

• Altering the distribution patterns of graphene reinforcement across the flanges and web, while keeping the geometrical parameters constant, can enhance the critical buckling end-shortening and load-bearing capacity by approximately 80% and 25%, respectively. • The study revealed that the suggested approach (LW-TSDT) accelerates the running time by about 31% compared to the FEM. • In cases where web buckling is predominant, variation in graphene distribution across the flanges has negligible influence on the web's stability response. • Disregarding the specific graphene distribution patterns, the point of highest membrane stress occurs at the junction of the flange and web. The role of local buckling on the behavior of slender members under compression has received considerable attention in structural engineering. For thin-walled sections, in particular, there is a noticeable decrease in the axial compressive stiffness, resulting in a substantial reduction in their load-bearing capacity due to the occurrence of local buckling. The principal purpose of this article is to explore the potential improvements in the postbuckling characteristics of polymeric composite channel section struts subjected to a progressive end-shortening by employing multi-layer graphene sheets reinforcements. The solution methodology incorporates the von Karman geometrical nonlinearity and is based on the layerwise third-order shear deformation theory (LW-TSDT). To verify the accuracy of the results obtained based on LW-TSDT and to evaluate its computational efficiency, a three-dimensional (3D) finite element model is also developed using ABAQUS for the comparative analysis. A thorough examination of nonlinear instability is conducted on composite laminated channel section struts, featuring distinctive graphene distribution patterns through the thickness directions of the flanges and webs to identify the most effective material distribution with the objective of a significant increase in critical end-shortening and axial compressive stiffness. The influence of the geometrical parameters on the critical end-shortening, postbuckling equilibrium paths, and load-bearing capacity of functionally graded graphene reinforced composite (FG-GRC) laminated channel section struts are elicited. The conducted parametric analyses emphasize that altering the distribution patterns of graphene reinforcement across the flanges and web can enhance the critical end-shortening and load-bearing capacity by 80% and 25%, respectively. [ABSTRACT FROM AUTHOR]

• The paper presents a novel approach for calculating the elastic critical moment of corrugated web girders. • The results obtained with the new proposal significantly enhance the outcomes of previous methods. • The new proposal is based on closed-form formulas to determine equivalent section properties. Using corrugated web girders offers several advantages, including increased resistance to lateral-torsional buckling. Researchers have proposed various methods for determining the critical moment value as a function of the cross-sectional geometry. Previous studies have suggested that the enhanced critical moment is attributable to a larger warping constant. In this paper, we present the results of a systematic numerical study using finite element analysis on girders with various corrugated web shapes. Bending along the weak axis demonstrates that corrugated web girders possess a higher moment of inertia. Furthermore, our torsion linear analysis indicates that the increase in the critical moment is primarily due to a larger torsional constant. We compare the elastic critical moment values obtained using finite element linear buckling analysis to those derived from theoretical expressions that introduce equivalent section properties. Our results illustrate that the equivalent section properties method provides values that closely resemble those obtained using finite elements. Finally, we provide closed-form expressions that can be used to estimate equivalent section properties for any girder with a corrugated web. Our findings suggest that employing these expressions to calculate the critical moment yields results that are satisfactory when compared to those obtained through finite element linear buckling analysis. [ABSTRACT FROM AUTHOR]

• Investigation of the interaction between buckling and lateral buckling of thin-walled beams with arbitrary open cross-section using nonlinear modeling in large rotation and with warping. • The dimensionless equilibrium equations are established. • Introduction of various dimensionless parameters that control the interaction between buckling and lateral buckling. • The proposed analytical solutions are validated and compared to numerical solutions obtained from B3Dw beam elements based on Asymptotic Numerical Method. This paper investigates the interaction between buckling and lateral buckling of thin-walled beams with arbitrary open cross-section using nonlinear modeling in large rotation and with warping. First, the equilibrium equations have been transformed into dimensionless ones, and within a nonlinear stability model, various dimensionless parameters are introduced to control the interaction between buckling and lateral buckling. In comparison to a reference of literature, this work focuses on the case of arbitrary sections and includes a greater number of higher-order terms in our analysis. These additions have an impact on the coefficients of the stability formula by expanding its applicability to non- symmetric sections. Then, the effect of the different dimensionless parameters, thus introduced on the stability curve, has been studied. The proposed solutions are validated and compared to numerical solutions obtained by a general finite element package including the warping developed by the authors using Asymptotic Numerical Method (ANM) to solve the initial nonlinear equations. [ABSTRACT FROM AUTHOR]

• A novel general numerical method, discrete Ritz method (DRM), is proposed for buckling analysis of arbitrarily shaped plates with arbitrary cutouts. • DRM combines the extended interval integral, Gauss quadrature, and variable stiffness, and builds a discrete energy system over a standard rectangular domain. • Cutouts with zero stiffness are used to simulate the shape of plates as well as inner cutouts. • Using variable stiffness and Gauss integration points in combination, DRM discretizes energy and uses cutouts to control the geometric boundary of the plate. • Standard energy functionals are established within a rectangular domain in terms of cutouts for arbitrarily shaped perforated plates, making the computation procedure standard. To overcome the difficulties of the Ritz method when dealing with complex geometric domain problem, a novel general numerical approach, discrete Ritz method (DRM), is proposed for buckling analysis of arbitrarily shaped plates with arbitrary cutouts. Accounting for a variety of boundary conditions, Legendre polynomials are adopted to construct the admissible function. By using the global trial function with variable stiffness properties within a virtual rectangular design domain, the deformation of arbitrarily shaped plates can be captured with the help of numerical integration using Gauss quadrature. The shapes and cutouts of plates are both numerically simulated by using cutouts, where the stiffness is assigned zero within the cutouts in the virtual rectangular domain. Moreover, boundary conditions and load potential can be applied to any contour of the plate. Based on the above formulation, standard energy functionals and computation procedures are established to extract the buckling eigenvalues and mode shapes. Variously shaped plates with arbitrarily shaped cutouts are investigated. Under several boundary conditions, multiple inplane loads are applied, and the results are compared with those obtained by other numerical and analytical methods in the literature. Demonstrating the stability and accuracy of the DRM. [ABSTRACT FROM AUTHOR]

