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Journal articles on the topic 'Buckling (Mechanics)'

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Author: Grafiati

Published: 4 June 2021

Last updated: 30 July 2024

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1

Khang, Dahl-Young, John A. Rogers, and Hong H. Lee. "Mechanical Buckling: Mechanics, Metrology, and Stretchable Electronics." Advanced Functional Materials 19, no. 10 (May 22, 2009): 1526–36. http://dx.doi.org/10.1002/adfm.200801065.

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2

Ansari, Reza, Mahdi Mirnezhad, Hessam Rouhi, and Majid Bazdid-Vahdati. "Prediction of torsional buckling behaviour of single-walled SiC nanotubes based on molecular mechanics." Engineering Computations 32, no. 6 (August 3, 2015): 1837–66. http://dx.doi.org/10.1108/ec-10-2014-0198.

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Purpose – Based on the molecular mechanics approach, the purpose of this paper is to analytically investigate the torsional buckling behavior of single-walled silicon carbide nanotubes (SiCNTs) with different values of diameter and chiral angles. Design/methodology/approach – To this end, the mechanical properties and atomic structure of a silicon carbide (SiC) sheet are evaluated based on the density functional theory (DFT) within the framework of the generalized gradient approximation. After that force constants of the total potential energy are theoretically obtained through establishing a linkage between the viewpoints of the quantum mechanics and molecular mechanics. Explicit expressions are presented to obtain the critical buckling shear strain corresponding to different types of chirality. The present model is capable to calculate the torsional buckling behavior of SiCNTs related to various chiral angles. The critical buckling shear strain is obtained for various types of chirality and compared with each other. Findings – It is concluded that for all diameters, zigzag nanotubes are more stable than armchair ones. Besides it is found that the minimum critical buckling shear strain is for nanotubes with (n, n/2) chiral vector. Originality/value – Investigating the torsional buckling behavior of single-walled SiCNTs with different values of diameter and chiral angle. Obtaining the mechanical properties and atomic structure of the SiC sheet based on the DFT calculations. Establishing a linkage between the molecular mechanics and quantum mechanics and obtaining the force constants of the molecular mechanics. Presenting the closed-form expression to calculate the critical buckling shear strain of single-walled SiCNTs corresponding to various types of chirality.

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3

Krieger, Kim. "Extreme mechanics: Buckling down." Nature 488, no. 7410 (August 2012): 146–47. http://dx.doi.org/10.1038/488146a.

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4

Farajpour, Ali, Hamed Farokhi, and Mergen H. Ghayesh. "Mechanics of Fluid-Conveying Microtubes: Coupled Buckling and Post-Buckling." Vibration 2, no. 1 (February 26, 2019): 102–15. http://dx.doi.org/10.3390/vibration2010007.

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This paper investigates the coupled mechanics of a fluid-conveying microtube embedded inside an elastic medium and subject to a pretension. The fluid-structure interaction model of the microsystem is developed based on Lagrange’s equations for the open system of a clamped-clamped microtube. A continuation model is used to examine the nonlinear mechanics of this microsystem prior to and beyond losing stability; the growth and the response in the supercritical regime is analysed. It is shown that the microtube stays stable prior to losing stability at the so-called critical flow velocity; beyond that point, the amplitude of the buckled microsystem grows with the velocity of the flowing fluid. The effects of different system parameters such as the linear and nonlinear stiffness coefficients of the elastic medium as well as the length-scale parameter and the slenderness ratio of the microtube on the critical speeds and the post-buckling behaviour are analysed.

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5

Pantano, A., M. C. Boyce, and D. M. Parks. "Mechanics of Axial Compression of Single and Multi-Wall Carbon Nanotubes." Journal of Engineering Materials and Technology 126, no. 3 (June 29, 2004): 279–84. http://dx.doi.org/10.1115/1.1752926.

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A recently developed procedure for modeling the deformation of single and multi-wall carbon nanotubes [13,14] is applied to nanotube buckling and post-buckling under axial compression. Critical features of the model, which is grounded in elastic shell theory, include identification of (a) an appropriate elastic modulus and thickness pair matching both the wall stretching and bending resistances of the single atomic layer nanotube walls, and (b) a sufficiently stiff interwall van der Waals potential to preserve interwall spacing in locally buckled MWNTs, as is experimentally observed. The first issue is illustrated by parametric buckling studies on a SWNT and comparisons to a corresponding MD simulation from the literature; results clearly indicating the inadequacy of arbitrarily assigning the shell thickness to be the equilibrium spacing of graphite planes. Details of the evolution of local buckling patterns in a nine-walled CNT are interpreted based on a complex interplay of local shell buckling and evolving interwall pressure distributions. The transition in local buckling wavelengths observed with increasing post-buckling deformation is driven by the lower energy of a longer-wavelength, multiwall deformation pattern, compared to the shorter initial wavelength set by local buckling in the outermost shell. This transition, however, is contingent on adopting a van der Waals interaction sufficiently stiff to preserve interlayer spacing in the post-buckled configuration.

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6

LU, QIANG, and RUI HUANG. "NONLINEAR MECHANICS OF SINGLE-ATOMIC-LAYER GRAPHENE SHEETS." International Journal of Applied Mechanics 01, no. 03 (September 2009): 443–67. http://dx.doi.org/10.1142/s1758825109000228.

