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This paper conducts the analytical investigation on the buckling of cylindrical shells with axially variable elastic modulus subjected to axial compressive load for the first time. First, it proves that the axially distributed elastic modulus can be expressed as the combination of constant and variable component. Then, governing differential equations for buckling analysis are derived and exactly solved by the combined perturbation method and Fourier analysis. Accordingly, the closed analytical solutions for the cylinder with arbitrarily variable elastic modulus are obtained, which reveal the explicit relations among buckling load, shell sizes and elastic modulus functions. Based on the presented analytical formulas, four types of elastic modulus variations for shell material which are uniform, periodic, linear and combined are studied in detail, and the results are also well verified. The derived analytical solutions in this paper can serve as benchmarks for buckling analyses of thin-walled cylinders with elastic modulus variations resulted from design, material manufacturing process, material imperfections and so on. [ABSTRACT FROM AUTHOR]

A family of locking-free Kriging-based Timoshenko beam elements with a new implementation of the discrete shear gap technique was recently developed (referred to as K-beam-DSG1 elements). Performance of the K-beam-DSG1 elements has been shown to be very satisfactory in the linear static analysis of beams for a wide variety of thicknesses. This paper presents further development of the K-beam-DSG1 elements to free vibration and bifurcation buckling analyses of prismatic and non-prismatic beams. Consistent Kriging-based mass matrices are used for free vibration analysis and similarly, consistent Krigingbased geometric stiffness matrices are used for buckling analysis. The results show that for most of the cases, the K-beam-DGS1 elements yield remarkably accurate natural frequencies and critical compressive loads using a reasonable number of elements to discretize the beam. For an axially functionally graded fixed-fixed supported beam, however, the elements fail to predict the critical load accurately. [ABSTRACT FROM AUTHOR]

Graphene platelets (GPLs) exhibit outstanding mechanical and physical properties and therefore are employed as a reinforcement in advanced polymer composite structures. The purpose of this paper is to analyze the biaxial buckling of functionally graded graphene-reinforced sandwich plates with a soft orthotropic core. A new high-order three-layer theory is developed for the accurate modeling and analysis of the sandwich structure. The sandwich plate is divided into three layers including two face sheets and a core and a different third-order kinematic assumption is dedicated to each layer. The transverse flexibility of each layer as well as the displacements continuity at the interfaces are considered. Additionally, the continuity conditions and the conditions of zero transverse stresses in the whole structure are satisfied. The plate is subjected to a biaxial compressive loading and the governing equations are derived using the principle of minimum potential energy. Analytical solutions are presented for simply supported boundary conditions to obtain the critical buckling load. The influences of plate geometry and GPL properties on buckling load are investigated. The results obtained in specific cases are compared with the published results and the validity of the present results is confirmed. It can be drawn that the use of GPL increases the buckling load of graphene-reinforced sandwich plates. [ABSTRACT FROM AUTHOR]

This article considers a bidirectional functionally graded (BDFG) beam with various distributions of volume fraction. The impact of these distributions on the buckling and bending response of BDFG beam with general boundary conditions is investigated via a quasi-3D solution. It is assumed that the beam is exposed to a set of in-plane varying compressive loads and there mechanical characteristics change in both directions. Also, the BDFG beam is considered to be exposed different external mechanical loads. Hamilton's principle is employed to derive the governing equations, which are then solved using analytical solution to obtain buckling and bending characteristics. The precision of the current formulation is investigated via a comparison with available data in literature. Some numerical results are presented and discussed to assess the effect of different parameters such type of volume fraction, boundary condition, varying load, and beam geometry on the buckling and bending of BDFG beam. [ABSTRACT FROM AUTHOR]

Additive manufacturing (AM) offers new possibilities to fabricate and design lightweight lattice materials. Due to the superior mechanical properties of these lattice structures, they have the potential to replace honeycombs as cores in sandwich panels. In addition to the advantage of the integral fabrication thanks to AM, additively manufactured lattice core sandwich panels may be also used as heat exchangers, enabling a multifunctional use of the core. To ensure a reliable and safe structure, the mechanical response of lattice core sandwich panels under given load conditions must be predictable. In conventional sandwich panels subjected to compressive loads, the sandwich's global buckling and the face sheets' local buckling are the dominant failure modes. In constrast, core strut buckling may be the critical failure mode in lattice core sandwich panels. Therefore, an analytical 2D model to predict the local buckling of lattice core struts is considered in this study. Furthermore, the critical load for global buckling is obtained based on the first-order shear deformation theory. Thus, the transition from local buckling to global buckling depending on the length-to-thickness ratio is captured by the presented model. The comparison with finite element modeling of the sandwich model with truss cores has proved the accuracy of the derived model. [ABSTRACT FROM AUTHOR]

The woven structure made of naturally curved (in-plane) ribbons has smooth geometry and fewer geometric imperfections, but there is no study of its buckling mechanical properties under vertical loads. The aim of this paper is to investigate buckling mechanical properties of spherical woven structures. Three spherical woven structures with different ribbon types and six new spherical woven structures with different ribbon widths and thicknesses were designed and the quasi-static vertical compression tests were carried out. The buckling load of spherical woven structures were studied by nonlinear finite element and ring buckling theory. Results indicate that the failure mode of the spherical weave structure under vertical loading can be divided into two stages, where a flat contact region forms between the spherical weave structure and the rigid plate and inward dimple of ribbons. Spherical weave structures using naturally curved (in-plane) ribbon weaving have better buckling stability than those woven with straight ribbon. Based on theoretical and finite element analysis, we propose a buckling load equation and buckling correction factor equation for the new spherical weave structure under vertical compression load. The formula is validated and has good agreement with the test results, which could help to design the stability of spherical weave structures with in-plane ribbons. [ABSTRACT FROM AUTHOR]

In practical engineering, a thin-walled cylindrical shell structure is more easily subjected to localized axial compression loads caused by external adjacent structures or devices. However, until now there are few studies to reveal the buckling behavior of cylindrical shells under such nonuniform loading conditions based on initial imperfection sensitivity. Therefore, buckling analysis of cylindrical shell under localized axial compression loads is investigated in this paper. Based on the buckling test, the influence of the morphology and amplitude of measured initial geometric imperfection are studied using the finite element method. Meanwhile, the inherent reason for initial geometric imperfection affecting the buckling load is elaborated. The influence of amplitude, distribution range, and different combinations of local dent imperfections are also elucidated. In addition, the effects of inclined loading imperfection and uneven shell thickness distribution imperfection are analyzed in the form of deterministic numerical simulation. Finally, a new buckling load knockdown factor that can reasonably consider the influence of loading imperfection and shell thickness variation imperfection is proposed. This work elucidates the initial imperfection sensitivity of the thin-walled cylindrical shell structures under localized axial compression load and can provide useful guidance for the buckling design and preventing buckling failure of these structures. [ABSTRACT FROM AUTHOR]