In this work, an experimental and numerical methodology is proposed to study the elasto-plastic buckling response of thin cylindrical shells with spigot support under axial compression. A multi-3D digital image correlation system is used to measure the geometrical imperfections as well as the buckling response of the shell. Further, a coordinate measuring machine is employed to measure the edge loading imperfections of the shell. Next, interpolation methods are employed to transfer the measured imperfections to a finite element (FE) model. The effect of interference between the spigot and shell on the nonlinear buckling response of the shell is studied. The numerical results of FE models embedded with the measured edge and radial imperfections are compared with the experimental response. This study emphasizes the importance of including geometrical/loading imperfections for accurately estimating the buckling load of cylindrical shells used in launch vehicle applications. • Buckling of Aluminum cylindrical shells with spigot support under axial compression. • Measurement of geometrical imperfections using a 3D DIC setup and a Laser scanner. • Measurement of edge imperfections using a Coordinate Measurement Machine. • Experiments using a multi-DIC setup to capture the full-field buckling response. • High-fidelity FE model to simulate buckling of cylindrical shell with spigot support. [ABSTRACT FROM AUTHOR]

Triaxial weaving can form two-dimensional structures into three-dimensional structures using initially straight and flat ribbons. However, most of the 3D structures fabricated with conventional weaving methods using straight ribbons have some topological defects. To obtain smoother 3D surface structures, Baek proposed a novel weaving method using naturally curved (in-plane) ribbons to fabricate three-dimensional curved structures. We believe that an ellipsoidal weave with smooth geometric properties must have new mechanical properties. To this end, the buckling behavior of an ellipsoidal weave with naturally in-plane curved ribbons is investigated with a test and dimensional analysis in this research. The results of the calculations and experiments show that the failure modes of an ellipsoidal weave under vertical loading are divided into the inward deformation of the ribbon, overall wave buckling, and "blister" buckling along the strong radius. The aspect ratios, ribbon width, and thickness have a great effect on the buckling behavior of ellipsoidal weaves. The high load capacity and strong stability of ellipsoidal weaves with thicker or wider ribbons are exhibited. Moreover, the geometric size limit of the curved ribbons of an ellipsoidal weave is obtained with experiments. In addition, in this research, the buckling load equation and initial stiffness equation for an ellipsoidal weave are proposed using the method of testing and theoretical analysis. Our study can provide a theoretical basis for the stable design of an ellipsoidal weave structure. • Studied the buckling behavior of ellipsoidal grid-shells by experimental. • The failure mode of ellipsoidal weave with naturally curved ribbons are investigated. • Width and thickness of ribbons on the buckling behavior of the ellipsoidal weaves. • The buckling load equation and initial stiffness of ellipsoidal weaves are carried out. [ABSTRACT FROM AUTHOR]

This work provides an assessment of Equivalent Single Layer (ESL) and Layerwise finite element models, aimed for panel flutter and buckling analysis of supersonic variable stiffness composites, exploring variable-order shear deformation theories and Lagrange z -expansions. Numerical applications focus on simply supported panels with curvilinear fibre composite layers, including a cross-ply configuration for comparison purposes, and various side-to-thickness ratios. The accurate prediction of transverse shear and bending–twisting coupling is highlighted, as rather necessary for proper tailoring and analysis of supersonic curvilinear composites, especially when including in-plane loads. This is attainable through high-order ESL descriptions, in thin panels, even without thickness stretching. • Refined models for aeroelastic stability analysis of variable stiffness composites. • Variable-order ELS and LW descriptions assessed for flutter and buckling response. • Proper modelling of curvilinear fibre composites in pre-stressed supersonic panels. [ABSTRACT FROM AUTHOR]

One of the most effective nondestructive methods to estimate the buckling load of imperfection sensitive thin-walled structures is vibration correlation technique (VCT). Although this technique can determine the buckling load for several types of structures without reaching the instability point, it is still under development for composite sandwich plates and shells. In this paper, experimental and numerical verification of VCT approach are presented for the estimation of the buckling load of the composite sandwich plates with iso-grid cores loaded in compression. In the experimental section, four specimens are designed and fabricated using a new silicone rubber mold, and hand lay-up technique. The modal test is performed on the first specimen by exciting the sandwich plates using the modal hammer method in the different applied loads. Then, the variation of the natural frequency with the applied compressive load is recorded up to actual experimental buckling load. Besides, numerical models, including nonlinear effects, are created in full details to calculate the variation of the natural frequencies with the applied load, and to be compared with the experimental results. Finally, the buckling test is carried out on all specimens to validate the experimental and numerical results of VCT approach. The results demonstrate that the maximum difference between the predicted buckling load using the VCT approach on the experimental and numerical results with an experimental buckling load is less than 3%. Also, VCT provides a reliable estimate of buckling load when the composite sandwich plates with iso-grid cores have been loaded up to at least 67% of the experimental buckling load. • Experimental and numerical validation of VCT approach were presented for the estimation of the buckling load of the composite sandwich plates with iso-grid cores. • The modal analysis of the composite sandwich plates with iso-grid-cores was performed using the modal hammer method. • Finite element models, including nonlinear effects such as geometric and thickness imperfection, was performed. • The maximum difference between the predicted buckling load using the VCT approach on the experimental and numerical results with an experimental buckling load was less than 3%. • It was shown that VCT provides a reliable estimate of buckling load when the composite sandwich plates with iso-grid cores have been loaded up to at least 67% of the critical load. [ABSTRACT FROM AUTHOR]

This paper provides a review of recent developments in research and design practice surrounding the structural use of stainless steel, with an emphasis on structural stability. The nonlinear stress-strain characteristics of stainless steel, which are discussed first, give rise to a structural response that differs somewhat from that of structural carbon steel. Depending on the type and proportions of the structural element or system, the nonlinear material response can lead to either a reduced or enhanced capacity relative to an equivalent component featuring an elastic, perfectly plastic material response. In general, in strength governed scenarios, such as the in-plane bending of stocky beams, the substantial strain hardening of stainless steel gives rise to capacity benefits, while in stability governed scenarios, the early onset of stiffness degradation results in reduced capacity. This behaviour is observed at all levels of structural response including at cross-sectional level, member level and frame level, as described in the paper. Current and emerging design approaches that capture this response are also reviewed and evaluated. Lastly, with a view to the future, the application of advanced analysis to the design of stainless steel structures and the use of 3D printing for the construction of stainless steel structures are explored. • Constitutive modelling of stainless steel reviewed. • Influence of material nonlinearity of structural stability explained. • Current and emerging structural stainless steel design methods described. • Future trends, including design by advanced analysis and 3D printing, explored. [ABSTRACT FROM AUTHOR]