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The unique lattice structure and properties of graphene have drawn tremendous interests recently. By combining continuum and atomistic approaches, this paper investigates the mechanical properties of single-atomic-layer graphene sheets. A theoretical framework of nonlinear continuum mechanics is developed for graphene under both in-plane and bending deformation. Atomistic simulations are carried out to deduce the effective mechanical properties. It is found that graphene becomes highly nonlinear and anisotropic under finite-strain uniaxial stretch, and coupling between stretch and shear occurs except for stretching in the zigzag and armchair directions. The theoretical strength (fracture strain and fracture stress) of perfect graphene lattice also varies with the chiral direction of uniaxial stretch. By rolling graphene sheets into cylindrical tubes of various radii, the bending modulus of graphene is obtained. Buckling of graphene ribbons under uniaxial compression is simulated and the critical strain for the onset of buckling is compared to a linear buckling analysis.

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7

Garlock, Maria E. Moreyra, Spencer E. Quiel, Peter Y. Yang, Jose Alos-Moya, and Jonathan D. Glassman. "Post-Buckling Mechanics of a Square Slender Steel Plate in Pure Shear." Engineering Journal 56, no. 1 (March 31, 2019): 27–46. http://dx.doi.org/10.62913/engj.v56i1.1142.

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Thin (slender) steel plates possess shear strength beyond the elastic buckling load, which is commonly referred to as the post-buckling capacity. Semi-empirical equations based on experimental tests of plate girders have been used for decades to predict the ultimate post-buckling strength of slender webs. However, several recent studies have shown that the current models for predicting the ultimate shear post-buckling capacity of thin plates are based on some incorrect assumptions regarding their mechanical behavior. As a result, the current design equations provide an approximate estimate of capacity for the range of parameters in the test data upon which they are founded. This paper explores the fundamental behavior of thin plates under pure shear. Such a fundamental examination of shear post-buckling behavior in thin plates is needed to enable design procedures that can optimize a plate’s shear strength and load-deformation performance for a wider range of loading and design parameters. Using finite element analyses, which are validated against available results of previous experimental tests, outputs such as plastic strains, von Mises stresses, principal stresses, and principal stress directions are examined on a buckled plate acting in pure shear. The internal bending, shear, and membrane stresses in the plate’s finite elements are also evaluated. In this study, these evaluations are performed for a simply supported plate with an aspect ratio equal to 1.0 and slenderness ratio equal to 134. Results show that localized bending in the plates due to the out-of-plane post-buckling deformations appear to be a significant factor in the ultimate shear post-buckling capacity of the plate. Also, the compressive stresses continue to increase beyond the onset of elastic buckling in some regions of the plate, contrary to current design assumptions. Overall, this study provides new insights into the mechanics of shear post-buckling behavior of thin plates that can be exploited for design procedures that are consistent with mechanical behavior.

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8

Liu, Cai Hua, Z. H. Ye, Cong Xin Chen, Xia Ting Feng, Q. Shen, and G. F. Xiao. "Mechanical Analysis of Buckling Failure of Bedding Rock Slopes." Key Engineering Materials 326-328 (December 2006): 1125–28. http://dx.doi.org/10.4028/www.scientific.net/kem.326-328.1125.

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As a typical model of steep-tilt or moderate-tilt bedding rock slopes, buckling failure differs greatly from tensile or shear failure. The mechanical characteristic of buckling failure is analyzed, and the geo-mechanics model of buckling failure is put forward. The process of buckling failure includes three phases: slope terrane creep deformation, the lower of slope terrane bend deformation, and terrane structure collapse. Using pressure bar failure theory, a formulation for calculating critical load of buckling failure is developed, which shows that critical load decreases with bend length increasing. The relationship between critical slope length and bend length is analyzed. It is indicated that critical slope length decreases with bend length increasing, and that critical slope length reaches minimal value while critical load is zero. The minimal slope length can be considered as a limit value while analyzing buckling failure of bedding slope, and its calculation equation is developed.

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9

Chang-jun, Cheng, and Lui Xiao-an. "Buckling and post-buckling of annular plates in shearing, Part I: Buckling." Computer Methods in Applied Mechanics and Engineering 92, no. 2 (November 1991): 157–72. http://dx.doi.org/10.1016/0045-7825(91)90237-z.

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10

Zhou, Li Jun, Jian Gao Guo, and Bao Long Li. "The Theoretical Investigation on Critical Buckling Stress of Graphene Nanosheets." Materials Science Forum 859 (May 2016): 79–84. http://dx.doi.org/10.4028/www.scientific.net/msf.859.79.

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The elastic buckling behaviors of graphene nanosheets are investigated via molecular structural mechanics based finite element method. The size-and chirality-dependent critical buckling stresses of monolayer and bilayer graphene nanosheets are calculated for different geometrical dimensions and boundary constraints, respectively. By analogy with classical buckling theory of elastic plate, the analytical expressions of critical buckling stress are derived for the graphene nanosheets with different boundary constraints, and the comparisons of analytical results with the counterparts obtained by molecular structural mechanics simulation show a good consistency.

