Buckling Behavior Research Articles

Prediction of Thermal Postbuckling Behavior Of Uniform Shear Flexible Column Undergoing Large Lateral Deflections Through An Intuitive Formulation

This paper presents a simple intuitive formulation to predict the thermal postbuckling behavior of uniform shear flexible columns, subjected a uniform temperature rise from its stress free condition, undergoing large lateral deflections. The two ends of the columns are restrained to move axially, so that a mechanical equivalent of the constant compressive load is developed, due to the increase in temperature. The proposed formulation is based on the use of nonlinearities existing in both the axial displacement and lateral deflection, which differs from the von-Karman type nonlinearity due to the moderately large lateral deflections only. In this paper, a simple analytical formula is developed to predict the thermal post buckling behavior of columns, considering both the nonlinearities. The numerical results obtained from the developed intuitive formulas match very well, for the slender columns. Since, there are no results available in the literature, to compare the current results with the case of the shear flexible columns, the authors are of the opinion that the trends of these results, given in this paper, show that there is a reasonable probability that the present results are reliable.

Theoretical and Numerical Studies of Elastic Buckling and Load Resistance of a Shuttle-Shaped Double-Restrained Buckling-Restrained Brace

A new type of shuttle-shaped double-restrained buckling-restrained brace (SDR-BRB) is proposed, which adopts the form of a shuttle-shaped deformation section similar to its bending moment distribution as the external restraining system. The SDR-BRB has the advantages of superlong size, high load-carrying capacity, and lightweight components, and is suitable for use in large-span spatial structures and bridge structures with an exposed BRB. First, the calculation formula of the elastic buckling load of a pin-ended SDR-BRB is derived based on the equilibrium method, which is verified through the eigenvalue buckling analysis method, and the effects of the main geometric parameters on its elastic buckling behavior are evaluated. The effects of multiple key factors on the load-carrying capacity of the SDR-BRB are then studied by parametric analysis. The results show that the restraining ratio, initial imperfection, and gap have significant effects on the ultimate load-carrying capacity and overall stability of the SDR-BRB, while the effect of the diameter–thickness ratio is relatively small. On this basis, the fitting formula of the critical restraining ratio of the SDR-BRB considering the influences of initial imperfection and gap is proposed and verified by finite element analysis. The research lays a foundation for further research into the elastic–plastic hysteretic behavior and design method of an SDR-BRB.

An Investigation of Thermal Postbuckling of Uniform Columns on Variable Winkler Foundation by Using Rayleigh-Ritz and Heuristic Formulations

An investigation of the two different formulations, to predict the thermal buckling and postbuckling behavior of uniform hinged-hinged and clamped-clamped columns on the elastic variable Winkler foundations, is presented in this paper. The first one is the Rayleigh-Ritz and the second one is relatively simple heuristic formulation. Though the effect of the uniform Winkler foundation is thoroughly studied for the columns and other structural members, the variable Winkler foundation is not received much attention by the researchers. In the present investigation, two types of variable Winkler foundations, wherein the first and second terms of the foundations contain a constant and the variable parts, which varies with two types of sine functions, are considered. It is shown that the expressions obtained from the two formulations, for the ratios of the thermal postbuckling to the buckling load parameters are, not only the same but also validate the results, for the specified values of the central deflection and foundation stiffness parameters. A comprehensive set of numerical results are presented in this investigation, to obtain the thermal postbuckling behavior of uniform hinged-hinged and clamped-clamped columns on the variable Winkler foundations.

Exploring buckling and post-buckling behavior of incompressible hyperelastic beams through innovative experimental and computational approaches

The objective of this paper is to conduct a comprehensive investigation into the buckling and post-buckling behavior of hyperelastic beams through both computational and experimental means. Natural rubber is used in the construction of a beam with a square cross-section. To determine the mechanical properties of natural rubber, a uniaxial tensile test is performed in accordance with ASTM D412. In finite element modeling (FEM), the nonlinear behavior of rubber is modeled using hyperelastic theory and the Yeoh strain energy function. The Static-Riks method is also implemented using Abaqus for the analysis of nonlinear buckling. To validate the present investigation results with FEM, an experimental test of digital image correlation (DIC) is conducted. The critical buckling force obtained via numerical methods exhibits an error of nearly 5% when compared to the corresponding results obtained from experimental testing. In order to ascertain the impact of various design parameters on the buckling behavior of the system, a comprehensive parametric analysis has been conducted. The parameters studied include the cross-sectional thickness, length of the structure, eccentric loads, as well as the mechanical properties of the materials used in the system. Consistent with the FEM outcomes, the critical buckling force exhibited by the hyperelastic beam demonstrates a positive correlation with increasing levels of hardness, cross-sectional thickness, and eccentric loads. The buckling behavior of the system is adversely affected by increasing its length. To ultimately validate the precision and reliability of the model, a supervised neural network (NN) learning method is employed.