An efficient modelling technique based on one dimensional (1D) beam finite element analysis for buckling of thin-walled laminated composite beams having open/closed sections is proposed. The formulation derived has sufficient generality for accommodating arbitrary stacking sequences of the individual beam section walls, and includes all possible couplings between axial, shear, bending and torsional modes of deformation. The effects of transverse shear deformation of the section walls and out-of-plane warping of the beam section are considered where provision exists to restrain or allow warping deformation. The incorporation of shear deformation leads to a problem in the finite element implementation of the proposed beam kinematics, but this is successfully addressed adopting a novel modelling concept. Numerical results obtained for the sample cases of open sections I beams and closed section box beams are presented. The numerical results are benchmarked/compared to data available in open literature, and it is shown that the proposed model performs very well. Finally, a study of the effect of axial and end moment loading, acting alone or in combination, on the buckling response of thin-walled composite beams is presented. [ABSTRACT FROM AUTHOR]

The multistable elastic behavior of a shallow dome with a cosine-curved profile is investigated in this work. The dome exhibits snap-through instability and could be used as a building block for energy dissipation mechanism in structures subjected to cyclic loading and high deformation demands. Numerical and experimental studies were carried on the geometric and material properties of the cosine-curved domes (CCD) under concentrated load at the apex. Finite element analyses (FEA), validated by experimental tests on 3D printed specimens, were conducted to study the controlling geometric and material properties of the CCD. Three types of response were recognized and discussed based on the force- and strain energy-displacement curves. Limitations on the geometric parameters that govern the recoverability of the original shape and the stability state upon load removal are also identified. In addition, empirical relations to estimate the limit-point load and displacement, and to characterize the snap-through response were developed. Good agreement was observed using the determined limits on the geometric parameters and the developed relations with the results from FEA and experimental tests. • Constrained cosine-curved domes exhibit snap-through instability. • The shallow thin domes can be monostable, bistable, or pseudo-bistable. • Numerical simulations and testing on 3D printed domes confirm behavior. • Empirical expressions for multilinear response are proposed. • Arranging domes in series yields hysteretic response and elastic energy dissipation. [ABSTRACT FROM AUTHOR]

This paper presents an analytical and numerical investigation of the relationship between the compressive load level and the natural frequency variation toward a vibration correlation technique for the buckling load calculation of imperfection-sensitive isotropic cylindrical shell structures. Firstly, a back-to-basic s study is proposed and the linear equation between the applied load and the square of the loaded natural frequency is revisited. Such review considers the Flügge-Lur'e-Byrne's linear shell theory for the free vibrations of an isotropic unstiffened cylindrical shell under uniform axial loading. The demonstrated linear equation is rearranged for expressing the square of the applied load as a quadratic function of the square of the loaded natural frequency. The suggested formulation provides the analytical support to a novel vibration correlation technique that has been empirically proposed and experimentally validated for unstiffened cylindrical shells. Aiming a numerical verification based on finite element models, two cylindrical shells are defined. At first, the critical buckling load and the fundamental natural frequency for different load levels are determined and compared to the analytical results for validation of the numerical models. The finite element models are extended considering geometric nonlinearities, more realistic boundary conditions and three magnitudes of a benchmark measured initial geometric imperfection. The numerical results are considered for analyzing the variation of the natural frequency in the surroundings of buckling and for verifying the vibration correlation technique. • The free vibration of an axially loaded simply supported cylinder is revisited to verify an existing VCT. • A new insight to define a VCT which does not depends on the similarities between buckling and vibration modes is proposed. • The capability of the VCT to provide conservative estimations is corroborated through detailed numerical models. [ABSTRACT FROM AUTHOR]

Abstract The paper investigates the stability and post-buckling states of compressed thin-walled composite struts with predamage as a result of low-velocity impact. The struts were made of a GFRP composite material with a symmetrical lay-up by the autoclave technique. The produced channel-section struts were subjected to 20 J impact in different areas of the structure: on the web and on the flange. The struts with composite damage were subjected to axial compression to investigate the effect of composite material damage on the stability and operation of the structure in the post-buckling range. A numerical analysis was performed by the finite element method to compare two models of composite material damage: the proposed Simplified Damage Model (SDM) and the model developed by Fardin Esrail and Christos Kassapoglou. The limit load when the structure loses its stability was determined by the progressive failure criterion, according to which damage initiation in the composite material is based on the Hashin criterion while damage evolution is described with the energy criterion. Highlights • Investigation of low velocity impact influence on stability and collapse of struts. • Two damage models were used (SDM – own study and EKM) in FEM analysis. • The numerical models were verified in experimental tests. [ABSTRACT FROM AUTHOR]

Abstract A number of classic problems in the stability of thin walled structures in the elastic-plastic range which have been examined to some extent by the present author over the years are collected and discussed in order to highlight the advantages and drawbacks of analytical and numerical approaches. Issues related to the modes interaction, to the material modelling and to the imperfection sensitivity are examined with respect to well-known conundrums in the theory of stability and it is shown that the combination of all these aspects is such that any numerical analysis, despite the availability of modern very powerful nonlinear FE packages, must be preceded by a careful examination of the particularities of the problem at hand. In fact, a capable insight into the mechanics of the problem is shown to remain paramount in order to attain a good agreement with experimental results and provide reliable predictions for a large number of engineering tasks. Highlights • Some classic problems in the elastic-plastic stability of thin walled structures are presented. • The discrepancy between flow and deformation theory is examined. • The possible drawbacks of numerical analyses are pointed out. [ABSTRACT FROM AUTHOR]

