Buckling Behavior Research Articles

Kresling tube metamaterial exhibits extreme large-displacement buckling behavior

The present contribution proves that Kresling-patterned tubular origami metamaterials can exhibit a nonlinear buckling behavior in compression characterized by extremely significant and sudden twisting, as well as by extreme transverse dilation/contraction. It is proved that such an extreme buckling behavior can be achieved by tuning the ratio between stiffness parameters controlling the relative compliance of in-plane deformation of facets with respect to their bending and folding about creases. The modeling strategy adopted in the present contribution is discrete in nature and consists of an extensional-rotational spring model where energy barriers are introduced to prevent the interpenetration of adjacent facets.

Buckling and post-buckling analysis of composite wing box under loads with torsion-bending coupling

In this paper, a mathematical model for the effect of different torsion-bending ratios on buckling and failure loads under complex operating conditions was proposed, and the buckling, post-buckling and failure behavior and mechanism of carbon fiber composite wing box were studied by combining experiments and simulations. A high-precision computational simulation model was established by considering detailed bolt arrangement information, as well as damage and failure of composite materials. The predicted buckling loads, failure loads, and damage modes are in good agreement with the experimental results. The results show that, under the condition of constant bending moment, as the torque increases, the linear strain of the box section remains consistent, while the shear strain increases significantly, leading to a change in the buckling mode and failure distribution. When the torsion-bending ratio is less than 2.0, the loading form of the structure is greatly affected by the torque. On the contrary, the buckling and failure loads are exponentially close to the pure torsional state. The mathematical model and simulation model in this study can provide an important reference for the structural design and failure mechanism analysis of large composite wing boxes.

Influence of Aspect Ratio on the Flexural and Buckling Behavior of an Aluminium Sandwich Composite: A Numerical and Experimental Approach.

In the field of engineering materials, lightweight and ultra-lightweight composites are used in real time to a greater extent, with high-performance targeting for tailor-made systems in aerospace, automotive, and biomedical applications. Sandwich composites are among the most popular lightweight materials used in structural and vehicle-building applications. In the present investigation, one such sandwich composite laminate composed of aluminum face sheets and a high-density polyethylene core was considered to analyze sandwich composites' flexural and buckling behavior experimentally and numerically. The influence of aspect ratios, such as length to thickness and width to thickness, on the flexural and buckling performance of sandwich composite laminates was explored in the study. Laminates with different widths, namely, 10, 12, and 15 mm, and a uniform thickness and length of 3 mm and 150 mm, respectively, were used for flexural analysis, whereas laminates with widths of 10, 12, and 15 mm and a uniform thickness and length of 3 mm and 350 mm, respectively, were used for buckling analysis. The geometrical influence of the laminates on mechanical performance was studied through performance measures such as critical bending load, flexural stiffness, inter-laminar shear stress, and critical buckling load. A significant influence of aspect ratio on the mechanical behavior of the laminates was observed using both experimental and numerical approaches. Flexural behavior was observed to be better at greater widths, namely, 15 mm, and with a minimum support span of 90 mm due to reduced spring back effects and increased bending resistance. A maximum width of 15 mm allowed for a higher buckling load capacity similar to that of bending resistance. A critical buckling load of 655.8 N seemed to be the maximum and was obtained for the highest aspect ratio, b/t = 5. The soft core and ductile metal face sheets offered combined resistance to both bending and buckling. A lower aspect ratio (span to thickness) rendered these sandwich laminates better in terms of both bending and buckling.

Efficient buckling and post-buckling analysis of porous FG sandwich beams by new RPIM-HOCM mesh-free approach

The main purpose of this paper is to analyze buckling and post-buckling behavior of porous functionally graded (FG) beams and sandwich beams using a new efficient optimal mesh-free high order algorithm. The proposed solver combines mesh-free approach based on radial point interpolation method with high order continuation method (RPIM-HOCM). It is assumed that the FG beam and FG layers of sandwich beam are made from a mixture of ceramic and metal such that bottom surface of the plate is metal-rich, whereas top surface is ceramic-rich. So, constitutive equation as well as material properties are considered to change smoothly and gradually in the thickness direction via a mathematical relationship distribution. Non-linear strong form of the beam buckling problem which is based on the first-order shear deformation theory (FSDT) is derived using the virtual displacements theorem. The proposed coupling (RPIM-HOCM) is presented and validated firstly by comparing obtained numerical results with those computed using a reference algorithm. Then, RPIM-HOCM solver is used to investigate the effect of power-law index, porosity distribution, span-to-height ratio, boundary conditions and skin-core–skin thickness ratio on critical buckling load and post-buckling behavior.