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11

Antman, S. S., and C. L. Adler. "Design of Material Properties That Yield a Prescribed Global Buckling Response." Journal of Applied Mechanics 54, no. 2 (June 1, 1987): 263–68. http://dx.doi.org/10.1115/1.3173005.

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In the context of the large buckling of a nonlinearly elastic column under end thrust, this paper treats the design of (constitutive) functions appearing in bifurcation problems so as to produce a prescribed first bifurcating branch (e.g., a branch having a prescribed number of wiggles, which produce a prescribed pattern of hysteresis with snap bucklings in loading-unloading processes). The solution of this design problem also yields a method for determining a constitutive function from a single buckling experiment. A dual variational formulation is used to reduce the design problem to the solution of a linear Volterra integral equation of the first kind with a singular kernel. Effective numerical methods for the solution of such ill-posed equations are described and then applied to some physically interesting examples. Generalizations are discussed.

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12

Chang-jun, Cheng, and Lui Xiao-an. "Buckling and post-buckling of annular plates in shearing, part II: Post-buckling." Computer Methods in Applied Mechanics and Engineering 92, no. 2 (November 1991): 173–91. http://dx.doi.org/10.1016/0045-7825(91)90238-2.

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13

KAN, KEVIN H. M., and EMILY D. CRANSTON. "Mechanical testing of thin film nanocellulose composites using buckling mechanics." TAPPI Journal 12, no. 4 (May 1, 2013): 9–17. http://dx.doi.org/10.32964/tj12.4.9.

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The Young’s modulus of multilayer films containing cellulose nanocrystals (CNCs) and polyethyleneimine (PEI) was measured using a buckling-based method and compared to analogous films containing nanofibrillated cellulose (NFC) and PEI [1]. For films 61 nm to 1.7 μm thick, the Young’s modulus was constant but strongly dependent on relative humidity. Films were stiffer at lower relative humidities, with modulus values of 16 ± 5, 12 ± 1, and 3.5 ± 0.3 GPa at 30%, 42%, and 64% relative humidities, respectively. CNC/PEI films had larger elastic moduli than NFC/PEI films. Both types of nanocellulose multilayer films showed the same modulus dependence on relative humidity over the range studied. Results suggest that ambient water might have an even more pronounced role in nanocomposites than in traditional natural fiber-reinforced composites. This straightforward buckling-based method has quantified mechanical properties and provided a useful comparison between CNC and NFC films. Furthermore, it qualitatively assesses that the components in the composite film are highly compatible and that the hydrophilicity and hygroscopicity of cellulose and PEI combined do not allow for the full mechanical potential of crystalline cellulose nanoelements to be exploited. This work is one approach toward finding dependable methods to characterize nanocellulose, specifically cellulosic thin films, which is increasingly important as we extract nanocellulose from wood, plants, algae, bacteria, and animals and enter a new age of cellulose materials.

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14

Kang, Huairong, Pengfei He, Cunman Zhang, Ying Dai, Zhongde Shan, Yong Zang, and Hong Lv. "Tensile progressive damage and compressive postbuckling analysis of open-hole laminate composites." Journal of Reinforced Plastics and Composites 39, no. 17-18 (June 28, 2020): 637–53. http://dx.doi.org/10.1177/0731684420920355.

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Laminate composites contain holes as a means of connection in industrial applications. A better understanding of the mechanical properties of open-hole components is necessary. Herein, progressive damage postbuckling analysis models are proposed for investigation of tensile damage and compressive buckling behaviors of open-hole laminate composites. The progressive damage model is based on failure criteria provided by the continuum damage mechanics model; virtual crack closure technology was employed to calculate the energy release rate for crack delamination in compressive postbuckling analysis. The models were utilized to analyze variations in the tensile and compressive mechanical properties, failure process, and buckling evolution of open-hole laminate composites using finite element analysis. The tensile failure patterns and failure processes of plies with different open-hole laminate composite angles were obtained and analyzed. Buckling characteristics, as well as the progression of buckling onset, buckling propagation, crack delamination, unstable delamination, and global buckling, were investigated. The influence of delamination crack length and crack distribution on the buckling properties of open-hole laminate composites are discussed in detail. Additionally, unstable and stable buckling characteristics were examined. The numerical results were in good agreement with theoretical and experimental results; damage initiated at the edge of a hole propagated to two sides with the onset of matrix damage, followed by fiber damage. The fiber damage of a 0°-ply led ultimately to laminate failure. The laminate with a symmetrical crack distribution showed stable buckling, whereas a short, nonsymmetrical distribution of cracks usually led to unstable buckling and delamination.

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15

Becque, Jurgen. "Inelastic Plate Buckling." Journal of Engineering Mechanics 136, no. 9 (September 2010): 1123–30. http://dx.doi.org/10.1061/(asce)em.1943-7889.0000075.

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16

Geramifard, Negar, Behnoush Dousti, Christopher Nguyen, Justin Abbott, Stuart F. Cogan, and Victor D. Varner. "Insertion mechanics of amorphous SiC ultra-micro scale neural probes." Journal of Neural Engineering 19, no. 2 (April 1, 2022): 026033. http://dx.doi.org/10.1088/1741-2552/ac5bf4.