Abstract This paper presents the generalisation of an energy-based method for the modal decomposition of buckled shapes of thin-walled members. This comprehensive method is derived and validated for fully decomposing the elastic buckling solution of a thin-walled member into the pure buckling mode classes of global, distortional, local, shear and transverse extension. The first three modes are de-facto prerequisites for buckling capacity predictions found in current design standards for thin-walled structures. In the literature, two main methods, namely the generalised beam theory (GBT) and the constrained finite strip method (cFSM), are widely employed for modal decomposition. Recently, an alternative energy-based approach has been presented for the decomposition of buckling modes into the classical local, distortional and global modes. This method is generalised in the present study to achieve a complete decomposition that also accounts for shear and transverse extensional modes in addition to global, distortional and local modes. In this method, each of the buckling classes is separated by imposing constraints that are defined by enforcing specific criteria on the total strain energy of the member. The adopted criteria are based on the fundamental mechanical assumptions of the GBT which were also implemented in the conventional cFSM and later were further detailed for modal classification in the generalised cFSM. This paper is accompanied by a paper in which derivation of a modified global torsion mode for sections with closed loops is presented and the applicability of the proposed method is demonstrated using a series of numerical examples. Highlights • Modal finite strip method (mFSM) is proposed for analysis of thin-walled structural members. • The particularity of the method due to the use of strain energy for the derivation of modal spaces is discussed. • The constraint matrices defining the global, distortional, local, shear and transverse extension modes are derived. • The proposed method can be applied to modal decomposition of members with arbitrary cross-sections. [ABSTRACT FROM AUTHOR]

Abstract This paper is a companion to (Khezri and Rasmussen, 2019) [1], where the generalised strain energy-based method for the modal decomposition of buckled shapes of thin-walled members is introduced. The paper presents the application of the proposed method for full modal decomposition to various thin-walled members. A series of numerical examples are presented in order to verify the robustness and capabilities of the proposed modal finite strip method (mFSM). In addition, the problem of global torsional modes in sections with closed cell(s) is revisited in this paper. In sections with closed loops, the classical global torsion modes does not exist due to presence of in-plane shear strains. In the context of the proposed energy-based method, a modified global torsion buckling mode is derived that allows for the occurance of shear in closed cell. The pure global buckling curves obtained incoporating the modified global torsion base vectors are compared with the generalised constrained FSM (cFSM) and generalised beam theory (GBT) results. It is shown that the proposed modal decomposition method is capable to accurately capture the modal behaviour of thin-walled sections. Highlights • Modal finite strip method (mFSM) is proposed for analysis of thin-walled structural members. • The particularity of the method due to the use of strain energy for the derivation of modal spaces is discussed. • A modified global torsion mode is derived for analysis of sections with closed part(s). • Extensive numerical examples illustrate the applicability of the new method. [ABSTRACT FROM AUTHOR]

Abstract Traditional buckling experiments of imperfection-sensitive structures like cylindrical shells can cause the permanent failure of the specimen. Nevertheless, an experimental campaign is crucial for validation of the design and numerical models. There is, therefore, interest in nondestructive methods to estimate the buckling load of such structures from the prebuckling stage. The vibration correlation technique allows determining the buckling load without reaching the instability point. Recently, a novel empirical vibration correlation technique based on the effects of initial imperfections on the first vibration mode demonstrated interesting results when applied to composite and metallic unstiffened cylindrical shells. In this context, this paper explores this novel approach for determining the axial buckling load of a metallic orthotropic skin-dominated cylindrical shell under internal pressure, which represents a simplified downscaled model of a launcher propellant tank. An experimental campaign consisting of buckling tests and noncontact vibration measurements for different axial load levels is conducted considering the specimen without and with three different internal pressure levels. The experimental results validate the above-mentioned vibration correlation technique for determining the axial buckling load of pressurized cylindrical shells. Moreover, finite element models are calibrated in order to evaluate the frequency variation within a broader and dense range of the axial loading leading to an assessment of the considered maximum load level and number of load steps as related to the deviation of the estimation. The results corroborate the applicability of the vibration correlation technique as a nondestructive experimental procedure to assess the axial buckling load of imperfection-sensitive orthotropic skin-dominated cylindrical shells under internal pressure. Highlights • A VCT test of an orthotropic skin-dominated cylindrical shell under different internal pressure levels is presented. • An algorithm based on the MAC to assess the numerical natural frequency variation during axial loading is proposed. • The experimental and numerical results corroborate that VCT can provide realistic and conservative buckling loads. [ABSTRACT FROM AUTHOR]

Abstract Experimental study is carried out to investigate the behavior and strength of square hollow structural section (SHS) columns, strengthened with an innovative polymer-mortar system. Thirteen specimens of cold-formed SHS columns with different variables are chosen. Three short-column and ten long-column SHS specimens were experimentally tested. The local and overall buckling of specimens are measured in the laboratory. The tested specimens are subjected to an axial compressive load. The effect of the thickness of polymer-mortar applied directly to the well-prepared steel surface was studied. The effect of slenderness ratio (kL/r) and width-to-thickness ratio (b/t) on the effectiveness of mortar strengthening was also discussed. Different failure modes are discussed as well as complete axial strength curves are drawn for different cross-sections and member lengths. A maximum axial strength gain of 31.6% was achieved for SHS short columns strengthened with 6 mm thickness polymer-mortar layer. For long columns, a maximum strength gain of 76.7% was achieved with 6 mm thickness polymer-mortar layer applied on four sides. In all mortar-strengthened SHS short and long columns, the axial and lateral deflection, and the axial strain were reduced. The axial strength of SHS long slender columns increased greatly as the overall slenderness ratio increases. Highlights • Cold-formed steel members is an economical alternative in design for low-rise buildings compared to hot-rolled. • Buckling is an important phenomenon to be considered by designers for steel members under compression. • Effectiveness of polymer-mortar strengthening system in increasing the axial strength of slender columns increases greatly as the overall slenderness ratio increases. • The axial strength of HSS columns increases as the plate slenderness ratio (b/t) increases. • Polymer-mortar strengthening system has a great effect on reducing axial, lateral displacement, and axial strain of the strengthened specimens. [ABSTRACT FROM AUTHOR]