This study focuses on variations in the hysteretic behavior of buckling-restrained braces (BRBs) configured with or without out-of-plane eccentricity under cyclic loading. Quasi-static experiments and numerical simulations were carried out on concentrically and eccentrically loaded BRB specimens to investigate the mechanical properties, energy dissipation performance, stress distribution, and high-order deformation pattern. The experimental and numerical results showed that compared to the concentrically loaded BRBs, the stiffness, yield force, cumulated plastic ductility (CPD) coefficient, equivalent viscous damping coefficient and energy dissipation decreased, and the yield displacement and compression strength adjustment factor increased for the eccentrically loaded BRBs. With the existence of the out-of-plane eccentricity, the initial yield position changes from the yield segment to the junction between the yield segment and transition segment under a tensile load, while the initial high-order buckling pattern changes from a first-order C-shape to a second-order S-shape under a compressive load. [ABSTRACT FROM AUTHOR]

This study proposed novel designs for achieving self-centering (SC) behavior using superelastic shape memory alloy (SMA) buckling-restrained plates (BRPs). Compared with previous studies relying on small-diameter SMA bars, this study employed large-dimensional SMA plates that could provide sufficient strength for real construction projects. The design concept and configurations of SMA-BRPs were first introduced. Corresponding tests were then conducted. Three specimens were tested, including one that was unsatisfactory and two that were acceptable. Based on the initial examination of the behavior and failure mode of the unsatisfactory trial specimen, the corresponding modifications were made to achieve the improved performance of two acceptable specimens. Subsequently, the hysteresis and SC behaviors, energy dissipation capacity, and yielding strength degradation of the two acceptable specimens were investigated. Both specimens exhibited high-quality flag-shaped behaviors in their tension–compression cycles, with their strengths reaching around 200 kN under tension and more than 310 kN under compression, representing one of the largest strength values shown by a single SMA element in the literature. Asymmetric behavior was observed under tensile and compressive loadings, primarily due to the asymmetric behavior of the SMA base material, high-mode inelastic buckling under compression and friction between the SMA core plate and buckling-restraining device. After the tests, finite element models were developed to obtain an in-depth understanding of the detailed behavior of SMA-BRPs. The studies showed that SMA-BRPs successfully achieved the SC buckling-restraining design target. The design incorporating end restrainers was preferred due to its flexibility, which reduces application restraints. [ABSTRACT FROM AUTHOR]

By experimental methods, 26 specimens were designed to conduct elastic and elastic–plastic buckling tests on cylindrical shells containing cracks. This study discusses the influence of factors such as the length–diameter ratio, the diameter–thickness ratio, the crack length, the inclination of the crack, etc., on the buckling load. Additionally, finite element models were established to compare with experimental results. For the PMMA cylindrical shell, the results showed that as the length–diameter ratio of the cylindrical shell increased, the buckling load first decreased and then increased. For the 6063 aluminum alloy cylindrical shell, with increasing length–diameter ratio, diameter–thickness ratio, and crack length of the cylindrical shell, the buckling load decreased accordingly. However, concerning the crack inclination, as the crack inclination increased, the buckling load increased accordingly. This indicates that the larger the crack inclination, the higher the load capacity of the cylindrical shell containing cracks. Through finite element simulations of cylindrical shells with cracks, it was found that through compressive mechanical properties, both elastic and elastic–plastic buckling loads yielded results that are closer to the experimental results. Additionally, the inclusion of contact effects in numerical simulations further improved the agreement with the experimental results, and the variation trend of the buckling load in the finite element simulation was consistent with the experimental results. The research findings provide valuable references for the assessment of load capacity in structures containing cracks. [ABSTRACT FROM AUTHOR]

The nonlinear buckling and postbuckling of functionally graded carbon nanotube reinforcement composite (FG-CNTRC) plates resting on the nonlinear effect of elastic foundation under combined load including external pressure and axial compression loads with uniformly distributed temperature rises are fully investigated in this paper. The FG-CNTRC plates are reinforced by FG-CNTRC stiffeners and the plate-foundation interaction is modeled using a nonlinear model. The higher-order shear deformation plate theory with the geometrical nonlinearities of von Kármán is applied to establish the basic formulations. Additionally, by using the anisotropic higher-order shear deformation beam theory, a new smeared stiffener technique is successfully developed for FG-CNTRC stiffeners. Galerkin's method is used to achieve the equilibrium equation system in the nonlinear algebraic forms, and the critical load and postbuckling load–deflection curve expression are explicitly determined. The numerical investigations discuss the influences of FG-CNTRC stiffeners, hardening/softening nonlinear elastic foundation, uniformly distributed temperature rises, geometrical and material features on nonlinear stability of stiffened FG-CNTRC plates. [ABSTRACT FROM AUTHOR]

Carbon nanotubes (CNTs) exhibit a unique buckling behavior due to their slender tubular geometry and thin-walled circular cross section. This study aims to analyze effect of nonlinear cross-sectional deformation on buckling of CNTs. To accomplish this, CNTs are modeled as beam structures, and the analysis is conducted using the Variational Asymptotic Method (VAM) and a geometrically exact beam theory, as well as nonlinear finite element analysis (FEA). The study considers various loading cases, including pure axial compression and combined loading scenarios, such as bending-axial compression and torsion-axial compression. The results of the study indicate that inclusion of cross-sectional deformation-induced nonlinearity reduces the critical buckling load of CNTs. The reduction is 2–5% for pure axial compression and 10–40% for combined loading cases. The results are validated against existing literature and commercial finite element software, ABAQUS®. Additionally, parametric studies with different slenderness and radius-to-thickness ratios were carried out to further understand the impact of these parameters on buckling of CNTs. Finally, the study presents 3D deformed shapes of CNTs during buckling by combining the results of the 1D analysis and the 2D cross section analysis. The findings show that nonlinearity associated with radius-to-thickness ratio has a significant impact on the cross-sectional ovalisation of CNTs and is critical in evaluating their buckling behavior. This aspect of nonlinearity is often overlooked in continuum modeling methods of CNTs, making this study an important contribution to the field. [ABSTRACT FROM AUTHOR]