Metastructure with torsion-compression coupling behaviors: Additive-manufacturing, experimental and numerical investigations

A novel cylinder shell lattice structure with torsion-compression/tension coupling (TCC) effects composed of curved ligaments was designed, manufactured, and tested. The deformation mechanisms were investigated based on experiments and finite element simulation, and a systematic parametric investigation was conducted to study various factors influencing the torsional buckling behaviors and TCC effects. The TCC metastructures were fabricated with hybrid process including 3D printing and casting mould involving the application of polyurethane elastomer material. Compared with the design of compression-torsion coupling (CTC) structures, torsion was taken as the active loading mode in this article. The results show that different torsional behaviors can be obtained by altering microstructure parameters. And the main cause of TCC effects is stretching or bending of curved struts along the axial direction. This study is deemed to be helpful in the design of torsional metamaterials, which can be useful in flexible electronics, customized micromachine, and biomechanical devices.

Lateral torsional buckling analysis of corrugated steel web girders using homogenization approach

Corrugated web beams have become popular in recent years due to their high strength-to-weight ratio, ductility and high shear resistance without stiffeners. The developments in the automated production of corrugated steel plates have further amplified their use as structural elements in bridges and buildings. In this paper, we develop a strain energy-based homogenization scheme to convert corrugated sections into equivalent flat sheets with modified elastic properties. The thin-walled theory is implemented in a one-dimensional (1D) finite element (FE) framework along with a modified analytical expression to study the lateral torsional buckling of corrugated web girders. The homogenization-based FE modelling reduces the computational requirement of finer mesh sizes on the corrugation profile. The present thin-walled FE model is implemented to different corrugation profiles and lengths, and their responses are compared with methodologies available in the literature. The effects of the geometrical parameters and loading on the lateral torsional buckling behaviour are investigated and important observations are made for structural designs.

Buckling Analysis of Laminated Plates with Asymmetric Layup by Approximation Method.

This study investigated thin-walled plate elements with a central cut-out under axial compression. The plates were manufactured from epoxy/carbon laminate (CFRP) with an asymmetric layup. The study involved analyzing the buckling and post-buckling behavior of the plates using experimental and numerical methods. The experiments provided the post-buckling equilibrium paths (P-u), which were then used to determine the critical load using the straight-line intersection method. Along with the experiments, a numerical analysis was conducted using the Finite Element Method (FEM) and using the ABAQUS® software. A linear analysis of an eigenvalue problem was conducted, the results of which led to the determination of the critical loads for the developed numerical model. The second part of the calculations involved conducting a non-linear analysis of a plate with an initial geometric imperfection corresponding to structural buckling. The numerical results were validated by the experimental findings, which showed that the numerical model of the structure was correct.

A seven-parameter high-order finite element model for multi-stable analysis of variable stiffness laminated shells

Variable angle fiber composites provide large design space for multi-stable structures. However, they require reliable numerical models to accurately predict their mechanical behavior characterized by a complex material response and large deformation. To this end, we propose an accurate yet efficient model for stability analysis of variable angle fiber laminated shells. In this model, first a seven-parameter shell formulation with Equivalent Single Layer theory, which is suitable for three-dimensional constitutive laws, is utilized to accurately characterize the large deformation. The fiber orientation angle is described by a linear variation from the center to the end of the shell. Then, to improve the accuracy and to reduce the computational cost, the spectral/hp element with high-order polynomial basis functions is adopted for discretization. Finally, complex nonlinear equilibrium paths are effectively tracked by the Riks method. By comparison with ABAQUS solutions, the proposed model shows to be efficient and accurate for variable angle fiber laminates under various conditions, in which both the buckling, the snap-through and tristability behaviors are studied. Moreover, variable angle fiber shells provide more design possibilities than straight fiber shells. By opportunely varying the fibers angle of each lamina, it is possible to control the stable states as well as to obtain multiple stable configurations (bi- and tri-stability).