Abstract The paper investigates the possibility of bifurcation buckling from axisymmetrical equilibrium states of a heated circular plate with immovable edge. The plate is composed of a functionally graded material whose mechanical and physical properties are varied in the thickness direction according to the power law. Because of high compressive circumferential stresses that develop near the edge, the symmetrically deformed plate can buckle into asymmetric equilibrium configurations characterized by local circumferential waves (wrinkles). The problem of determining wrinkling thermal loads is formulated using the von Karman nonlinear plate theory based on the concept of physically neutral surface and solved by the power series method. The existence of wrinkling loads is examined for various pressure levels and boundary conditions. The calculation results are compared to the finite-element solution obtained by a general-purpose shell element. Highlights • Existence of wrinkling phenomenon of pressurized and heated circular FGM plates is examined. • The critical thermal loads that causes the plate to wrinkle are determined by the power series method. • Clamped plates exhibit wrinkling upon heating, whereas simply supported plates do not. • Findings on the wrinkling loads and modes agree with the finite-element simulations. [ABSTRACT FROM AUTHOR]

Abstract This paper is focused on the stability of polymer disks subjected to uniform radial edge compression and proposes a methodology to determine the critical pressure at the onset of buckling. The methodology involves the design and fabrication of a tooling system to compress the outer disk surfaces and move material inward in order to apply a uniform radial pressure in the free (unconstrained) volume of the disks. The main objective is to circumvent the application of classical analytical solutions to polymers that exhibit a decrease of the stress-strain curve and negative values of the tangent modulus after initial yielding through determination of the critical pressure at the onset of buckling by matching the experimental and finite element predicted evolutions of the force vs. displacement. A lower bound stress solution is provided to perform a simple and fast conversion of the experimental data into the critical pressure of the polymer disk at the onset of buckling. The results of this investigation can be successfully applied to characterize the forming conditions that give rise to out-of-plane buckling deformation of the polymer centre during the production of a new generation of polymer-metal coins. Highlights • Innovative tool system to compress the outer disk surfaces and move material inward to apply a uniform radial pressure in the free disk volume. • New methodology to determine the critical pressure of polymer disks subjected to uniform radial edge compression at the onset of buckling. • Lower bound solution to perform a fast conversion of the experimental data into the critical pressure of the polymer disks at the onset of buckling. • Potential application of the methodology in the design of a new type of polymer-metal coins. [ABSTRACT FROM AUTHOR]

Abstract Cold-formed steel (CFS) is an emerging construction material that has been gaining momentum over the past few years. While the behavior of structural members made of CFS has been extensively studied at ambient conditions, the performance of these members under extreme events such as that associated with fire, is yet to be understood. In order to bridge this knowledge gap, this paper presents outcome of numerical studies aimed at understanding fire response of CFS beams. More specifically, this study explores the effect of temperature-induced shear-based instability on response of C-shaped CFS beams with slotted webs. For studying this phenomenon, a three-dimensional nonlinear numerical model is developed using the finite element (FE) simulation environment; ANSYS. The developed FE model is designed to incorporate temperature-dependent material properties as well as to account for unique geometric features and restraint conditions, as to accurately trace thermal and structural response of CFS beams. Once validated, the developed model was utilized to examine the effect of a number of factors namely; channel depth, web perforation pattern, as well as boundary conditions, on temperature-induced buckling susceptibility of CFS beams. The obtained results showed that these examined factors can significantly affect shear response of CFS channels with slotted webs at elevated temperatures. Findings observed from FE simulations were also shown to agree with that obtained from especially derived design expressions that give due consideration to geometric features and temperature-dependent material properties of slotted webs. This study concludes that in order to accurately capture the response of fire-exposed CFS beams, an accurate presentation of geometric and material features in such members is essential. Highlights • Vulnerability of CFS beams with slotted webs to temperature-induced instability is discussed. • A model for tracing fire response of CFS beams with slotted webs under dominant shear is presented. • Effect of critical parameters on shear response of fire exposed CFS beams with slotted webs is quantified. [ABSTRACT FROM AUTHOR]

Abstract This paper outlines an elastoplastic design approach for beam and plate structures subjected to transverse pressure loads and thermal stresses. The purpose of this study is to overcome the limitations of yield-limited designs by exploiting plastic design theorems. The feasible design space of a clamped beam/plate structure subjected to combined thermomechanical loads is explored considering shakedown (stabilized plasticity) as the design criteria. Analytic and numerical solutions are developed that show that allowing shakedown to occur extends the design space and acceptable loading range. In addition, the structures considered here are also prone to buckling due to thermal loads. In this work, interactions between thermal buckling and shakedown are investigated using numerical parametric studies. It is found that buckling enhances elastoplastic shakedown performance which expands the feasible design domain significantly when high aspect ratio beams are considered. In particular it is shown that the enhancement is 2–4 times for the range of aspect ratios examined. Highlights • The design space of structures is determined based on shakedown and thermal buckling. • A shakedown based design method is compared to traditional first-yield based designs. • Numerical and analytical design maps are in good agreement for beams/plates. • Considering shakedown extends the design space up to 2 times for low aspect ratios. • Buckling enhances the shakedown performance of high-aspect ratio beams by 2–4 times. [ABSTRACT FROM AUTHOR]

Abstract This study examined the buckling of spherical caps fabricated under different conditions of wall-thickness reduction. The spherical caps were fabricated using photosensitive resin and had a base diameter of 150 mm and height of 41.1 mm; they were subjected to uniform external pressure. In total, 42 spherical caps—6 with full thickness reduction and 36 with partial thickness reduction—were fabricated through rapid prototyping; after their external surface and wall thickness were measured, all caps were tested to collapse to experimentally and numerically evaluate their buckling properties, namely buckling pressures and collapse modes. Moreover, the effects of site, magnitude, and range of the thickness reduction on the buckling properties were evaluated. Herein, the experimental and numerical results are comparatively presented in tables and figures. Highlights • Spherical caps of various site, range, and magnitude of thickness reduction were built. • Buckling pressures and collapse modes of 42 such caps were obtained experimentally. • A semianalytical formula for evaluating their load-bearing capacity is identified. [ABSTRACT FROM AUTHOR]