A new beam element only having the translational displacement degrees of freedom is developed to analyze fracture and buckling behaviors of bilayer beams or columns with delamination using the multilayer modeling method. By comparing their degrees of freedom, it is found that the present beam element is equivalent to the conventional Timoshenko beam element. The upper and lower layers are both divided into one or several sublayers, which are modeled by the developed beam elements. The element stiffness matrix, load vector, and geometric stiffness matrix using the linear interpolation polynomial are derived by the principle of minimum potential energy. To illustrate the effectiveness, accuracy, and efficiency, both the fracture and buckling analyses are conducted. Four typical fracture specimens (i.e., homogeneous and asymmetric double cantilever beams, single leg bending, and asymmetric end-notched flexure specimens) are analyzed using the developed beam element, and the obtained energy release rate and its components using the virtual crack closure technique are compared with those of analytical and conventional two-dimensional (2D) finite element solutions. Further, buckling analysis of bilayer beam-columns with delamination is conducted, focusing on the effect of the number of sublayers. The results show that the developed beam element is capable of effectively and efficiently calculating the convergent stress intensity factor ratio, total energy release rate and its components, and critical buckling load of delaminated bilayer beams or columns with relatively few elements, but without introducing the interface continuity condition in comparison to the conventional modeling method. [ABSTRACT FROM AUTHOR]

The stability behaviour of unsymmetrical laminated structures made of fibre-reinforced plastics is significantly influenced by bending–extension coupling and the comparatively low transverse shear stiffnesses. The aim of this work is to improve the analytical stability analysis of unsymmetrically laminated structures. With the discrete plate theory, the stability of laminated structures can be reduced to single laminated plates. The structure is divided into individual segments, and the surrounding structure is modelled by rotational elastic restraints. The governing equations for single plates under specific boundary conditions can be solved exactly with Lévy-type solutions. In this study, Lévy-type solutions for the mentioned boundary conditions under biaxial compressive load is described for the classical laminated plate theory, the first-order shear deformation theory and the third-order shear deformation theory (TSDT). In addition to transverse shear, bending–extension couplings of unsymmetrical cross-ply and antisymmetrical angle-ply laminates are considered. For the implementation of boundary conditions for the rotational restraints in the context of TSDT, a new set of conditions is formulated. The investigation shows very good agreement of the buckling load with comparative finite element analyses for different layups. [ABSTRACT FROM AUTHOR]

A thin-walled steel cylindrical shell is a common engineering structure that has an efficient load-carrying capacity. This structure is more easily subjected to partial axial compression loads in application, and buckling is the main failure mode. However, there are few available design methods for partial axially compressed steel cylindrical shells. Motivated by this, a design method called the localized perturbation load approach (LPLA) is proposed in this paper. The finite element framework for the application of LPLA is established. The location and number of perturbation loads are determined by considering the imperfection sensitivity and the buckling failure mode of partial axial compressed cylinders. A series of buckling experiments are carried out to validate the LPLA method. In addition, the reliability of LPLA for the design of cylindrical shells with different imperfection locations and dimensions is also verified. The results show that LPLA can give conservative and reliable lower-bound buckling loads. Therefore, LPLA can be used as a design method for thin-walled steel cylindrical shell structures under partial axial compression in actual engineering. [ABSTRACT FROM AUTHOR]

In this paper the vibration correlation technique (VCT) has been used as a nondestructive method for predicting the buckling load of the composite lattice-core sandwich conical shells. This technique is capable of predicting the buckling load of different structures without reaching the failure point through modal testing. The composite lattice-core sandwich conical shell has been fabricated using a filament winding process. To perform the expriment, the fundamental natural frequency of the specimen is measured under stepped axial compression loading. The procedure is followed up without actually reaching the instability point when the structure collapses and is no longer usable. A finite element model has also been built in ABAQUS in order to determine the correlation between natural frequency and applied compressive load. A comparison of the results indicated that the VCT has provided a reliable estimate of the buckling load of composite lattice-core sandwich conical shells, especially when the structure is loaded up to at least 66% of the experimental buckling load and accuracy of the VCT decreases when the maximum load is lower than 43% of the buckling load. Results also revealed that the linear fitted curve is unsuitable for the correlation between frequency of vibration and applied load in order to predict buckling load. [ABSTRACT FROM AUTHOR]

Thin-walled cylindrical shells under axial compression load are prone to buckling. The influencing factors leading to a reduction of the buckling load are a major design challenge. The sensitivity to imperfection increases with rising slenderness. In literature, cylinders with the same parameters and different slenderness are rarely tested in a larger number of samples. In this contribution, seven cylindrical shells, six of them nominally identical, are tested on two different test rigs and compared with twelve specimens with a smaller radius and same wall thickness from a previous series of tests. It is shown how the imperfection sensitivity is dependent on the R/t-ratio. Additionally, it is demonstrated how the quality of the test set ups corresponds with the achieved buckling load. Finally, the suitability of selected design approaches is determined based on the test results. Based on that, recommendations for the choice of a suitable approach are given. [ABSTRACT FROM AUTHOR]

In high-pressure and high-temperature gas wells, tubing string buckling behavior is a significant engineering problem to be addressed. To solve this problem, a finite element model of tubing string buckling with geometric nonlinearity and contact nonlinearity is established, and the buckling behavior of tubing string in the whole wellbore section is simulated. The effects of axial compression, connector and wellbore diameter on tubing string buckling are studied. It is found that a variety of complex buckling forms may co-exist in the same wellbore and that with the increase of axial compression load, the lateral displacement of tubing string increases gradually, and the buckling state of tubing string gradually intensifies. Under the same axial compression load, buckling is relieved when the effect of the connector is considered, indicating that the connector has the effect of delaying the buckling and promoting the transfer of axial force. Wellbore diameter has a great influence on the buckling critical load and the buckling behavior of tubing string. The work presented in this paper can provide a technological basis for tubing string buckling behavior analysis in high pressure and high temperature gas wells. [ABSTRACT FROM AUTHOR]

Arch and serpentine structures are two fundamental structural forms with significant applications in various fields. When subjected to compressive loading at both ends, these structures undergo flexural-torsional post-buckling, resulting in complex deformation modes that are challenging to describe using basic functions (e.g., trigonometric functions and polynomial functions), posing significant challenges in finding analytical solutions. In this study, we propose a novel approach to address this issue. By representing the lateral displacement with a trigonometric series expansion and utilizing the equilibrium equation, the angular displacement is expressed in terms of special functions known as Mathieu functions. Furthermore, the energy method is employed to obtain analytical solutions for the flexural-torsional post-buckling deformation components. The theoretical findings are validated through experiments and finite element analysis. Based on the theoretical results, explicit analytical expressions for the maximum principal strain and the bending-torsion ratio of the structures are derived, offering valuable insights for the design of arch and serpentine structures in practical applications. [ABSTRACT FROM AUTHOR]