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Abstract Objective. Trauma induced by the insertion of microelectrodes into cortical neural tissue is a significant problem. Further, micromotion and mechanical mismatch between microelectrode probes and neural tissue is implicated in an adverse foreign body response (FBR). Hence, intracortical ultra-microelectrode probes have been proposed as alternatives that minimize this FBR. However, significant challenges in implanting these flexible probes remain. We investigated the insertion mechanics of amorphous silicon carbide (a-SiC) probes with a view to defining probe geometries that can be inserted into cortex without buckling. Approach. We determined the critical buckling force of a-SiC probes as a function of probe geometry and then characterized the buckling behavior of these probes by measuring force–displacement responses during insertion into agarose gel and rat cortex. Main results. Insertion forces for a range of probe geometries were determined and compared with critical buckling forces to establish geometries that should avoid buckling during implantation into brain. The studies show that slower insertion speeds reduce the maximum insertion force for single-shank probes but increase cortical dimpling during insertion of multi-shank probes. Significance. Our results provide a guide for selecting probe geometries and insertion speeds that allow unaided implantation of probes into rat cortex. The design approach is applicable to other animal models where insertion of intracortical probes to a depth of 2 mm is required.

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17

WANG, Q., V. K. VARADAN, Y. XIANG, Q. K. HAN, and B. C. WEN. "ON INSTABILITY OF SINGLE-WALLED CARBON NANOTUBES WITH A VACANCY DEFECT." International Journal of Structural Stability and Dynamics 08, no. 02 (June 2008): 357–66. http://dx.doi.org/10.1142/s0219455408002697.

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This technical note is concerned with the buckling of single-walled carbon nanotubes with one atomic vacancy. An elastic beam theory is developed to predict the buckling strain of defective CNTs, and the strain prediction via the continuum mechanics model is verified from comparison studies by molecular dynamics simulations. The results demonstrate the effectiveness of the continuum mechanics theory for longer CNTs. In addition, a local kink is revealed in the morphology of the buckling of shorter defective CNTs via molecular dynamics.

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18

Pugno, Nicola Maria. "Self-Buckling at the Nanoscale." Advances in Science and Technology 76 (October 2010): 147–52. http://dx.doi.org/10.4028/www.scientific.net/ast.76.147.

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In this paper the self-buckling of nanostructures, such as nanotubes, fullerenes and peapods, is analytically treated; this surprising phenomenon is due to the interaction among the nanostructures caused by the surface energy; it is peculiar of the nanoscale and has not a macroscopic counterpart. The influence of the surrounding nanostructures on one of them in a crystal is nearly identical to that of a liquid having surface tension equal to the surface energy of the solid. For the beneficial implications of the self-buckling on the overall mechanical strength see Pugno (2010; The design of self-collapsed super-strong nanotube bundles, Journal of the Mechanics and Physics of Solids, Available Online).

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19

Soong, T. C., and I. Choi. "Buckling of an Elastic Elliptical Ring Inside a Rigid Boundary." Journal of Applied Mechanics 52, no. 3 (September 1, 1985): 523–28. http://dx.doi.org/10.1115/1.3169094.

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The buckling of a thin, elastic ring confined in an elliptical hole whose circumference is smaller than that of the ring is studied. The effect of post-buckling slippage of the ring along the boundary with a corresponding curvature change is included. Buckling configurations with no friction that are (a) symmetric to one axis, and (b) symmetric to both axes, and (c) buckling configurations with no-slip are presented. Buckling with a strain energy consideration added as a criterion and buckling merely from compatibility alone are discussed. Results include curves for buckling loads of different ellipticities for different radius-to-thickness ratios.

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20

Yidris, Noorfaizal, J. Loughlan, Mohamed Thariq Hameed Sultan, and Azmin Shakrine Mohd Rafie. "Failure Mechanics of Uniformly Compressed Thin-Walled Box-Section Struts." Applied Mechanics and Materials 225 (November 2012): 172–77. http://dx.doi.org/10.4028/www.scientific.net/amm.225.172.

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It is well known that the structural performance of thin-walled compression members is subject to the effects of local buckling and material yielding. Due to these effects, the compressive carrying capability of short strut members can be significantly reduced. This paper employs finite element simulation to examine the post-buckled response of thin-walled box-sections that covers complete loading history of the compression struts from the onset of elastic local buckling through the nonlinear elastic and elasto-plastic post-buckling phases of behaviour up to final collapse and unloading. A detailed account of the growth and redistribution of stresses on the surfaces is given in the paper. The results from finite element simulations are shown to compare well with the analytical method of analysis.

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21

Rajan, A., R. Pramanik, A. Narayanan, and A. Arockiarajan. "Mechanics of viscoelastic buckling in slender hydrogels." Materials Research Express 6, no. 5 (February 22, 2019): 055320. http://dx.doi.org/10.1088/2053-1591/ab0691.

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22

Pandey, Mahesh D., and Archibald N. Sherbourne. "Mechanics of Shape Optimization in Plate Buckling." Journal of Engineering Mechanics 118, no. 6 (June 1992): 1249–66. http://dx.doi.org/10.1061/(asce)0733-9399(1992)118:6(1249).