Abstract The paper investigates the effects of the geometrical imperfections in buckling analyses of plated steel elements at elevated temperatures and provides an alternative branch-switching procedure to perform post-buckling analyses without introducing initial imperfections into the model. This procedure is appealing since the choice of appropriate imperfections in classical analyses is not straightforward, above all at elevated temperature. Several numerical analyses show that the choice of the imperfections is not trivial and that the buckling mode may vary with temperature. They also show that the proposed branch-switching procedure is an interesting preliminary tool to understand the instability behaviour of steel structural members. Highlights • Buckling of compressed steel plated elements at elevated temperatures is studied. • A branch-switching procedure performed without introducing imperfections is proposed. • The procedure is an interesting preliminary tool to study the post-buckling behaviour. • Linear buckling analyses may not capture the buckling mode at high temperature. • Imperfections based on modes at ambient temperature do not always give safe results. [ABSTRACT FROM AUTHOR]

Abstract This paper focuses on the stability of steel columns with cruciform section under uniform compressive and shear stresses. The complex finite strip method (CFSM) is employed to solve the buckling of open thin-walled steel columns. CFSM results are validated against other numerical techniques. CFSM has high convergence, accuracy and superior computational efficiency. Due to the use of complex functions, it can also capture shear buckling. The influence of longitudinal stiffeners and section geometry on the buckling behavior of stiffened cruciform sections is investigated. The buckling behavior of cruciform sections is compared against U, I, and T section steel columns. Highlights • Complex FSM is employed to solve the buckling of cruciform steel columns. • The solution can capture shear bucking due to the use of complex functions. • Influence of longitudinal stiffeners on buckling of cruciform columns is evaluated. • Torsional buckling is critical in stiffened cruciform steel columns. • Stability of cruciform columns is compared against other common open steel sections. [ABSTRACT FROM AUTHOR]

Abstract Aluminium alloys have high strength-to-weight ratios and great durability; thus, they have been extensively used in structural applications. Channel sections have a smooth and aesthetically pleasing line shape, good integrity, and are easy to connect. An experimental program using 28 specimens and a numerical study that generated 100 results were conducted on aluminium alloy columns of plain and lipped channel sections. The nominal length of columns ranged from 300 mm to 3000 mm. The generated 128 results were evaluated with respect to the existing design specifications from America, Australia/New Zealand, Europe and China. Furthermore, the direct strength method (DSM) and the continuous strength method (CSM) were also used to predict results for comparison. The results showed that the design specifications produced conservative compression strengths of aluminium alloy columns of both plain and lipped channel sections. The CSM provided more accurate and consistent design strengths. In addition, the reliability levels of the four international design codes, DSM and CSM for channel sections of aluminium alloy columns were also evaluated. Highlights • Aluminium alloy column tests on plain and lipped Channel sections were performed. • Finite element models were developed and validated against the test results. • A parametric study on cross-section slendernesses and column length was performed. • Compression resistances predicted by the design specifications are overly conservative. • The CSM and DSM provide more accurate and consistent predictions. [ABSTRACT FROM AUTHOR]

Abstract Elevated cylindrical metal silos are often supported on a ring beam which rests on discrete column supports. The ring beam plays an important role in redistributing the majority of the discrete forces from the column supports into a more uniform stress state in the cylindrical wall, which is necessary to reduce the potential for buckling of the shell wall. Traditional design treatments assumed that the discrete support forces can be fully redistributed by the ring beam, producing circumferentially uniform axial membrane stresses in the silo shell. But it has previously been shown that only a very stiff ring beam can produce even relatively uniform axial membrane stresses in the shell. The ring beam stiffness must be evaluated relative to the stiffness of the silo shell in compatible deformation, since even a thin shell is extremely stiff in its own plane. A test for the ring beam to shell stiffness ratio was previously devised by the authors to determine the ring beam stiffness needed to achieve uniform membrane stresses. This new study assesses ring beams of practical dimensions and stiffness, to evaluate their effectiveness in smoothing the shell axial membrane stresses towards the uniform condition and then to find their effect on the buckling resistance of the shell. This study explores the stress resultants in a closed section ring beam of practical dimensions that is less stiff than the ideal stiffness using a finite element parametric study of the flexible ring beam and connected silo shell. The results show that the ring beam stress resultants, relative to those in an isolated ring beam under the same loading, can be directly related to the established shell to ring beam stiffness ratio (ψ). This treatment may be used to significantly enhance current design practice which, according to the Eurocode EN 1993-4-1 for silos, assumes that the shell applies the full uniform transverse loading onto an isolated ring beam. Highlights • Closed form design equations for the isolated ring beam were algebraically derived. • The interaction between the cylindrical shell and the supporting ring beam was explored. • Complementary FE analyses show that shell-ring stiffness ratio is applicable for practical design. • Simple algebraic expressions empirically amend the algebraic equations for stress resultants and displacements for design. [ABSTRACT FROM AUTHOR]

Abstract This study presents a novel three-dimensional elasticity-based numerical solution for buckling analysis of a functionally grated material (FGM) plate with a side crack or an internal crack, which is first shown in literature. The distributions of material properties are assumed to follow a power law through plate thickness. The buckling loads of cracked plates are found by the Ritz method with admissible functions constructed by the moving least-squares (MLS) technique. The admissible functions are formed by multiplying a set of regular polynomials in the z coordinate with shape functions in x - y coordinates, established by MLS along with a set of basis functions consisting of regular polynomials and proposed crack functions. The proposed crack functions yields the correct singularity order for stresses at a crack front and shows the displacement and slope discontinuities across the crack, which enhances the ability of the Ritz method to handle problems with cracks. In order to validate the proposed solutions, convergence studies for buckling loads of cracked homogeneous plates are performed and a comparison is presented between the present results, previously published ones, and those obtained from commercial finite element software. The proposed approach is further applied to analyze the buckling of Al/Al 2 O 3 FGM rectangular plates with side cracks and skewed rhombic plates with central internal cracks while considering the effects of material distributions, plate thickness, skew angles, crack lengths, inclination angles and positions, boundary conditions, and loading conditions on the buckling loads of these plates. Highlights • Buckling analyses of cracked FGM plates are thoroughly carried out. • The MLS-Ritz method along with three-dimensional elasticity is employed. • Crack functions are proposed to enrich basis functions for MLS. • Comprehensive convergence studies on buckling loads are performed. • Effects of material properties and crack configurations on buckling are studied. [ABSTRACT FROM AUTHOR]