Impact of web perforation size and shapes on structural behavior: a finite element analysis

Purpose Various designs of corrugated webs include trapezoidal, sinusoidal, triangular and rectangular profiles. The increasing use of curved plates has prompted the creation of I-sections made of steel with a corrugated web design. This study aims to examine the effectiveness of an I-beam steel section that features a perforated-triangular web profile. Design/methodology/approach In the current study, finite element analysis was conducted on corrugated-perforated steel I-sections using ANSYS software. The study focused on inspecting the design of the perforations, including their shape (circle, square, hexagon, diamond and octagon), size of perforations (80 mm, 100 mm and 120 mm) and layout (the position of web perforation), as well as examining the geometric properties of the section in term of bending, lateral torsional buckling, torsion and shear behavior. Findings The study revealed that perforations with diamond, circle and hexagon shapes exhibit good performance, whereas the square shape performs poorly. Moreover, the steel section’s performance decreases with an increase in perforation size, regardless of loading conditions. In addition, the shape of the web perforations can also influence its stress distribution. For example, diamond-shaped perforations have been found to perform better than square-shaped perforations in terms of stress distribution and overall performance. This was because of their ability to distribute stress more evenly and provide greater support to the surrounding material. The diagonal alignment of the diamond shape aligns with principal stress directions, allowing for efficient load transfer and reduced stress concentrations. Additionally, diamond-shaped perforations offer a larger effective area, better shear transfer and improved strain redistribution, resulting in enhanced structural integrity and increased load-carrying capacity. Originality/value Hence, the presence of lateral-torsional buckling and torsional loading conditions significantly impacts the performance of corrugated-perforated steel I-sections.

Optimisation and testing of wire arc additively manufactured steel stub columns

Wire arc additive manufacturing (WAAM), a method of directed energy deposition (DED) for metal 3D printing, is capable of producing intricate parts at a relatively high rate and low cost. Despite the great potential of WAAM for applications in construction, knowledge of the performance of WAAM structural elements is still lacking, and the geometric freedom is yet to be fully harnessed. This study is therefore aimed at investigating the local buckling behaviour of carbon steel WAAM elements and exploring the opportunity for improved structural efficiency through optimisation. An optimisation study was initially conducted to derive optimal stiffener layouts for square hollow sections (SHS) under compression. A total of six plain SHS with a broad range of width-to-thickness ratios, along with two SHS strengthened with optimised stiffeners, were manufactured via WAAM and tested. The six benchmark WAAM SHS profiles were examined to allow direct comparisons with conventionally-produced SHS. 3D laser-scanning was carried out to capture the geometric features of the WAAM specimens, and digital image correlation (DIC) was adopted for the full-field measurement of their structural responses during testing. The WAAM SHS stub columns were shown to have comparable load-carrying capacities to conventionally-produced SHS in the stocky range, but exhibited inferior local buckling behaviour in the slender range. Comparisons with the Eurocode 3 (EC3) resistance predictions showed that the existing Class 3 slenderness limit and effective width method specified in EC3 for plated structures may be overly optimistic for WAAM steel elements owing to their typically larger geometric imperfections. Finally, the SHS strengthened with optimised stiffeners were shown to exhibit significantly improved structural efficiency over both the WAAM and conventionally-manufactured plain SHS, bringing disproportionate increases in load-carrying and deformation capacity relative to the increases in mass.

Molecular Dynamics study on buckling behavior of vertically aligned carbon nanotube (VACNT) bundles with characterized waviness

The buckling behavior of vertically aligned carbon nanotube (VACNT) bundles with a characterized waviness ratio was studied using the principle of sinusoidal waves. A MATLAB algorithm was used to generate bundles with a user-specified waviness ratio, and 12 VACNT models were used under a constant strain of 0.01/ps uniaxial compression with three variable parameters: waviness ratio, number of VACNTs within the bundle, and presence of van der Waals interactions; moreover, the findings suggest that these parameters significantly influenced the critical buckling stress (σcomp) and buckling behavior of the bundle. Increasing the waviness resulted in a significant reduction of approximately 59.96% between a bundle with no waviness and a bundle with a waviness ratio of 0.33. Including van der Waals interactions played a critical role in strengthening the overall VACNT bundle, whereas eliminating them changed the buckling pattern and behavior of the bundles, furthermore, increasing the number of VACNTs in a bundle increased the critical buckling stress of the overall bundle. This study provides insight into the structural behavior of VACNT bundles, which is expected to impact the design of any system in which the collective mechanical behavior of the VACNT bundles is critical. These findings can improve the study of composite materials in lithium-ion batteries for high-capacity CNT composite anodes.