Additive Manufacturing (AM) is rapidly evolving due to its unlimited design freedom to fabricate complex and intricate light-weight geometries with the use of lattice structure that have potential applications including construction, aerospace and biomedical applications, where mechanical properties are the prime focus. Buckling instability in lattice structures is one of the main failure mechanisms that can lead to major failure in structural applications that are subjected to compressive loads, but it has yet to be fully explored. This study aims to investigate the effect of surface-based lattice structure topologies and structured column height on the critical buckling load of lattice structured columns. Four different triply periodic minimal surface (TPMS) lattice topologies were selected and three design configurations (unit cells in x, y, z axis), i.e., 2 × 2 × 4, 2 × 2 × 8 and 2 × 2 × 16 column, for each structure were designed followed by printing using HP MultiJet fusion. Uni-axial compression testing was performed to study the variation in critical buckling load due to change in unit cell topology and column height. The results revealed that the structured column possessing Diamond structures shows the highest critical buckling load followed by Neovius and Gyroid structures, whereas the Schwarz-P unit cell showed least resistance to buckling among the unit cells analyzed in this study. In addition to that, the Diamond design showed a uniform decrease in critical buckling load with a column height maximum of 5193 N, which makes it better for applications in which the column's height is relatively higher while the Schwarz-P design showed advantages for low height column maximum of 2271 N. Overall, the variations of unit cell morphologies greatly affect the critical buckling load and permits the researchers to select different lattice structures for various applications as per load/stiffness requirement with different height and dimensions. Experimental results were validated by finite element analysis (FEA), which showed same patterns of buckling while the numerical values of critical buckling load show the variation to be up to 10%. [ABSTRACT FROM AUTHOR]

As part of the ongoing revision of the Eurocodes, design provisions in EN 1999‐1‐1 on the buckling of longitudinally welded aluminium compression members have been subjected to a critical review. The numerical investigations described in part 1 of the paper were conducted because a need for improvement was identified. In part 2 of the paper, the main observations are presented in qualitative terms. Those observations are: the influence of the allocation of the materials to buckling classes, the influence of the imperfections plus the cross‐section geometry including the position and size of the HAZ within the cross‐section. Part 3 will conclude this paper by discussing the proposed design approaches in detail. [ABSTRACT FROM AUTHOR]

This study investigates the effects of nanoclay (NC) particles on the buckling behavior of carbon/Kevlar intraply hybrid composites. The laminates containing various amounts of NC particles (0.5%, 1%, 1.5%, 2%, and 3% by weight) were manufactured using hand layup stacking followed by vacuum bag molding process. The prepared samples were subjected to axial and lateral compressive loads under fixed‐fixed and fixed‐free boundary conditions, respectively, and the relevant critical buckling loads were determined. Furthermore, the failure modes were examined via microscopic views taken from the damaged areas on the samples to fully understand the influences of NC particles on buckling characteristics. The findings demonstrated that the buckling behaviors of the samples were significantly affected by the introduction of NC particles. Compared with the composite samples without any NC particles, the composite samples with 1 wt% NC particles showed an increase of 21.12% and 25.33% in the axial and lateral critical buckling loads, respectively. However, the inclusion of NC particles with an amount that higher than 1 wt% showed a decreasing trend in terms of critical loads for both buckling loadings, which can be viewed as a measure of load‐bearing capability. Moreover, the samples filled with 3 wt% NC particles exhibited a decrement on critical loads compared with those of samples without any NC particle filler. With the help of microscopic views, the failure modes were detected as matrix fragmentation and delamination for both buckling loadings. [ABSTRACT FROM AUTHOR]

Curved panels are structural elements that form the skin of wings, fuselages and tail booms in aircraft. Buckling of these structures would adversely affect aircraft performance. Due to this, the problem of buckling has been extensively researched in the past. Most of the research has been restricted to the analysis of flat composite panels and analysis of curved panels through simplifications involving geometry, material properties and boundary conditions. The present study aims to develop an analytical solution that can predict the critical buckling load for a wider range of problems. An analytical solution was developed in order to obtain the critical buckling load for a doubly-curved composite laminate under compression, shear, moment or any combination of the three loads. The assumptions of the classical laminate plate theory were used in order to obtain the displacement fields as well as strains of the laminate. The energy method was employed in order to obtain the critical buckling load for various load cases. The values obtained through the analytical solution are compared to the critical buckling loads obtained through finite element analysis (FEA). The highest deviation of critical buckling load from FEA was calculated to be 16.55%. Variation of the critical buckling load with respect to the radius of curvature, boundary conditions and stacking sequence was analyzed. The developed solution was also found to be valid for cases when radii of curvatures are unequal as well as when the length and breadth of laminate are unequal. [ABSTRACT FROM AUTHOR]

In this work, the buckling analysis of functionally graded materials (FGMs) plates exposed to different load conditions is investigated using an efficient and simple refined plate theory. Uniaxial and biaxial compression loads along with simply supported boundary conditions on rectangular FGM plates are investigated. The effective material properties are computed using the simple power law equation of the volume fraction of the plate constituents. The governing equations are obtained from the principle of virtual works. The accuracy of present analytical solution is confirmed by comparing the present results with those available in existing literature. It can be concluded that the present theory is not only accurate, but also simply in predicting the buckling analysis of functionally graded plates. [ABSTRACT FROM AUTHOR]

In this work, a firefly algorithm was implemented and used to optimise composite structures in the postbuckling regime. In the first case studied, the goal was to maximise the post-buckling load of a rectangular plate subjected, independently, to shear load and uniaxial compression. The orientations of the layers served as design variables, while a maximal transverse displacement was considered as a constraint. Next, a reinforced flat panel was studied, with the goal of maximising the shear load in the post-buckling regime while constrained by the Tsai-Wu criterion. The design variables were the positions of the stiffeners and the orientations of the layers of the laminate. The degree of improvement in the maximum post-buckling load depended on the specific problem and ranged from 2.5 to 36 % compared to baseline designs. The selection of the structures chosen for the analyses ensured that the firefly algorithm was tested with progressively more challenging optimisation problems. The results suggested that the firefly algorithm could be used in the design of laminated composite structures. [ABSTRACT FROM AUTHOR]