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23

Chen, Dayong, Jinhwan Yoon, Dinesh Chandra, Alfred J. Crosby, and Ryan C. Hayward. "Stimuli-responsive buckling mechanics of polymer films." Journal of Polymer Science Part B: Polymer Physics 52, no. 22 (September 19, 2014): 1441–61. http://dx.doi.org/10.1002/polb.23590.

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24

Sui, Qianqian, Changliang Lai, and Hualin Fan. "Buckling analyses of double-shell octagonal lattice truss composite structures." Journal of Composite Materials 52, no. 9 (July 26, 2017): 1227–37. http://dx.doi.org/10.1177/0021998317723446.

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To reveal the compression failure modes of one-dimensional hierarchical double-shell octagonal lattice truss composite structures (DLTCSs), finite element modeling and equivalent continuum models were developed. DLTCS has three typical failure modes: (a) fracture of the strut, (b) global buckling, and (c) local buckling. Failure mode maps were constructed. It is found that column of long enough length will collapse at global buckling. When the column length decreases, the failure mode will turn to local buckling and strut fracture successively. Bay length greatly influences the buckling mode. Longer bay length could change the buckling mode from global buckling to local buckling. Compared with single-shell lattice truss composite structure, DLTCS has advantage in load carrying when the column fails at strut fracture or global buckling, while local buckling tolerance of DLTCS is smaller.

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25

Baozong, Huang, Yang Wencheng, and Shen Xiangfu. "Localized analysis of thin-walled structure's buckling/initial post-buckling and its accuracy." Acta Mechanica Sinica 7, no. 2 (May 1991): 162–68. http://dx.doi.org/10.1007/bf02486844.

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26

KORAYEM, A. H., W. H. DUAN, X. L. ZHAO, and C. M. WANG. "BUCKLING BEHAVIOR OF SHORT MULTI-WALLED CARBON NANOTUBES UNDER AXIAL COMPRESSION LOADS." International Journal of Structural Stability and Dynamics 12, no. 06 (December 2012): 1250045. http://dx.doi.org/10.1142/s0219455412500459.

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We investigate the buckling behaviors of short multi-walled carbon nanotubes (MWCNTs) under axial compression by using molecular mechanics (MM) simulations. The effects of the number of walls, length and chiral angle of MWCNTs on the buckling behaviors are examined. The results show that the buckling behaviors of short MWCNTs are rather different from single walled carbon nanotubes (SWCNTs) and slender MWCNTs. Moreover, it is observed that the buckling strains of short MWCNTs vary inversely proportional to the number of nanotube walls. For slender MWCNTs, the buckling strains fluctuate as the number of walls increase. It increases for beam-like buckling mode, decreases for shell-like buckling mode and is approximately constant for the shell-beam-like buckling mode. The increase in the length of MWCNT has also led to a significant decrease of the buckling strain for short MWCNTs. However, chirality does not have a significant effect on the buckling strain of MWCNTs nor alter the buckling mode of short MWCNTs.

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27

Genoese, Alessandra, Andrea Genoese, and Ginevra Salerno. "Buckling and post-buckling analysis of single wall carbon nanotubes using molecular mechanics." Applied Mathematical Modelling 83 (July 2020): 777–800. http://dx.doi.org/10.1016/j.apm.2020.03.012.

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28

Parvaneh, Vali, Mahmoud Shariati, Hamid Torabi, and Amir Masood Majd Sabeti. "Influence of Boundary Conditions and Defects on the Buckling Behavior of SWCNTs via a Structural Mechanics Approach." Journal of Nanomaterials 2011 (2011): 1–6. http://dx.doi.org/10.1155/2011/297902.

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The effects of boundary conditions and defects on the buckling behavior of SWCNTs are investigated using a structural mechanics model. Due to the application of carbon nanotubes in different fields such as NEMS, where they are subjected to different loading and boundary conditions, an investigation of buckling behavior of nanotubes with different boundary conditions is necessary. Critical buckling loads and the effects of vacancy and Stone-Wales defects were studied for zigzag and armchair nanotubes with various boundary conditions and aspect ratios (length/diameter). The comparison of our results with those of the buckling of shells with cutouts indicates that vacancy defects in carbon nanotubes can most likely be modeled as cutouts of the shells. Finally, a hybrid vacancy defect and Stone-Wales defect are also developed, and their effect on the critical buckling loads is studied.

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29

Ghasemi, Morteza, and Abdolrahman Jaamialahmadi. "Buckling analysis of orthotropic smart laminated nanoplates based on the nonlocal continuum mechanics using third-order shear and normal deformation theory." Journal of Thermoplastic Composite Materials 32, no. 5 (May 2, 2018): 593–618. http://dx.doi.org/10.1177/0892705718771114.