Elastic Buckling of Oblate Hemi-Ellipsoidal Shells Subjected to Hydrostatic Pressure

This study investigates the elastic buckling behavior of oblate hemi-ellipsoidal shells (OHES) subjected to non-uniform external hydrostatic pressure. The virtual work-energy of OHES consists of virtual strain energy due to membrane, bending, in-plane stress resultants, and virtual work of hydrostatic pressure. For buckling analysis, the geometric stiffness matrix is obtained from the strain energy due to in-plane stress resultants. A finite element procedure via a C1 continuity axisymmetric element is applied to solve the critical hydrostatic pressure from the eigenvalue buckling problem. The buckling pressure of the hemi-ellipsoidal dome subjected to uniform external pressure is verified with the previous research and FEM commercial software. Present results also indicate that the maximum in-plane stress of the hemi-ellipsoidal shell shapes are near the apex point as the axisymmetric buckling shape. In the case of hydrostatic pressure, the critical hydrostatic pressure of OHES is determined and are in good agreement when compared with the experimental results in published research. Furthermore, the shape ratio influences the difference in critical load results between uniform pressure and hydrostatic pressure, especially when the shape ratio is higher than 0.5 and the [Formula: see text] ratio is less than or equal to 100. Seawater depth limitations in subsea engineering are also presented and found that the shell thickness and shape ratio are the major factors affecting critical seawater depth.

Numerical assessment of stainless steel starred rolled angle sections under compression

This paper shows a numerical investigation of short-to-intermediate austenitic and duplex stainless steel welded starred columns with fixed supports prone to failure by torsional buckling. A finite element model, developed by the same authors in prior work and validated against experimental results, was used (i) to assess the cross-section geometrical properties – secondary warping and torsion constants, (ii) austenitic and duplex stainless steel material mechanical properties, (iii) the elastic buckling behaviour, and (iv) the columns' ultimate resistance. A parametrical analysis was carried out through a broader coverage of cross-section dimensions and member lengths. Finally, the obtained ultimate strengths are used to evaluate if the Eurocode 3: Part 1.4 – column buckling curve “b” – can adequately predict the ultimate column strength. Comparisons between numerical failure load and predicted Eurocode buckling ultimate torsional load showed excessive conservatism. Given this, modifications were proposed in European code following the same methodology, i.e., changing the column buckling curve.

Local buckling and axial compressive behavior of stainless-clad bimetallic steel-plate composite walls

This study investigated the local buckling and axial compressive behavior of stainless-clad bimetallic steel-plate composite (SC) walls. Stainless-clad bimetallic steel is a high-performance steel that combines the merits of both the substrate and cladding materials, showing good mechanical properties. An experimental database was compiled to evaluate the effect of normalized faceplate slenderness ratio on the local buckling and axial compressive behavior of SC walls. Experimental investigations were conducted on six stainless-clad bimetallic steel-plate composite walls with parameter of normalized faceplate slenderness ratios. Finite element models were developed and benchmarked for parametric studies. Test results and finite element analysis results were incorporated into the database. The enhanced database were utilized to evaluate the application of the current design provisions in calculating the axial compressive strength. It was found that CECS:546–2018, Eurocode 4, and AISC 360–22 cannot provide reasonable estimation of axial compression strength. Finally, a simplified equation was suggested for estimating the axial compressive strength of SC walls. The design method was conservative for both non-slender and slender steel faceplates.

A unified modeling strategy of the stability and progressive damage behavior of CFRP double-blade composite stiffened structures (DCSS) under uniaxial compression

As a typical thin-walled structure, CFRP double-blade composite stiffened structure (DCSS) is widely used in the aerospace field and its stability and failure behavior demand a comprehensive understanding. In this work, a novel, unified modeling strategy is proposed for predicting the stability behavior and progressive damage processes of the DCSS under compression. A user-defined materials subroutine of the based-strain 3D-Hashin criterion and continuum damage mechanics model is developed using the FORTRAN language to simulate the intra-laminar damage initiation and propagation processes in the DCSS skin, stiffeners, and triangle zones. Moreover, the damage initiation and the extension of the inter-laminar in the skin and the skin–stiffener interface are revealed using the cohesive zone model. Furthermore, various experimental methods are employed to obtain the buckling, post-buckling and collapse behavior of the DCSS. The digital image correlation technique is used to describe the buckling and post-buckling displacement fields and the failure behavior of stiffened structures. Strain gauges are adopted to accurately acquire the buckling behavior of the DCSS. Finally, the buckling load, ultimate load, displacement data and failure modes of the stiffened structure obtained from the developed 3D finite element model are verified with the experimental results. The high correlation between the numerical and experimental results confirms the reliability of the proposed modeling strategy.