A semi-analytical method is established to investigate post-buckling behavior of functionally graded graphene platelets reinforced composite (FG-GPLRC) plate with initial geometric defects under non-uniform in-plane compression loads. Buckling governing equations are derived base on a new unified framework of transverse shear deformation plate theory, and the reliability and accuracy of proposed method are validated. Parametric studies are systematically performed for the first time to elaborate the effects of GPLs, structural characteristics, initial geometric defects, loading cases and thermal environment on post-buckling behavior of FG-GPLRC plate. This article can provide theoretical guidance for the design and optimization of FG-GPLRC plate. [ABSTRACT FROM AUTHOR]

The mechanical post-buckling behaviour of variable stiffness layered composite beams reinforced by curvilinear fibres subjected to compressive loads is investigated here using a sine function-based shear flexible beam model. The neutral axis stretching force stemming from the axial movement restraints is accounted for through von Karman's assumption based geometrical nonlinearity. Furthermore, the modified beam constitutive equation arising from the consideration of the Poisson's effect is introduced in the formulation for the laminated beam analysis with general lay-up or ply sequences. The governing equations incorporating the incremental stiffness matrices are formed through the minimization of total potential energy principle and are solved by numerical method. The solutions for the developed governing equations are evaluated iteratively based on eigenvalue analysis and the characteristics of post-buckling of laminated beams can be inferred through the relationship between the beam deflection level and post-buckling axial load. An in-depth analysis selecting many design parameters for instance lamina's curvilinear fibre angles, beam slenderness ratio, lay-up and edge conditions, load type and so on is dealt with in bringing out the behaviour of variable stiffness laminated beam in linear and post-buckling regions. Also, the influence of flexible end supports by restraining elastically against ends rotation is studied on the beam elastic stability behaviour. [ABSTRACT FROM AUTHOR]

In this paper, an analytical solution for exploring the buckling characteristics of functionally graded (FG) plate is presented based on a quasi-3D shear deformation theory. It is considered that the plate is subjected to different types of in-plane compressive load. The FG plate is placed on three-parameter foundation WinklerPasternak-Kerr. The overall material properties of FG plate are assumed to be varied across the thickness and are estimated through the Voigt micromechanical model. The governing equations are obtained on the base of the quasi-3D deformation theory that contain undetermined integral forms and involves only four unknowns to derive. Equations of motion are derived from the principal of virtual work and the analytical solution is used to determine the critical buckling loads. By the discussion of numerical examples and the comparison with those of the reports in the literature, the convergence and the reliability of the present approach are validated. Finally, the parametric investigations of the in-plane buckling are carried out, including the influence of boundary conditions, elastic foundation, plate geometric parameters and power law index. The results reveal that the critical buckling loads are strongly influenced by several parameters such as boundary conditions, elastic foundation parameters and geometric shape of the plate. [ABSTRACT FROM AUTHOR]

A reliability assessment formulation for stiffened panels using the Model Correction Factor Method (MCFM) is derived from semi-empirical design equations of the IACS Common Structural Rules (CSR) for double-hull oil tankers. The approach consists of using the IACS-CSR buckling strength requirements of stiffened panels as a simplified response model that is calibrated iteratively at the design points calculated by the first-order reliability method using the results of non-linear finite element analysis of the stiffened panel. The approach is applied to a deck stiffened panel of a Suezmax oil tanker, designed according to the CSR for Double Hull Oil Tankers that has been used in the development of codes for the structural design of ships. The stiffened panels are subjected to uniaxial compressive loads induced by the hull girder vertical bending moment in a typical seagoing operational condition of the oil tanker in full load. It is shown that the application of the MCFM leads to a fast convergence towards the design point since the IACS-CSR formulation can capture the correct failure mode of the stiffened panels and the important mechanical features related to the prediction of their ultimate strength providing a convenient response surface model for reliability assessment. • This paper presents a reliability assessment for stiffened panels using the Model Correction Factor Method. • The IACS-CSR buckling strength requirements of stiffened panels as a simplified response model that is calibrated. • The approach is applied to a deck stiffened panel of a Suezmax tanker, designed according to the Common Structural Rules. • The stiffened panels are subjected to uniaxial compressive loads induced by the hull girder vertical bending moment. • The application of MCFM leads to a fast convergence since the IACS-CSR formulation can capture the correct failure mode. [ABSTRACT FROM AUTHOR]

Cutouts are commonly found in aerospace, ships, and marine structures, which have a great influence on mechanical properties such as stress concentration, natural frequency, and structural load-bearing performance of the structure. In this study, buckling behaviors of a square plate with a circular flanged cutout at the center are explored numerically, aiming to address the influence of different cutout parameters on the elastic and elasto-plastic buckling behaviors of the perforated plate. The flanged-perforated plate is subjected to uniaxial compressive loads, and the four edges are simply supported in the out-of-plane direction. The influence of various cutout parameters on the elastic and elasto-plastic buckling behaviors of the perforated plate is examined through a series of buckling analysis. In addition, structural weight reduction of the uniaxial compressed perforated square plates is carried out under the constraint of the elastic buckling stress of the plate structure. The findings indicate that different cutout parameters have a significant impact on the buckling performance of the plate. Perforated plates with flanging exhibit higher buckling strength than those without flanging, and variations in plate geometric parameters (such as the plate slenderness ratio and cutout radius ratio) are associated with increases in elastic buckling stress and elasto-plastic ultimate strength. The results of this paper can provide references for the design of flanged-cutouts in engineering. [ABSTRACT FROM AUTHOR]

In this paper, analytical and finite element solutions of mechanical buckling of a thick Functionally Graded (FG) plate have been investigated. Boundary conditions have been assumed as simply supported at all edges and three different loadings have been applied. In analytical section the procedure of developing the critical buckling force by third order shear theory has been presented and then the stability Equations have been reduced from 5 to 2. In continue, the problem has been solved using numerical simulation by ABAQUS. To validate the FEM, results have been compared and validated with analytical solution. The results show that the bi-axial compression loading case with the loading ratio of R to one and R to zero are the most possible and most unlikely case in buckling occurrence, respectively. [ABSTRACT FROM AUTHOR]