Isogeometric Dynamic Buckling Analysis of Trimmed and Multipatch Thin-Shell Structures

This paper extends our previous work on the isogeometric dynamic buckling analysis of thin-shell structures to the trimmed and multipatch situation where features such as cutouts and stiffeners can be easily incorporated. To be specific, a modified generalized- time integration scheme combined with a geometric nonlinear isogeometric Kirchhoff–Love shell element is used to simulate the complex buckling and postbuckling behaviors of thin-shell structures. The developed method can damp properly high-frequency contents while maintaining second-order accuracy in the dynamic buckling analysis. For the integration of arbitrary-shaped trimmed elements, a geometrically exact blending function method is developed to improve the efficiency of the dynamic shell buckling analysis. To deal with multipatch geometries, a penalty-based weak coupling approach is developed, where coupled patches with nonconforming trimmed interfaces or even with prescribed angles, such as stiffeners, can be analyzed. We demonstrate the accuracy, stability, and flexibility of the proposed framework with several numerical examples. In particular, the influences of “free” and “partially free” control points, penalty factor, trimming, as well as different modeling strategies on the dynamic solutions of shell structures are investigated.

Dynamic and Thermal Buckling Behaviors of Multi-Span Honeycomb Sandwich Panel with Arbitrary Boundaries

Dynamic and Thermal Buckling Behaviors of Multi-Span Honeycomb Sandwich Panel with Arbitrary Boundaries

Nonlinear stability and design of prestressed stayed columns in fire considering non-uniform temperature distribution

Prestressed stayed columns are vulnerable to fire due to material weakening. The fire behaviour of the stayed columns is investigated with non-uniform temperature distributions considered using steady state analysis within ABAQUS. This study aims to reveal the load-carrying capacity reduction of stayed columns in fire and propose a design method. Results show that ultimate loads decrease with temperature increasing, and the stayed columns approximate failure at the temperatures higher than 600°C. The failure deflected mode maintains similar to the dominant linear buckling mode for the uniform temperature distribution, and the sensitivity of ultimate loads to prestressing levels becomes less significant at higher temperatures. Moreover, compared to buckling and ultimate behaviour, initial post-buckling behaviour shows more significant sensitivity to temperature distributions. The non-uniform distribution can lead to asymmetric deflected mode due to stiffness re-distribution from the material weakening at elevated temperatures, and the post-buckling behaviour of the cases with rotational symmetric mode dominance is sensitive to prestressing levels. Finally, a fire design method is proposed based on the ultimate load reduction in fire.

A Hermitian Cn finite cylindrical layer method for 3D size‐dependent buckling and free vibration analyses of simply supported FG piezoelectric cylindrical sandwich microshells subjected to axial compression and electric voltages

AbstractWithin the framework of the consistent couple stress theory (CCST), we develop a Hermitian Cn (n = 1, 2) finite cylindrical layer method (FCLM) for carrying out the three‐dimensional (3D) analysis of the size‐dependent buckling and free vibration behaviors of simply supported, functionally graded (FG) piezoelectric cylindrical sandwich microshells. The microshells of interest are placed under closed‐circuit surface conditions and subjected to axial compression and electric voltages. We derive a 3D weak formulation based on Hamilton's principle for this study. In the resulting formulation, the microshell is artificially divided into nl microlayers, with the elastic displacement components and the electric potential selected as the primary variables. By incorporating a layer‐wise kinematic model into our weak formulation, we develop a Hermitian Cn FCLM, which can be used for analyzing FG piezoelectric cylindrical sandwich microshells. Each primary variable is expanded as a double Fourier series in the in‐surface domain and is interpolated in the thickness direction using Hermitian Cn polynomials. The accuracy and the convergence rate of our Hermitian Cn FCLMs are validated by comparing the solutions they produce for FG piezoelectric cylindrical macroshells and FG elastic cylindrical microshells with the relevant exact and approximate 3D solutions which have been reported in the literature. The material length scale parameter of our FCLMs is set at zero in the comparison made with the FG piezoelectric macroshells. In contrast, the piezoelectric and flexoelectric effects are ignored in the comparison made with the FG elastic microshells. The impact of some essential factors on the critical load, critical voltage, and natural frequency of simply supported FG piezoelectric cylindrical sandwich microshells is assessed. The important factors are identified as piezoelectricity, flexoelectricity, the material length scale parameter, the inhomogeneity index, the radius‐to‐thickness ratio, the length‐to‐radius ratio, and the magnitude of the applied voltage and the applied load.

