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

Mechanical metamaterials are valued for their diverse properties and potential applications. Due to the instability and large deformability of soft mechanical metamaterials (SMMs), geometric reorganization will occur and lead to some unusual properties. It is possible to change the properties of materials by varying the parameters. Conventional SMMs contain a periodic distribution of holes with the same size and shape, which can be changed to a lesser extent. Periodic dispersion of regular through-hole patterns of various sizes or shapes into elastomers, resulting in metamaterials with more mechanical functionality and deformation scenarios. In this paper, we investigated the influence of parameters on the buckling mechanical behavior of SMMs and the buckling mechanical behavior of structures with multiple sizes and geometric shapes. The parameters studied include geometric parameters (pore shape, porosity and area ratio) and physical parameters (Poisson's ratio and compression mode). Simulation of the buckling behavior of SMMs uses the finite element method. The finite element software ABAQUS is used, taking into account the almost incompressible characteristics of materials, the triangular quadratic plane strain hybrid element is selected (CPE6H). Numerical calculation gives the following results: Area ratio, pore shape and compression mode have obvious effects on buckling behavior, but Poisson's ratio has little effect; the influence of parameters on the buckling critical strains varied for SMMs with various pore shapes; very different buckling behaviors will result from swapping out the pattern of holes with the same size or shape for holes with two different sizes or shapes; the expression of buckling behavior is also varied when the mix of hole shapes is modified. These findings demonstrate that the design parameters may be used to achieve the desired buckling behaviors. This is a new method that can be used to control the deformation of structures; modify the properties of the SMMs without changing stiffness; simplify the structures without significantly changing the material properties. The design path of mechanical metamaterials is increased. [ABSTRACT FROM AUTHOR]

In the present paper, the effect of aspect ratio on the initial buckling response of an elastically supported rectangular FGM plate, the thin plate spline radial basis function (RBF) method can be used. This method involves the use of a thin plate spline to interpolate the displacement field of the plate, allowing for accurate analysis of the plate's behavior. The higher-order shear deformation theory (HSDT) is used for the analysis of the FGM rectangular plate resting on two parameters of elastic foundation. The displacement field consists of five unknown variables and approximately parabolic distribution of the transverse stress profile through the plate thickness and tangential stress-free boundary conditions on the plate surface. The governing differential equations (GDEs) of the plate are developed in the framework of Hamilton's principle. The thin plate spline radial basic function-based Meshfree method is used for discretizing the GDEs. To demonstrate the accuracy and efficacy of the present approach, the results obtained by the present approach are compared with the results given in the literature. The effect of various aspect ratios, grading index, span-to-thickness ratio, and two parameters of elastic foundations on the normalized buckling load is proposed. Some new results are also presented, which may be beneficial for future research works. The novelty of the present is the effects of aspect ratio on the elastically supported FGM plates. [ABSTRACT FROM AUTHOR]

Buried water pipelines are vulnerable to fail or break due to excessive loading or ground displacements. Accurate evaluation of pipe performance and serviceability relies on the proper understanding of pipe-soil interactions (PSI). Analytical methods are important approaches to studying PSI. However, a systematic and thorough literature review to analyze the existing research trends, technological achievements and future research opportunities is not available. This work investigates analytical methods that analyze the stress and deformation of pipes in terms of cross-sectional, transverse and longitudinal PSI problems. First, scientometric analysis is performed to acquire relevant research works from online databases and analyze the existing data of influential authors, productive research sources and frequent key word occurrence in the fields of interest. Second, a qualitative discussion is performed in the three categories of PSI: (1) cross-sectional, including ovalization and circumferential behaviours; (2) transverse, including seismic fault crossing, weak soil zones, ground settlement and pipe uplift; and (3) longitudinal. Third, six research opportunities are discussed, including the role of friction in cross-sectional deformation, combined effects of bending and compression, choice of soil reaction models and calibration of key parameters, effect of pipe flaws, soil spatial variability and behaviours of curved pipes. This study helps beginners familiarize themselves with PSI analytical methods and provides experienced researchers with ideas for future research directions. [ABSTRACT FROM AUTHOR]