In this paper, a new buckling-controlled member (BCM) is introduced for use in space structures. This member is composed of four components; namely: the encasing, joints, core, and adjustable nuts. The core is intended to act as a structural element to resist the axial loads by its yielding under compression loading. The steel encasing is supposed to confine the steel core. Adjustable steel nuts on the steel core act as lateral bracings and are responsible for lateral load transmission between the encasing and core. The joints at the two ends of the supports of the member. Six experimental tests have been performed under compression load to show the efficiency of the new member. The test results reveal that the proposed member can provide the needed ductility and can delay the brittle buckling of the members. Also, the BCM is capable of considering buckling modes and controlling the plastic range. The experimental and numerical results have also been compared. Additional numerical evaluations have been carried out using finite element models, in which the effects of different parameters of the member have been investigated. The obtained results showed that the arrangement of inner elements is the main factor affecting ductility and postponing the buckling of the members. In the end, the effects of the BCMs on the overall behavior of four double-layer space structures have been studied. The obtained results of analyses indicated that the BCMs can enhance the strength and ductility of space structures, thereby reducing the risk of collapse. Also, the seismic collapse of the space structure was postponed. [ABSTRACT FROM AUTHOR]

Purpose: The objective of the present work is to present the design optimization of composite cylindrical shell subjected to an axial compressive load and lateral pressure. Design/methodology/approach: A novel optimization method is developed to predict the optimal fiber orientation in composite cylindrical shell. The optimization is carried out by coupling analytical and finite element (FE) results with a genetic algorithm (GA)-based optimization scheme developed in MATLAB. Linear eigenvalue were performed to evaluate the buckling behaviour of composite cylinders. In analytical part, besides the buckling analysis, Tsai-Wu failure criteria are employed to analyse the failure of the composite structure. Findings: The optimal result obtained through this study is compared with traditionally used laminates with 0, 90, ±45 orientation. The results suggest that the application of this novel optimization algorithm leads to an increase of 94% in buckling strength. Originality/value: The proposed optimal fiber orientation can provide a practical and efficient way for the designers to evaluate the buckling pressure of the composite shells in the design stage. [ABSTRACT FROM AUTHOR]

The purpose of this research was the analysis of the stability of compressed thin-walled composite columns with closed rectangular cross-sections, subjected to axial load. The test specimens (made of carbon–epoxy composite) were characterized by different lay-ups of the composite material. Experimental tests were carried out using a universal testing machine and other interdisciplinary testing techniques, such as an optical strain measurement system. Simultaneously with the experimental studies, numerical simulations were carried out using the finite element method. In the case of FEA simulations, original numerical models were derived. In the case of both experimental research and FEM simulations, an in-depth investigation of buckling states was carried out. The measurable effect of the research was to determine both the influence of the cross-sectional shape and the lay-up of the composite layers on the stability of the structure. The novelty of the present paper is the use of interdisciplinary research techniques in order to determine the critical state of compressed thin-walled composite structures with closed sections. An additional novelty is the object of study itself—that is, thin-walled composite columns with closed sections. [ABSTRACT FROM AUTHOR]

Buckling of the longitudinal rebar is one of the main forms of plastic hinge failure in reinforced concrete (RC) columns after an earthquake. This rebar buckling significantly impacts the seismic bearing capacity and energy dissipation capacity. To restrain the development of longitudinal rebar buckling behavior and delay the degradation of lateral strength in RC columns, this paper developed a new type of buckling restraint rebar (BRR) consisting of three components: longitudinal rebar, a restraint sleeve, and foam material. First, the BRR mechanical properties under compression and tension‐compression cyclic loading were obtained through quasi‐static loading tests. Then, the BRR compression and tension‐compression cyclic loading processes were numerically simulated based on ABAQUS finite element software. The simulated results were compared with the test results. Finally, a stress–strain constitutive model for this new BRR was proposed based on this study. Results showed that the restraint sleeve could significantly enhance the lateral stiffness and the bearing capacity of longitudinal reinforcement after yielding. The compressive performance of BRR was mainly affected by the length and wall thickness of the sleeve. The cyclic performance was mainly affected by the length of the sleeve and the clearance between the sleeve and the reinforcement. The BRR constitutive model proposed in this paper can accurately reflect the influence of restraint sleeves on the stiffness of longitudinal reinforcement after yielding. [ABSTRACT FROM AUTHOR]

The compression load of straight bars, for which the cross-sections are smaller compared to their length, causes a phenomenon of bending along the longitudinal axis. Upon reaching a certain level, called the critical level of the stresses, the bending deformations begin to increase beyond the bearing limit of the bar. It yields instantly, due to an unstable elastic deformation state, although the material's resistance limit has not been exceeded. The irreversibility of the phenomenon is dangerous especially for the railway tracks and is not fully mastered by calculation methods. They can eventually establish the level of the critical demand, which has values specific to each rail configuration. It is accepted that for loads lower than this level, buckling of the respective rail does not occur. The longitudinal tension in the railway tracks occurs due to the expansion caused by their heating under the action of the sun's rays, but also due to the friction between the rails and the train wheels. This paper proposes the realization of a study model of the buckling of the railway tracks. This model is represented by an assembly, built in the SOLIDWORKS application for which a Buckling simulation was made. The imposition of two distinct temperatures on the rails and crossties is the source of the model's request. The increase in the temperature of the component parts of the assembly causes their expansion, so implicitly the appearance of some longitudinal deforming forces, specific to the buckling phenomenon. [ABSTRACT FROM AUTHOR]

This study experimentally investigated the effects of nanoparticle reinforcement on the buckling behavior of composite materials. Different sizes of carboxylic acid functionalized multi-walled carbon nanotubes were used as nanoparticles. E-glass fiber-reinforced composite materials with polymer matrix in the [0°/90°/0°/90°]s cross-ply array with and without carbon nanotube reinforcement were produced by hand lay-up and vacuum bagging. Three types of carbon nanotubes in different sizes and proportions of 0.1%, 0.2%, 0.3%, 0.4%, and 0.5% by weight were added to the epoxy resin. For the buckling test, the samples with two clamped and two free sides were attached to the universal testing machine to apply a uniaxial compressive load. As a result of the experiments, it was found that the addition of carbon nanotube in certain proportions increases the critical buckling load of composite materials. The highest increase in the critical buckling load (26.10% increase) was achieved with a carbon nanotube reinforcement of 0.2% by weight, having an outer diameter of 10–20 nm, internal diameter of 5–10 nm, and length of 0.5–2 mm. As the carbon nanotube sizes added to the epoxy resin decreased, the buckling strength increased. [ABSTRACT FROM AUTHOR]