Strength prediction of built-up radially battened columns in torsional buckling

The built-up radially battened column (RBC) has found its promising application in public buildings due to its aesthetical form and good load-bearing capacity. Like the X-shaped column, torsional buckling may be the major failure mode of the RBC under axial compression. However, current specifications lack rational design methods for the torsional buckling strength prediction of this innovative column. This paper will focus on the torsional buckling behaviour of the RBC and propose its corresponding strength design formulas. At first, the key sectional properties of the radially continuous-web tube columns (RCTC) are derived theoretically and are proven to be consistent with the numerical calculation result. Then, a finite element model (FEM) using the shell element of RCTC is established, accordingly, the elastic torsional buckling behaviour of RCTCs is investigated, and an expression for accurately estimating the elastic torsional buckling load of RCTCs is proposed. Afterward, the FEM of built-up RBCs is established to conduct the elastic buckling analysis and elastoplastic bearing capacity prediction. The elastic torsional buckling load of built-up RBCs is predicted by modifying the expression for RCTCs via the number of battens and the proportion of the area of battens. A key design parameter, the normalized slenderness ratio, is also obtained. Finally, the strength design recommendation of the RBCs for torsional buckling is presented on the ground of numerous elastoplastic FEM results by changing the normalized slenderness ratio, and a limit RBCs’ dimension that can prevent the built-up RBC from the torsion buckling is further proposed. These results are expected to guide the design of the RBC and promote its application in engineering.

A new analytical approach to the nonlinear buckling and postbuckling behavior of functionally graded graphene reinforced composite laminated cylindrical, parabolic, and half‐sinusoid shallow imperfect panels

AbstractThis paper presents and analyzes the nonlinear buckling responses of three types of shallow imperfect panels (cylindrical panel, parabolic panel, and half‐sinusoid panel) made from functionally graded graphene reinforced composite (FG‐GRC) on nonlinear elastic foundations subjected to axial compressive load in thermal environments. The nonlinear governing equations are formulated on Reddy's higher‐order shear deformation shell theory (HSDST) and take into account von Karman‐type nonlinearity. A new approximation technique to determine the stress function in average sense is developed and Galerkin's method is used to obtain the algebraically nonlinear equation system. Then, the simple calculation process can be used to solve the obtained equation systems, and the formulations to calculate the critical buckling loads and postbuckling load‐deflection curves are expressed in explicit form. The results can be flexibly applied to FG‐GRC panels with different curvatures in engineering designs. The effects of panel types, geometrical parameters, temperature increase, initial imperfection, and nonlinear elastic foundations on the critical buckling loads and postbuckling curves of cylindrical, parabolic, and half‐sinusoid FG‐GRC panels are discussed in numerical results. Numerical results also show a small disadvantage in the load‐carrying capacity of cylindrical panels compared to parabolic panels and half‐sinusoid shallow panels.Highlights Postbuckling of cylindrical, parabolic, and half‐sinusoid panels are studied. The panels are made of functionally graded graphene reinforced composite. Reddy's higher‐order shear deformation shell theory is applied. A new approximation technique to determine the stress function is developed. Critical buckling loads and postbuckling expressions are explicitly obtained.

Effects of stacking sequences on the axial compressive buckling behavior and failure characteristics of channel-section CFRP/Al laminate columns

Open-section composite profiles are often used as columns in civil engineering structures. Their thin-walled nature makes these sections prone to buckling phenomena when loaded in compression. This paper presents a study on the axial compressive performances and failure behavior of channel-section CFRP/Al laminate columns with two different stacking sequences. Typical mechanical responses and failure characteristics were first explored through experiments. Then the damage propagation mechanisms of the two kinds of columns were further compared based on a three-dimensional progressive damage model. The results indicated that column with CFRP layers stacked on the exterior surfaces exhibited smaller delaminated areas compared with the ones with aluminum alloy layers stacked exteriorly, thus resulting in the higher load-bearing capacities. Finally, a concise theoretical calculation equation for buckling load was derived, based on which further structural parametric analysis were performed.

Buckling and failure behavior of the silicon carbide (SiC) ceramic cylindrical shell under hydrostatic pressure

The present study explores the buckling and failure behavior of the silicon carbide (SiC) ceramic cylindrical shell under hydrostatic pressure using experimental and nonlinear numerical methods. An innovative experiment setup is designed and built. The hydrostatic test of the SiC ceramic cylindrical shell is carried out. The buckling deformation of the shell is captured by a high-speed camera and the strain response is recorded by strain gauges. In order to compare with the experimental results, the failure behavior of the SiC ceramic cylindrical shell subjected to hydrostatic pressure is simulated using a nonlinear numerical approach. Both the ultimate tensile strength and ultimate compression strength of the material are taken into consideration. The maximum equivalent stress is used as the failure criterion. The buckling mode simulated by the numerical method is in good agreement with the deformation shape observed in the test. As for the buckling pressure, the deviation from the experimental result is only 3.62%. Both the experimental and numerical results show that the failure of the SiC ceramic cylindrical shell under hydrostatic pressure is a typical coupling failure of strength damage and structural instability.