Abstract The vibration and stability problems of functionally graded material (FGM) cylindrical shells subjected to external pressures with mixed boundary conditions (MBCs) using first order shear deformation theory (FOSDT) is studied. The governing equations of FGM cylindrical shells (FGMCSs) are displayed according to the Donnell type shell theory and solved using the Galerkin's method. The novelty in this study is to obtain closed-form solutions of the eigen-value problem in mixed boundary conditions within the framework of the FOSDT. Finally, the effects of different volume fractions, FG profiles and shell characteristics on the critical parameters of FGMCSs with MBCs are studied in detail. Highlights • Vibration and stability of FGM cylindrical shells (FGMCSs) within FOSDT is studied. • The governing equations are displayed according to the Donnell type shell theory. • The equations solved using the Galerkin's method under mixed boundary conditions (MBCs). • The expressions for critical external pressures and frequency are found. [ABSTRACT FROM AUTHOR]

Abstract Influence of the ultimate strength of stee This study presents a new fiber reinforced polymer tube/filling strengthening method (i.e., FRP tube/filling strengthening) that creates a new composite compression member with a novel mechanical behavior, "bilinear behavior." Previous experimental and theoretical studies have been conducted based on the ultimate state of the section. To thoroughly study the stiffness and entire loading process of this novel member, finite element analysis (FEA) models are built in this paper. First, the model development process considers the initial defections and interface properties, and these models are verified by the experimental results. Two models of typical load-axial displacement curves describe the experimental results: a Bilinear model and a Trilinear model. Second, finite element modeling (FEM) is used to conduct a parametrical analysis that considers 7 parameters, and the results identify the mechanism of the strengthened member. Specifically, the Bilinear model corresponds to an unreinforced or relatively weakly reinforced specimen, and the Trilinear model corresponds to a relatively strongly reinforced specimen. If the exterior restraint system is weak, then the core steel buckles and subsequently yields; this behavior is described by the Bilinear model. If the exterior restraint system is strong (e.g., the length or the bending stiffness of the exterior restraint system is great), then the specimen can continue to bear a higher force after steel yielding until elastic-plastic buckling occurs; this behavior is described by the Trilinear model. Third, the FEA results and previous experimental and theoretical studies are used to obtain the stiffness and load-axial displacement curves, which are helpful for the design process. In general, relatively accurate FEA models are built in this paper that are capable of describing the mechanical behaviors of the novel member. Highlights • Accurate FEA models that consider the initial imperfections, interface properties are built. • The mechanism of the member is revealed by parametric studies. • The stiffness and the load-displacement curves are obtained. [ABSTRACT FROM AUTHOR]

Abstract Face-to-face built-up cold-formed steel channel sections are becoming increasingly popular for column members in cold-formed steel structures; its applications include cold-formed steel trusses, space frames and portal frames. In such an arrangement, the independent buckling of the members is resisted by intermediate fasteners. In the literature, no research is available for such face-to-face built-up cold-formed steel columns. The issue is addressed herein. This paper presents the results of 36 experimental tests, conducted on face-to-face built-up cold-formed steel channel-sections covering a wide range of slenderness from stub to slender columns. A nonlinear finite element model is then described that shows good agreement with the experimental results. The finite element model includes material non-linearity, initial imperfections and modelling of intermediate fasteners. Both finite element and experimental results are compared against the design strengths calculated in accordance with the American Iron and Steel Institute (AISI), Australian and New Zealand Standards (AS/NZS) and Eurocode (EN 1993-1-3). The verified finite element model is used for the purposes of a parametric study comprising 90 models. The effect of fastener spacing on the axial strength was investigated. From the results of experiments and finite element investigations, it is shown that the design in accordance with the AISI & AS/NZS and Eurocode (EN 1993-1-3) is generally conservative by around 15%, however, AISI & AS/NZS and Eurocode (EN 1993-1-3) can be un-conservative by 8% on average for face-to-face built-up columns failed through local buckling. Highlights • Experimental tests were conducted on face-to-face built-up CFS channel-sections. • Initial geometric imperfections were measured for all test specimens using a laser scanner. • Nonlinear finite element models were developed which includes material nonlinearity and initial imperfections. • The column strengths were compared against the design strengths calculated in accordance with AISI & AS/NZS and EN 1993-1-3. • The AISI & AS/NZS and EN 1993-1-3 design strengths are generally conservative by around 15% but un-conservative by 8% on average for columns failed through local buckling. [ABSTRACT FROM AUTHOR]

Abstract The following paper presents a Finite Element formulation based on the Generalized Beam Theory (GBT), to analyse the buckling behaviour of isotropic conical shells under various loading and boundary conditions. The formulation offers the solution of the 1st order analysis from which the pre-buckling stresses are computed, including stress concentrations, and the linear (bifurcation) buckling solution. Due to the variable cross-section of conical shells, the mechanical and geometrical properties are no longer constant along the bar's axis as they are in the case of cylindrical structures and thin-walled prismatic bars. Special focus is given to the effect of the pre-buckling stress concentrations and non-conventional cross-section deformation modes. The proposed formulation is validated by comparing results obtained from GBT and Shell Finite Element Analyses. Highlights • 1st variation of strain energy is computed using conical shell theory and GBT. • GBT-based bar Finite Elements are used for conical shells. • 1st order analysis yields the pre-buckling stresses. • Linear buckling analysis yields the bifurcation loads and mode shapes. • The effect of the pre-buckling stress concentrations is assessed. [ABSTRACT FROM AUTHOR]