This research endeavors to examine the effect of stiffener shapes on the structural capacity of stiffened-plate structures, specifically focusing on Tee (T), Angle (L), and Flat (I) stiffened plates. The primary objectives are threefold: firstly, to quantify the critical load values during the buckling phenomenon for T, L, and I stiffened plates; secondly, to assess model deformation upon failure; and thirdly, to investigate whether the buckling behavior of T, L, and I stiffened plates correlates with distinct failure patterns. Employing numerical simulation through the finite element method, this study sheds light on previously unexplored aspects of structural behavior. The findings indicate that angle stiffeners exhibit superior load-bearing performance compared to flat bars. Notably, the research reveals a substantial increase in maximum compressive load by at least 15.90% with Tee bar and 8.25% with angle bar stiffeners when the stiffened panels undergo a 5 mm displacement, presenting a potential avenue for structural enhancement. Additionally, the study demonstrates that T bars outperform in terms of resisting buckling. Noteworthy is the novel approach of examining the combined effect of transverse frame, longitudinal frame, and hull girder under buckling scenarios, a facet not explored in previous research. Furthermore, the utilization of steel S355JR-EN10210 as a material introduces a unique dimension not previously considered in these scenarios. [ABSTRACT FROM AUTHOR]

Purpose: This paper proposes a novel shear deformation theory to study the static bending and buckling of nanoplates subjected to flexomagnetic influence. This is done using the revolutionary shear strain theory and establishing finite element formulations based on the finite element technique. Methods: This study uses a finite element method to solve the nanoplate bending and buckling problem while taking into consideration the flexoelectromagnetic effect. Results: The investigation's novel aspects are summarized: since the flexomagnetic effect makes the plate stiffer, the maximum deflection is lowered when this effect is included. This effect also has varying influences on the plate under various boundary conditions, particularly the maximum position of the deflection, stress, Hz, and Bz responses. The thinner the plate thickness, the more pronounced the flexomagnetic effect. The flexomagnetic effect causes the thickness distribution of the stress components, Hz, and Bz to diverge from that of conventional structures (where this effect is disregarded), particularly for plates with CFFF boundary conditions. The longer the length of the compression zone increases, the lower the critical buckling load of the plate. The greater the stiffness of the elastic foundation, the better the plate can withstand compressive loads. Conclusion: The findings of this work provide a significant scientific foundation for the computation and development of nanoplates with magnetic properties. To design a structure that meets the necessary criteria, it is crucial to carefully choose geometric characteristics, boundary conditions, and stiffness parameters of the elastic foundation. According to this study, potential areas for additional research include investigating the impact of the flexomagnetic effect on nanoplates including fractures, optimizing nanostructures that exhibit flexomagnetic effects, and calculating the influence of flexomagnetic effects and temperature on nanostructures. [ABSTRACT FROM AUTHOR]

Grid‐stiffened composite cylinders are widely used in a variety of applications and are subjected to static, dynamic, and impact loads. In terms of buckling strength, these structures outperform simple layered and sandwich composites of the same weight, and the presence of unidirectional fiber ribs contributes to their delamination resistance. The purpose of this research is to look into the buckling behavior of grid‐stiffened composite cylinders under low‐velocity and high‐energy axial impacts. The tests were carried out at room temperature using a 35 kg impactor with an impactor fall height of about 2.75 m. This study builds on previous research and considers the samples' thin skin, indicating that skin buckling is the primary buckling mode in such scenarios. According to static loading research, three types of buckling can occur in grid‐stiffened composite cylinders: local shell buckling, local rib buckling, and general buckling, and each of these can be controlled by adjusting the geometric properties. But, based on the loading speed in the weight‐drop test, controlling the specific type of buckling that occurs during impact loading is difficult. Examining residual structural effects can help determine the type of buckling and damage sustained during impact events. According to the results, the forces that cause buckling in grid‐stiffened composite structures under impact loads are 1.5–2 times greater than static loading conditions. Notably, once the forces are removed, these structures can return to their original positions, however with less stiffness. As a result, they absorb a significant amount of impact energy. Highlights: Composite cylinders with spiral ribs have higher static compression resistance.Dynamic loading increases local buckling forces in grid‐stiffened structures.Despite being damaged, grid‐stiffened cylinders bounce back quickly after impact.Skin buckling is a common mode of failure for grid‐stiffened composite.The global buckling force is greater than the local buckling force. [ABSTRACT FROM AUTHOR]

Considering the broad application prospect of high-strength steel (HSS) in engineering structure, and the limitations present in existing studies on interactive buckling of HSS welded thin-walled box section long column, test and finite element analysis (FEA) were used to investigate the interactive buckling behaviour exhibited by 12 specimens fabricated from Q420–Q960 steels. In the detailed analysis, various aspects were considered, including the failure mode, axial deformation, interaction between overall and local buckling deformation, and the ultimate bearing capacity. It was observed that the utilization rate of steel strength diminished with an escalation in both the plate width–thickness ratio and steel strength. An increase in the width–thickness ratio correlated with an earlier onset of local buckling, and the influence of steel strength was found to be negligible. Taking into account the influence of slenderness ratio and steel strength, a novel calculation formula for determining the limit of the plate width–thickness ratio for columns undergoing interactive buckling was derived. The limit of the plate width–thickness ratio experienced a decrease with an increase in steel strength, and the influence of the column slenderness was minimal. Subsequently, the ratios of calculated to simulated ultimate bearing capacities for non-compact section long columns were evaluated using Eurocode 3, ANSI/AISC 360–22, and JGJ/T 483–2020. Additionally, a novel calculation method for the ultimate bearing capacity of Q420–Q960 steel welded thin-walled box section long column was introduced, grounded in the direct strength method. • Interactive buckling behaviour of HSS welded thin-walled long column was study. • The plate width–thickness ratio limit decreases with an increase in steel strength. • A novel formula for determining the plate width–thickness ratio limit was derived. • A calculation method for the ultimate bearing capacity was proposed. [ABSTRACT FROM AUTHOR]

The local and global buckling capacity of the thin-walled box-section members formed by cold bending of ten BS700 high-strength steel (HSS) specimens are experimentally determined through an axial compression test. The mechanical properties of the materials are evaluated through material performance test, and a material model suitable for finite element analysis is proposed. The initial geometric imperfection of the members is measured, and it is found that the maximum initial deflection can be 1/1000 of the length of the members, as specified in the Chinese code. Based on the test, the ultimate bearing capacity and failure modes of the component with local and global interactive buckling are obtained. Further, a finite element model is established, and the corresponding results are compared with the test results. Furthermore, the test results are compared with those obtained using the existing specifications. The results show that the failure modes of the specimens are primarily local and global buckling failure. The influence of residual stress and initial geometric imperfection is considered in the proposed finite element model. Comparing the ultimate bearing capacity and load-displacement curves with the corresponding test results, it is found that the finite element model can effectively reproduce the test results. By comparing the test results with those obtained based on the steel structure design codes of China, the United States, and Europe, it is found that the test results are all higher than the existing code results, and the Chinese and European codes are relatively conservative with a difference of more than 20%, while the difference between the test results and the American code results is nearly 10%. Therefore, it is necessary to further improve the calculation methods of local and global buckling capacity of thin-walled box-section members of BS700 HSS under axial compression. [ABSTRACT FROM AUTHOR]