Dynamic response of 3D printed functionally graded sandwich foams

PurposeThe purpose of this study was to introduce three-dimensional printing (3DP) of functionally graded sandwich foams (FGSFs). This work was continued by predicting the mechanical buckling and free vibration behavior of 3DP FGSFs using experimental and numerical analyses.Design/methodology/approachInitially, hollow glass microballoon-reinforced high-density polyethylene-based polymer composite foams were developed, and these materials were extruded into their respective filaments. These filaments are used as feedstock materials in fused filament fabrication based 3DP for the development of FGSFs. Scanning electron microscopy analysis was performed on the freeze-dried samples to observe filler sustainability. Furthermore, the density, critical buckling load (Pcr), natural frequency (fn) and damping factor of FGSFs were evaluated. The critical buckling load (Pcr) of the FGSFs was estimated using the double-tangent method and modified Budiansky criteria.FindingsThe density of FGSFs decreased with increasing filler percentage. The mechanical buckling load increased with the filler percentage. The natural frequency corresponding to the first mode of the FGSFs exhibited a decreasing trend with an increasing load in the pre-buckling regime and an increase in post-buckled zone, whereas the damping factor exhibited the opposite trend.Originality/valueThe current research work is valuable for the area of 3D printing by developing the functionally graded foam based sandwich beams. Furthermore, it intended to present the buckling behavior of 3D printed FGSFs, variation of frequency and damping factor corresponding to first three modes with increase in load.

Postcritical Imperfection Sensitivity of Functionally Graded Piezoelectric Cylindrical Nanoshells Using Boundary Layer Solution

The nonlocal (NL) and the strain gradient (SG) based equivalent continuum theories were proposed for nanomechanics by accommodating the long-range molecular interactions and to bypass the computationally expensive atomistic simulations. Nanostructures are often made of smart materials (e.g., piezoelectric, piezoceramic, and flexoelectric) for multifunctional properties. Applications of nanostructures in critical systems deserve accurate analysis. The buckling and postcritical behavior of an axially loaded, piezoelectric, nonlocal strain gradient (NLSG) thin cylindrical shells with functionally graded elastic properties were presented in earlier studies following Donnell’s approach, leading to a set of stiff, nonlinear, partial differential equations, accommodating the prebuckling nonlinearity and large postcritical deflection. This study extends the previous work by accommodating geometric imperfections in the formulation. Furthermore, a consistent thickness-wise distribution for the electric potential is also adopted following the Maxwell equation. The boundary layer (BL) concept is employed to solve the resulting nonlinear equations via asymptotic expansions of the regular and the BL fields. The solution is numerically illustrated on moderately short shells, illustrating the influence of the geometric imperfections. The critical load remains imperfection sensitive, yet the imperfections change an unstable postcritical path into a stable one. The influence of the functional gradation and the external electric fields on the imperfection sensitivity behavior are illustrated.

Geometric imperfection measurement on welded hybrid steel box‐section girders

AbstractHigh‐strength steel materials (steel grades of S500 ‐ S960) gaining prominence in civil engineering, especially for large‐span bridges. In the case of bridges, the application of hybrid girders combining low‐ and high‐strength steel materials is an effective and economical solution. The hybrid girders generally consist of webs comprised of low‐strength steel and flanges made of high‐strength steel. In Europe, apart from some minor practical applications and research results in Sweden, these structure types are completely new solutions in bridges, and the theoretical background of their stability design is missing from the current European standardized design provisions. To determine the theoretical background of this girder type and to develop the design theories for application purposes it is essential to execute experimental laboratory test programs. Analyzing the local buckling and plastic behavior of hybrid steel plate girders through experiments is essential to have an approopriate knowledge on the geometrical and structural imperfections of the hybrid girders. Therefore, in the present paper the measurement of geometric imperfection on 14 welded hybrid steel box‐section girders with varying geometry is presented and their results are evaluated and discussed. The flanges of the examined hybrid girders are made of S700 or S500, the web of the specimens consists of S355 steel grade. The measured imperfection values are evaluated based on the steel grade and geometric parameters such as plate width or thickness. Using the measured imperfection, a numerical model will be developed to predict the bending and shear resistance of the specimens.