Abstract Prestressed tube stayed columns with one and two crossarms are investigated. The analyses are performed using SCIA Engineer software and ANSYS package and validated by tests of four stayed columns. First, the investigations concern the ideal (perfect) columns and cover linear buckling analyses (LBA) and geometrically nonlinear analyses (GNIA) to obtain critical loads and buckling modes under various prestressing levels. Second, the collapse loadings of the imperfect columns with initial deflections required by Eurocode EN 1993-1-1 are analysed with respect to relevant initial deflection modes and material behaviour (elastic for mild steel, nonlinear for stainless steel). All the analyses are performed for geometrical characteristics of the tested columns and the results concerning both the column with one or two crossarms are set against each other to assess the respective effectivity. In addition, the geometrical analysis of the prestressed ideal column with two crossarms and respective formulas concerning optimal prestressing and maximal critical loading are presented. Finally some recommendations for practical use are suggested. Highlights • Critical loadings of "perfect" (ideal) prestressed stayed columns and maximal loadings of "imperfect" (real) prestressed stayed columns of both columns with one and two crossarms made of stainless steel are presented. • Efficiency of the prestressed stayed columns with two crossarms in comparison with systems having just one crossarm is demonstrated. • Influence of sliding of stays at crossarm support is clarified. [ABSTRACT FROM AUTHOR]

Abstract Non-symmetric thin-walled open-sections are used extensively in metal structures. The behaviour of such sections is usually complex because their shear centre and centroid do not coincide, and as a result, they are often susceptible to lateral-torsional and/or flexural-torsional buckling. This paper develops an efficient and robust computational framework for practical application, including a refined beam-column element for non-symmetric sections, a cross-section analysis algorithm for determining pertinent properties of open-sections, and an Updated-Lagrangian (UL) solution method for large deflection analysis. Details of the derivation of element stiffness matrices and the related numerical procedures are provided. Several examples are given that demonstrate accurate results from its implementation within the educational structural analysis software MASTAN2. Highlights • An efficient and complete numerical framework is developed for practical design. • A refined warping beam-column element is presented with details provided. • A cross-section analysis algorithm is developed for any thin-walled open-section. • An Updated-Lagrangian (UL) solution method is established for allowing large deflection analysis. • Several benchmark examples are provided that demonstrate accurate results. [ABSTRACT FROM AUTHOR]

Abstract Purlins are usually connected to roof sheeting by sliding-clips, while wall sheeting is often screw-fastened to girts. This paper investigates the buckling of such two types of parallel purlin/girt systems inter-connected by multiple lines of sag rods. One single purlin braced by one sag rod at any place along the span is first analyzed, and its buckling deformation at any cross-section is seen as a flexibility coefficient which is then used to study the buckling of the purlin braced by multiple sag rods along span. A flexibility matrix is constructed, whose eigenvalues are the base of critical equations. In the case where the sag rods are placed with equal spaces along span, the eigenvalues are expressed in explicit forms, of which each represents one buckling mode. Threshold stiffness of the sag rods are presented for multiple sag rod bracings for these two types of sheet-to-purlin connection. Based on the findings of this paper, the differences of buckling behaviors between these two types of purlin systems have been revealed. The effect of local deformation of the web at the sag rod connecting points on the sag rod stiffness is also included. Parallel purlin systems are then investigated in a compact matrix form. After carrying out matrix operations and slight approximations, a key parameter is found to be used to reflect the effect of the number of purlins and zig-zag layout of sag rods in adjacent bays on the effective sag rod stiffness. Highlights • Buckling of parallel purlins braced by multiple lines of sag rods is studied. • Rotational restraints of roof sheeting to purlins are considered. • The reduced effectiveness of the sag rods are revealed systematically. • It's found parallel purlins can be analyzed as if they one single-purlin-system. • Two types of purlin-to-sheeting connections are analyzed and compared. [ABSTRACT FROM AUTHOR]

Graphical abstract fx1 Highlights • Similarity criteria are derived for thin-walled cylinders subjected to coupled thermo-mechanical loads. • Thermo-elastoplastic failure behaviors predicted by numerical model are validated by experiments. • Scaling laws are verified by numerical models, and source of error is discussed. [ABSTRACT FROM AUTHOR]

An experimental and numerical investigation of cold-formed steel built-up beams with different screw arrangements is presented in this paper. A total of 35 beams were tested under four-point bending with different screw arrangements in the moment span. The built-up sections were assembled using self-tapping screws from either two lipped channels connected back-to-back at the web to form an open section or two plain channels connected face-to-face at the flanges to form a closed section. Finite element (FE) models have been developed and validated against the test results for the built-up open section beams and built-up closed section beams, respectively. It is shown that the FE models can accurately predict the behaviour of cold-formed steel built-up beams with different screw arrangements. A parametric study on built-up beams with larger span and various screw spacing was further carried out using the verified FE models. The test and numerical results were compared with the design strengths predicted by the direct strength method (DSM) for cold-formed steel structures, with contingent considerations of the screws when determining the elastic buckling moments in the finite strip analysis. A reliability analysis was performed to evaluate the reliability of the current DSM equations. It is shown that the current DSM equations can predict the design strengths of built-up open section beams well in this study, with the assumption that the strength of the built-up section is the sum of two component profiles. However, the design equations for local buckling strength are generally conservative for the built-up closed section beams failed by local buckling. Meanwhile, the design equations for lateral-torsional buckling (LTB) strength cannot be directly used for the built-up closed section beams with relatively large screw spacing that failed by LTB with cross section distortion or separation of two component channels. It should be noted that LTB mode with cross section distortion was found in built-up closed section beams with large screw spacing. A modified design rule based on DSM is then proposed, which is shown to improve the accuracy of the predicted strengths. Moreover, the maximum longitudinal screw spacing for built-up closed section beams was also recommended for design practice. [ABSTRACT FROM AUTHOR]

A Pseudo Curved Beam (PCB) model is proposed to analyze the buckling behaviors of inflated arch. The wrinkling (local buckling) effect is considered in the PCB model by modifying the cross-sectional area and sectional moment of inertia in the stiffness matrix. The wrinkling angle, wrinkling and failure load are then predicted based on the proposed PCB model. The bending experiment and numerical simulation of a quarter-circle inflated arch are performed to verify the validation of the PCB model. The effects of load conditions, constraint conditions, structural geometric parameters, inflation pressure and material properties on the buckling characteristics of inflated arch are parametrically studied in the end. The method and results provide good references for the load-carrying design of inflated structures. [ABSTRACT FROM AUTHOR]