Buckling phenomenon is a common failure mode for composite materials under the effect of compressive loading which is mainly investigated in two stages as pre – buckling and post – buckling. At the pre – buckling phase, the deformations take place temporarily in elastic range. However, load carrying capacity of a member can be increased by regarding the post – buckling process. Therefore, it is important to determine the final and maximum load carrying ability of the structure. Since, at the end of the post – buckling, the body cannot carry load and crippling failure takes place. In this review article, crippling behavior of the composite structures is investigated. After describing the crippling phenomenon, this study mainly investigates both experimental and theoretical points of views. In this scope, affecting parameters such as stacking sequence, geometrical properties and boundary conditions are determined. Then, the improved theoretical approaches are stated. The compatibilities of the test results are assessed with theoretical studies. [ABSTRACT FROM AUTHOR]

Carbon nanotubes (CNTs) are extremely conductive and flexible, making them ideal for applications such as flexible electronics and nanoelectromechanical systems. However, in order to properly apply them in such devices, their long-term durability must be assessed. In the present study, we demonstrate cyclic loading of a thick MWCNT (175 nm) under axial compression, observed in situ under a transmission electron microscope (TEM). The force was applied via controlled displacement, while real-time TEM videos of the deformation process were gathered to produce the morphological data. The in situ observations combined with force–displacement curves revealed the onset of buckling instabilities, and the elastic limits of the tube were assessed. The MWCNT retained its original structure even after 68 loading–unloading cycles, despite observed clues for structural distortions. The stiffness of the tube, calculated after each loading cycle, was in a 0.15 to 0.28 TPa range—comparable to the literature, which further validates the measurement set-up. These in situ tests demonstrate the resilience of CNTs to fatigue which can be correlated with the CNTs' structure. Such correlations can help tailoring CNTs' properties to specific applications. [ABSTRACT FROM AUTHOR]

This paper analytically studies the buckling of a cylindrical shell having varying thickness under non-uniform axial compressive loads for the first time, which widely exists in engineering practice. A novel quadratic perturbation technique is developed to establish general buckling load formulas for the shell. This method overcomes the difficulties of traditional energy methods in solving high order determinants and deriving direct expressions for buckling loads when shell thickness and axial load are unknown. Applying presented formulas, various shell thicknesses and axial loads are analyzed, and a series of new results for buckling loads are obtained and validated. Even for classical cosine thickness variation under uniform axial compression, we also give general conclusions compared with Koiter's results by the energy method. The effects of thickness variations and load distribution parameters on buckling loads are analyzed in detail. The presented study in this paper fills the gap and establishes a foundation of buckling analysis for non-uniformly loading cylindrical shells with variable thickness. Certainly, the established formulas are general and available for buckling resistance capacity evaluation for the shells under all circumstances involving thickness variations or/and non-uniform axial compressive loads. [ABSTRACT FROM AUTHOR]

Purpose: The purpose of this paper is to propose a numerical prediction method of buckling loads for shell structures under axial compression and thermal loads based on vibration correlation technique (VCT). Design/methodology/approach: VCT is a non-destructive test method, and the numerical realization of its experimental process can become a promising buckling load prediction method, namely numerical VCT (NVCT). First, the derivation of the VCT formula for thin-walled structures under combined axial compression and thermal loads is presented. Then, on the basis of typical NVCT, an adaptive step-size NVCT (AS-NVCT) calculation scheme based on an adaptive increment control strategy is proposed. Finally, according to the independence of repeated frequency analysis, a concurrent computing framework of AS-NVCT is established to improve efficiency. Findings: Four analytical examples and one optimization example for imperfect conical-cylindrical shells are carried out. The buckling prediction results for AS-NVCT agree well with the test results, and the efficiency is significantly higher than that of typical numerical buckling methods. Originality/value: The derivation of the VCT formula for thin-walled shells provides a theoretical basis for NVCT. The adaptive incremental control strategy realizes the adaptive adjustment of the loading step size and the maximum applied load of NVCT with Python script, thus establishing AS-NVCT. [ABSTRACT FROM AUTHOR]

The buckling behavior of functionally graded carbon nanotube (FG-CNT) reinforced polymer-based moderately-thick plates subjected to in-plane biaxial compressive loads in elastic and thermal environments in the framework of first-order shear deformation plate theory (FSDPT) is investigated. First, the temperature-dependent properties of CNTs and nanocomposites are defined and their constitutive relations are established, then the stability and strain compatibility equations in elastic media are derived in the framework of the FSDPT. Then, by applying the Galerkin method to the basic equations, a closed-form solution is obtained for the critical biaxial compressive loads. The specific numerical analyzes and interpretations are made for various plate sizes and CNT patterns on the Winkler elastic foundation and in thermal environments within FSDPT and classical plate theory (CPT). [ABSTRACT FROM AUTHOR]

This paper aims to investigate the buckling behavior of circular hollow section (CHS) T-joints in retrofitted and non-retrofitted states under axial brace compressive loading. For this purpose, two types of analysis are carried out. The first one is evaluating the critical buckling load in various tubular joints, and the other one is investigating the post-buckling behavior after each buckling mode. More than 180 CHS T-joints with various normalized geometric properties were numerically modeled in non-retrofitted state to compute their governing buckling mode, i.e., chord ovalization, brace local, or global buckling. Then three joints with different buckling modes were selected to be retrofitted by fiber-reinforced polymer (FRP) patches to illustrate the improving effect of the FRP wrapping on the post-buckling performance of the retrofitted joints. In addition, FRP composite failures were investigated. The results indicate that the FRP retrofitting is able to prevent the brace local buckling, and that matrix failure is the most common composite failure in the retrofitted joints. [ABSTRACT FROM AUTHOR]

Optimizing the core thickness of a sandwich structure can be a computationally expensive task. In this work, an optimization approach for slender columns is presented. The approach iteratively determines the optimal thickness distribution using the second derivative of the eigenmodes as an input for the shape function. To demonstrate its capabilities, it is applied to simple columns constrained according to Euler's buckling cases. The optimization results are validated with detailed finite element models and compared to those from a nonlinear least squares‐based optimization. [ABSTRACT FROM AUTHOR]