Imperfection Sensitivity of Plastic Shear Buckling Behavior in Corrugated Web Stainless Steel beams

AbstractThe shear behavior of corrugated web beams can be highly sensitive to the presence of initial imperfections. The designer has, in general, no prior information about the mechanical and geometric imperfections of welded elements. As a solution, in a FEM‐based design, the eigen buckling deformations with an equivalent maximum magnitude are included as an equivalent initial imperfection in a nonlinear analysis to account for the simultaneous effects of geometric imperfections and residual stresses. Previous researchers investigated the effects of initial imperfections in the form of different eigenmodes found via linear buckling analysis. They concluded that the shear strength rises with mode number, with the first mode providing the most crucial condition. However, it is shown in this paper that such a methodology is not applicable to stainless steel corrugated web beams in the medium slenderness ratio range when shear yielding precedes shear buckling. It is observed that, unlike in elastic buckling, in plastic buckling the first buckling mode does not result in the minimum strength. The results show that in FEM‐based design, using the first mode instead of the critical mode as the shape of the initial imperfection can result in a maximum of 19% and 31% overestimation of the ultimate shear capacity for the imperfection amplitudes of tw and hw/200, respectively.

Shear Buckling Behavior of Tapered Steel Plate Girders with Sinusoidally Corrugated Webs

AbstractSteel plate girders with I‐section are frequently used in industrial buildings and bridge design as prismatic members that means as members with parallel flanges and rectangular webs. The structural efficiency can significantly be achieved if such members are designed with tapered webs that means with non‐rectangular webs. Depending on the flange inclination and the moment diagram, the stress in the webs of tapered plate girders is significantly affected also as known as Résal effect. Furthermore, the structural efficiency of plate girders can be improved if the flat webs are replaced by corrugated webs. The gain in out‐of‐plane stiffness due to the corrugated webs reduces the buckling sensitivity of the web. As tapered plate girders with sinusoidally corrugated webs under shear forces have not been subject of research up to now, a numerical investigation on the shear force resistance of such girders has been made. The most important findings are presented. It can be stated that the shear force resistance of tapered girders with corrugated webs cannot accurately be predicted by the existing calculation models for prismatic members.

Buckling and Free Vibration Analyses of Various Nanoparticle Reinforced Concrete Beams Resting on Multi-Parameter Elastic Foundations.

Given their considerable specific surface area and amorphous characteristics, nanoparticles exhibit excellent pozzolanic activity, and when undergoing a reaction with calcium hydroxide, this leads to the generation of a denser matrix by promoting the formation of a greater amount of C-S-H gel, thereby enhancing the strength and durability of the concrete and fortifying the overall structure. Indeed, the present study investigates a comparative study of the buckling and free vibration analyses of concrete beams reinforced with various types of nanoparticles. For its simplicity and accuracy, a higher-order shear deformation theory will be used to analytically model the reinforced concrete beam. Furthermore, the powerful Eshelby's model is used to derive the equivalent nanocomposite properties. The soil medium is simulated with Pasternak elastic foundation, including a shear layer, and Winkler's spring, interlinked with a Kerr foundation. The motion equations are derived using Hamilton's principle. Moreover, based on Navier's analytical methods, the closed-form solutions of simply supported beams have been obtained. Different parameters, such as type and volume percent of nanoparticles, geometrical parameters, choice of theory and soil medium, on the buckling and dynamic behavior of the beam, are exercised and shown. The major findings of this work indicate that the use of nanoparticles in concretes increases better mechanical resistance and amplifies the natural frequencies. In addition, the elastic foundation has a significant impact on the buckling and vibration performances of concrete beams.

A Simple Energy Method to Predict the Thermal Post Buckling Behaviour of Columns

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Buckling Behavior of a Functionally Graded Sandwich Plate

This research focuses on the buckling behavior of a porous Functionally Graded (FG) sandwich plate using the sinusoidal shear deformation theory and hyperbolic tangent and secant thickness stretching functions with novel displacement fields. The proposed model assumes a different thickness layer system with FGM on the top and bottom and a ceramic core. Hamilton's energy principle is applied to the FGM sandwich plates to understand their buckling behavior. The mesh convergence on Finite Element (FE) model is carried out, and the accuracy of the results is tested using the existing research. The present model results match reasonably well with the previously published literature. The impact of the transverse shear deformation, plate aspect ratio, size-to-thickness ratio, and volume fraction is investigated for different thickness layer systems.