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In this article, the nonlocal buckling behavior of biaxially loaded graphene sheet with piezoelectric layers based on an orthotropic intelligent laminated nanoplate model is studied. The nonlocal elasticity theory is used in the buckling analysis to show the size scale effects on the critical buckling loads. The electric potential in piezoelectric layers satisfies Maxwell’s equation for either open- or closed-circuit boundary conditions. Based on the third-order shear and normal deformation theory, the nonlinear equilibrium equations are obtained. In order to obtain the linear nonlocal stability equations, the adjacent equilibrium criterion is used. The linear nonlocal governing stability equations are solved analytically, assuming simply supported boundary condition along all edges. To validate the results, the critical buckling loads are compared with those of molecular dynamics simulations. Finally, the effects of different parameters on the critical buckling loads are studied in detail. The results show that by increasing the nonlocal parameter, the critical buckling load decreases. The piezoelectric effect increases the critical buckling load for both open- and closed-circuit boundary conditions. For open-circuit boundary condition, the variation in the critical buckling load is due to the stiffness and piezoelectric effects, but for closed circuit, it is due to the stiffness effect only. Also, the critical buckling load for open circuit is bigger than that of closed one.

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30

Buehler, Markus J., Yong Kong, and Huajian Gao. "Deformation Mechanisms of Very Long Single-Wall Carbon Nanotubes Subject to Compressive Loading." Journal of Engineering Materials and Technology 126, no. 3 (June 29, 2004): 245–49. http://dx.doi.org/10.1115/1.1751181.

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We report atomistic studies of single-wall carbon nanotubes with very large aspect ratios subject to compressive loading. These long tubes display significantly different mechanical behavior than tubes with smaller aspect ratios. We distinguish three different classes of mechanical response to compressive loading. While the deformation mechanism is characterized by buckling of thin shells in nanotubes with small aspect ratios, it is replaced by a rod-like buckling mode above a critical aspect ratio, analogous to the Euler theory in continuum mechanics. For very large aspect ratios, a nanotube is found to behave like a flexible macromolecule which tends to fold due to vdW interactions between different parts of the carbon nanotube. This suggests a shell-rod-wire transition of the mechanical behavior of carbon nanotubes with increasing aspect ratios. While continuum mechanics concepts can be used to describe the first two types of deformation, statistical methods will be necessary to describe the dynamics of wire-like long tubes.

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31

Spencer, Herbert H., and Herli Surjanhata. "On Plate Buckling Coefficients." Journal of Engineering Mechanics 112, no. 3 (March 1986): 249–59. http://dx.doi.org/10.1061/(asce)0733-9399(1986)112:3(249).

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32

Chu, Liu, Jiajia Shi, and Shujun Ben. "Buckling Analysis of Vacancy-Defected Graphene Sheets by the Stochastic Finite Element Method." Materials 11, no. 9 (August 27, 2018): 1545. http://dx.doi.org/10.3390/ma11091545.

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Vacancy defects are unavoidable in graphene sheets, and the random distribution of vacancy defects has a significant influence on the mechanical properties of graphene. This leads to a crucial issue in the research on nanomaterials. Previous methods, including the molecular dynamics theory and the continuous medium mechanics, have limitations in solving this problem. In this study, the Monte Carlo-based finite element method, one of the stochastic finite element methods, is proposed and simulated to analyze the buckling behavior of vacancy-defected graphene. The critical buckling stress of vacancy-defected graphene sheets deviated within a certain range. The histogram and regression graphs of the probability density distribution are also presented. Strengthening effects on the mechanical properties by vacancy defects were detected. For high-order buckling modes, the regularity and geometrical symmetry in the displacement of graphene were damaged because of a large amount of randomly dispersed vacancy defects.

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33

Brojan, M., A. Puksic, and F. Kosel. "Buckling and post-buckling of a nonlinearly elastic column." ZAMM 87, no. 7 (July 25, 2007): 518–27. http://dx.doi.org/10.1002/zamm.200710333.

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34

Shih, W. Y., L. Kudryavtsev, and K. K. Wang. "Elastic Buckling of a Circular Disk due to Internal Membrane Forces." Journal of Applied Mechanics 62, no. 3 (September 1, 1995): 813–16. http://dx.doi.org/10.1115/1.2777115.

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Residual internal stresses often remain in materials after thermal-mechanical processes. Considerable deformation, such as elastic buckling, may result from such stresses. Some cases of circular-plate buckling due to internal membrane forces are analyzed in this work. The internal membrane-force field is introduced with a nonuniform radial temperature distribution in the disk. Detailed analysis is performed and critical buckling criteria are tabulated for some specific sets of parameters. Although the membrane force in the plate is axially symmetric, symmetry breaking is found at buckling. When the temperature is higher at the disk center, the first buckling mode is domeshaped, which maintains the polar symmetry. The mode of buckling, however, changes to a saddle shape when the radial temperature distribution is reversed.

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35

Fu, Lei, and A. M. Waas. "Initial Post-buckling Behavior of Thick Rings Under Uniform External Hydrostatic Pressure." Journal of Applied Mechanics 62, no. 2 (June 1, 1995): 338–45. http://dx.doi.org/10.1115/1.2895936.