Linear buckling behavior of longitudinally singly- and multi-stiffened steel plates under normal and shear stresses

In this paper, the linear buckling behavior of longitudinally singly- and multi-stiffened plates with simply-supported edges under normal and shear stresses is investigated. A comprehensive parametric analysis using a finite element model validated against results collected from the literature is performed and the results are presented. About 65,000 eigenvalue analyses are executed, in which (a) several values of the plate’s aspect ratio, (b) different number, position and rigidity of stiffeners, and (c) different load configurations are considered. New practical insights about the ideal rigidity and position of the stiffeners are given, including the assessment of the optimum positions of longitudinally multi-stiffened plates under different normal stress ratios, which is not covered by the literature so far. Additionally, the gain of increasing the number of stiffeners is also discussed for different load combinations.

Thermal Buckling and Vibrational Analysis of Carbon Nanotube Reinforced Rectangular Composite Plates Based on Third-Order Shear Deformation Theory

In this paper, thermal buckling and free vibration of a rectangular plate reinforced with carbon nanotubes (CNT) are investigated within the framework of third-order shear deformation theory (TSDT). CNT distribution along the thickness direction of the plate is uniformly or functionally graded. The equivalent properties of the reinforced composite plate are calculated based on the extended rule of mixture. Governing equations of motion are derived using the Hamilton principle. Obtained governing differential equations are analyzed by utilizing Fourier series expansion along the longitudinal and latitudinal direction for simply supported edges boundary conditions whereas for other edges boundary conditions we used the differential quadrature method (DQM) to solve numerically. Validation of the present formulation is assessed by comparing the results with those reported in the open literature. The effect of CNT volume fraction, the different patterns of CNT distribution, temperature difference, aspect ratio, and thickness-to-length ratio on buckling and vibration behavior of carbon nanotube-reinforced composite (CNTRC) plate is studied. The numerical illustration reveals that in the FG-X pattern of CNT distribution natural frequency and thermal buckling load is more significant compared with the other patterns of CNT distribution.

Progressive failure and seismic fragility analysis for transmission towers considering buckling effect

Transmission towers are essential components supporting the operation of the power grid. Accurately predicting their ultimate bearing capacity and progressive failure improve the performance design of electrical power systems. This paper proposes a progressive failure method for transmission towers considering the buckling and post-buckling behaviors of steel angles. To simulate the nonlinear hysteretic behaviors of steel angles, a phenomenological hysteretic model (PHM) is introduced and embed into the ABAQUS software by calling a user-defined subroutine VUMAT. The accuracy and reliability of the PHM are verified through a full-scale test of a transmission tower. The comparison results demonstrate that the PHM can accurately reproduce the displacement and strain responses of the transmission tower and the ultimate bearing capacity, with a maximum error of <15%. The buckling failure of leg members is the main factor for the collapse of the transmission tower. The study also investigates the progressive failure process of the transmission tower under strong earthquakes and estimates the collapse fragility and seismic losses. The results reveal that early failures of steel angles may alter the local force transmission path of the tower and eventually lead to its collapse. This research provides suggestions for the structural optimization and design decision-making of transmission towers.

Nonlinear dynamic buckling behavior of axially loaded functionally graded graphene-enhanced composite laminated cylindrical shells in thermal conditions

Nonlinear dynamic buckling behavior of axially loaded functionally graded graphene-enhanced composite laminated cylindrical shells in thermal conditions

Static and dynamic instability of functionally graded graphene origami-enabled auxetic metamaterial beams with variable thickness in fluid

Functionally graded (FG) graphene origami (GOri)-enabled auxetic metamaterial (GOEAM) structures have shown great potential for various engineering applications due to their exceptional mechanical and physical properties such as high strength-to-weight ratio, tuneable stiffness and strength, and negative Poisson's ratio (NPR). This paper aims to investigate the buckling and dynamic instability behaviours of FG-GOEAM beams with variable thickness immersed in a fluid, with a particular focus on the influence of NPR. The material properties such as Young's modulus and Poisson's ratio of the GOEAM are determined by using a genetic programming (GP)-based micromechanics model. Within the framework of the first-order shear deformation theory and by employing Hamilton's principle and modelling the fluid effect as added mass, the governing equations of motion are established and are then discretised by means of differential quadrature (DQ) method to obtain a linear system of Mathieu-Hill equations from which the principal instability regions of the FG-GOEAM beam are determined by Bolotin's method. A comprehensive parametric study is conducted to reveal the effects of GOri's folding degree, distribution, weight fraction, as well as fluid density and beam dimensions on the static and dynamic instability behaviours of the FG-GOEAM beam immersed in fluid. Numerical results show that the FG-GOEAM beam with NPR considerably outperforms its pristine metallic counterpart in terms of resistance against static buckling and dynamic stability.