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The initial post-buckling behavior of thick rings under external uniform hydrostatic pressure is investigated. In the analysis, no assumptions are placed upon the relative magnitudes of the elongations and rotations, and the ring is assumed to be elastic and extensional. The importance of including certain nonlinear terms in the initial post-buckling stability analysis and the effects of nonzero shearing strains on the buckling load and the initial post-buckling stability are examined. It is shown that the classical Kirchhoff assumptions, when employed for a ring lead to nonvanishing through thickness strains, εzz and εzθ, with the latter being proportional to the through thickness coordinate z. An approximate first order shear deformation analysis and a two-dimensional elasticity analysis (without beam-type kinematical assumptions) of the initial post-buckling behavior of thick rings are presented and the thickness effects on the buckling load and the initial post-buckling behavior are examined. The formulation for the composite ring was reduced to that of an isotropic ring and the results thus obtained were compared with published one-dimensional results in the literature. It is found from both the shear deformation and the two-dimensional analysis that the initial post-buckling behavior of the isotropic ring and the composite rings studied are stable. The influence of thickness on the degree of stability in the immediate post-buckling response is characterized.

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Qu, Yilin, Feng Jin, and Jiashi Yang. "Buckling of flexoelectric semiconductor beams." Acta Mechanica 232, no. 7 (April 27, 2021): 2623–33. http://dx.doi.org/10.1007/s00707-021-02960-3.

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37

Atanacković, T. M. "Buckling of rotating compressed rods." Acta Mechanica 60, no. 1-2 (June 1986): 49–66. http://dx.doi.org/10.1007/bf01302941.

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38

Mang, H. A., S. Pavlicek, and X. Jia. "The buckling sphere." Computer Methods in Applied Mechanics and Engineering 309 (September 2016): 325–63. http://dx.doi.org/10.1016/j.cma.2016.05.033.

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39

He, X. Q., and X. H. Huang. "On the use of cellular automata algorithm for the atomic-based simulation of carbon nanotubes." Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 465, no. 2101 (October 7, 2008): 193–206. http://dx.doi.org/10.1098/rspa.2008.0233.

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A new method is developed for the simulation of carbon nanotubes (CNTs) based on the molecular mechanics (MM) and cellular automata (CA) algorithms. The proposed atomic-based CA algorithm (ACAA) is as accurate as the MM method, but much faster for the simulation of CNTs. In the ACAA model, a CNT is treated as a discrete system in which the interaction between atoms is described by using Tersoff–Brenner's many-body potential, but the solution framework is based on the conventional continuum mechanics. The buckling and post-buckling behaviours of defective CNTs are studied by using the ACAA. The numerical results show that the buckling occurs at the vacancy defect site. This phenomenon indicates that vacancy defects lead to a geometrical imperfection of CNTs. The study demonstrates that vacancy defects can significantly reduce the buckling load of CNTs.

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Jam, Jafar Eskandari, and Esmail Asadi. "Buckling Analysis of Composite Cylindrical Shells Reinforced by Carbon Nanotubes." Archive of Mechanical Engineering 59, no. 4 (November 1, 2012): 413–34. http://dx.doi.org/10.2478/v10180-012-0022-1.

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In this paper, the authors investigate a cylindrical shell reinforced by carbon nanotubes. The critical buckling load is calculated using analytical method when it is subjected to compressive axial load. The Mori-Tanaka method is firstly utilized to estimate the effective elastic modulus of composites having aligned oriented straight CNTs. The eigenvalues of the problem are obtained by means of an analytical approach based on the optimized Rayleigh-Ritz method. There is presented a study on the effects of CNTs volume fraction, thickness and aspect ratio of the shell, CNTs orientation angle, and the type of supports on the buckling load of cylindrical shells. Furthermore the effect of CNTs agglomeration is investigated when CNTs are dispersed none uniformly in the polymer matrix. It is shown that when the CNTs are arranged in 90_ direction, the highest critical buckling load appears. Also, the results are plotted for different longitudinal and circumferential mode numbers. There is a specific value for aspect ratio of the cylinder that minimizes the buckling load. The results reveal that for very low CNTs volume fractions, the volume fraction of inclusions has no important effect on the critical buckling load.

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Deniz, Mehmet Emin, Ramazan Bardakci, and Fırat Aydın. "Buckling in rectangular hybrid composite plates with angled groove-shaped cut-outs." Materials Testing 65, no. 3 (March 1, 2023): 332–45. http://dx.doi.org/10.1515/mt-2022-0317.

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Abstract In this paper, eight-layer composite laminates were produced using twill and plain woven glass and carbon laminate fibers as a reinforcement element and as a matrix with epoxy resin. All laminates having the layup of [(0°/90°)2]s but the hybrid laminate arrangement varies between the number of woven glass and carbon laminates. The buckling behaviour of woven composite laminates used for typical of the aerospace industry is investigated. Un-grooved and grooved with centered elliptical groove angles with 0°, 15°, 30°, 45°, 60°, 75° and 90° specimens were subjected to buckling tests. It was investigated how the woven type, laminate designation, and groove angles affect the buckling behaviour. Cut-out causes to decrease of buckling load of composite plates. It is understood that the buckling load increased with regard to the increase groove angle (from 0° to 90°) of the composite plates. As the laminate designation changed, the buckling load also changed significantly. The buckling load of composite plates is highly influenced by its weave type. As a fiber, it has been determined that the buckling behaviour of carbon fiber is better than glass fiber. In addition, it was concluded that the twill weave type is generally better than the plain weave type.

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Arbocz, J., M. Potier-Ferry, J. Singer, V. Tvergaard, and I. Elishakoff. "Buckling and Postbuckling." Journal of Applied Mechanics 56, no. 3 (September 1, 1989): 732. http://dx.doi.org/10.1115/1.3176163.

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Shield, T. W., K. S. Kim, and R. T. Shield. "The Buckling of an Elastic Layer Bonded to an Elastic Substrate in Plane Strain." Journal of Applied Mechanics 61, no. 2 (June 1, 1994): 231–35. http://dx.doi.org/10.1115/1.2901434.

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The solution for buckling of a stiff elastic layer bonded to an elastic half-space under a transverse compressive plane strain is presented. The results are compared to an approximate solution that models the layer using beam theory. This comparison shows that the beam theory model is adequate until the buckling strain exceeds three percent, which occurs for modulus ratios less than 100. In these cases the beam theory predicts a larger buckling strain than the exact solution. In all cases the wavelength of the buckled shape is accurately predicted by the beam model. A buckling experiment is described and a discussion of buckling-induced delamination is given.

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Elgindi, Mohamed B., Dongming Wei, Yu Liu, and Hailan Xu. "Buckling and post-buckling of graphene tubes." Mechanics of Advanced Materials and Structures 23, no. 4 (November 10, 2015): 402–6. http://dx.doi.org/10.1080/15376494.2014.981620.

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45

Xiao, Yang, and Cheng Chang-jun. "Buckling and post-buckling of annular plates on an elastic foundation." Applied Mathematics and Mechanics 12, no. 8 (August 1991): 785–97. http://dx.doi.org/10.1007/bf02458169.

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46

Faghfouri, Saeideh, and Franz G. Rammerstorfer. "Mode transitions in buckling and post-buckling of stretched-twisted strips." International Journal of Non-Linear Mechanics 127 (December 2020): 103609. http://dx.doi.org/10.1016/j.ijnonlinmec.2020.103609.

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47

Hunt, Giles W., Antoinette Tordesillas, Steven C. Green, and Jingyu Shi. "Force-chain buckling in granular media: a structural mechanics perspective." Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences 368, no. 1910 (January 13, 2010): 249–62. http://dx.doi.org/10.1098/rsta.2009.0180.

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Parallels are drawn between the response of a discrete strut on a linear elastic foundation and force-chain buckling in a constrained granular medium. Both systems buckle initially into periodic shapes, with wavelengths that depend on relative resistances to lateral displacement, and curvature in the buckled shape. Under increasing end shortening, the classical structural model evolves to a localized form extending over a finite number of contributing links. By analogy, it is conjectured that the granular model of force-chain buckling might follow much the same evolutionary route into a shear band.

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Li, Renfu, and George A. Kardomateas. "Thermal Buckling of Multi-Walled Carbon Nanotubes by Nonlocal Elasticity." Journal of Applied Mechanics 74, no. 3 (March 15, 2006): 399–405. http://dx.doi.org/10.1115/1.2200656.

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The small internal length scales of nanomaterials/nano-devices may call the direct application of classical continuum models into question. In this research, a nonlocal elastic shell model, which takes the small scale effects into account, is developed to study the thermal buckling behavior of multi-walled carbon nanotubes. The multi-walled carbon nanotubes are considered as concentric thin shells coupled with the van der Waals forces between adjacent nanotubes. Closed form solutions are formulated for two types of thermal buckling of a double-walled carbon nanotube: Radial thermal buckling (as in a shell under external pressure) and axial thermal buckling. The effects of small scale effects are demonstrated, and a significant influence of internal characteristic parameters such as the length of the C‐C bond has been found on the thermal buckling critical temperature. The study interestingly shows that the axial buckling is not likely to happen, while the “radial” buckling may often take place when the carbon nano-tubes are subjected to thermal loading. Furthermore, a convenient method to determine the material constant, “e0” and the internal characteristic parameter, “a,” is suggested.

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Hu, Jianying, Yu Zhou, and Zishun Liu. "The Friction Effect on Buckling Behavior of Cellular Structures Under Axial Load." International Journal of Applied Mechanics 10, no. 02 (March 2018): 1850013. http://dx.doi.org/10.1142/s1758825118500138.

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When soft cellular structures are compressed axially beyond critical limits, elastic instabilities induce buckling behavior. Although the nonlinear response of periodic materials with different shape voids has been widely investigated, the effect of the friction on the structural response has not yet been explored. In this paper, we develop a simple theoretical model for the buckling of holey column with holes. Meanwhile, we also numerically and experimentally explore the effect of friction on the buckling behavior of the cellular structures. We find out that friction could prevent conventional, global Euler buckling for holey column, which tends to choose the pattern switching mode, and our study also provides future perspectives for mechanics of buckling or optimal design for the cellular structures.

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50

Ojalvo, Morris. "The Buckling of Thin-Walled Open-Profile Bars." Journal of Applied Mechanics 56, no. 3 (September 1, 1989): 633–38. http://dx.doi.org/10.1115/1.3176139.

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The theory of buckling for thin-walled open-profile bars is criticized. Its several derivations are faulted for violating statics, using a variational theorem approximately, using an incorrect variational statement, and/or using an inconsistent filament representation of the bar. Significantly, the theory yields buckling loads that contradict engineering expectations. A theory to replace it with general equations for computing buckling loads is presented. A problem solved under the old and new theories shows how torsional buckling is viewed under the new.

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