The paper presents the results of research on fragments of thin-walled coverings made of aluminum alloy. The exmined structures were subjected to shear stresses leading to post-critical deformations. Three types of elements were analyzed: an element without stiffeners (the referencial one), an element with three stiffening ribs and an element with five stiffening ribs. The results of numerical analyzes and static experimental research were presented. Althought this kind of solutions is commonly used in various aircraft structures, the publications about it are usually hard to rich [8, 9, 15]. The research concerning ribbed stiffeners are usually performed inside laboratories of aerospace concerns and their results are not published in the open sources. The general direction of analyses of this solution is indicated in presented study. [ABSTRACT FROM AUTHOR]

The general theory of slender structure buckling by Grabovsky and Truskinovsky (Cont. Mech. Thermodyn. 19(3–4):211-243, 2007), (later extended in J. Nonlinear Sci. 26(1):83–119, 2016 by Grabovsky and the author), predicts that the critical buckling load of a thin shell under dead loading is closely related to the Korn's constant (in Korn's first inequality) of the shell under the Dirichlet boundary conditions resulting from the loading program. It is known that under zero Dirichlet boundary conditions on the thin part of the boundary of positive, negative, and zero (one principal curvature vanishing, and one apart from zero) Gaussian curvature shells, the optimal Korn constant in Korn's first inequality scales like the thickness to the power of −1, − 4 / 3 , and − 3 / 2 respectively. In this work we analyse the scaling of the optimal constant in Korn's first inequality for elliptic shells that contain a finite number of points where both principal curvatures vanish. We prove that the presence of at least one such point on the shell leads to the scaling drop from the thickness to the power of −1 to the thickness to the power of − 3 / 2 . To our best knowledge, this is the first result in the direction for constant-sign curvature shells, that do not contain a developable region. In addition, under the assumption that a suitable trivial branch exists, we prove that in fact the buckling deformation of such shells under dead loading, should be localized at the vanishing curvature points, as the shell thickness h goes to zero. [ABSTRACT FROM AUTHOR]

To investigate the mechanical deformation characteristics of the 'Segment-SCC-Steel Tube' combined bearing lining structure under internal and external pressure, the loading device and monitoring system for the stability analysis of the full-scale lining were proposed. The effect of cracked encased concrete and local external pressure on the instability mode of thin-walled steel pipes was explored by full-scale model experiment and three-dimensional FEM numerical simulation. The influence of SCC (Self-Compacting Concrete) and stiffening rings on the stability of steel pipes subjected to external pressure was discussed. The results show that SCC cracks occur and intensify with increasing internal pressure. The external water acts directly on the steel tube through cracking, resulting in wavy deformation, and the gap between the SCC and steel tube further increases. When calculating the critical external pressure for the steel pipe, the constraint of encased concrete can be ignored, and only the constraint effect of the stiffening ring can be considered. Therefore, the Von Mises formula was used to predict the critical external pressure between the stiffening rings with high accuracy. In addition, the stiffening ring can mitigate the crack propagation of nearby SCC. The steel tube remained in the elastic stage under internal pressure. In the full-scale experiment, the external pressure could not continue to rise after reaching 0.65 MPa. Nevertheless, the amplitude of the buckling wave continued to increase. It is considered that the steel pipe is in an unstable state, and the failure mode is dominated by single-lobe buckling. • According to the performance of the 'Segment-SCC-Steel Tube' lining structure, the influence of cracked encased concrete and local external pressure on the buckling mode of steel pipes is investigated. • The loading device of the full-scale model test is proposed for the external pressure stability analysis of the 'Segment-SCC-Steel Tube' lining structure, and the monitoring system combining distributed optical fiber and traditional vibrating wire sensors is established. • The mechanical deformation characteristics of the SCC and Steel Tube lining under internal and external pressure are revealed, and the influence of SCC and stiffening rings on the stability of steel pipes under external pressure is discussed. [ABSTRACT FROM AUTHOR]

The mechanical behavior of fibrous metamaterials is mainly determined by the interactions between the fibers composing the architecture. These interactions are usually of two different kinds: those directly depending on the positions of the fibers and those that need mediators, usually consisting of hinges, either inelastic or perfect, inducing restrictions on the kinematics of the fiber joints. In cases of interest, it has been observed that hinges can either have a certain torsional stiffness or behave as perfect joints, simply ensuring that the fibers remain interconnected, but not applying any constraint on the relative rotations between them. Here the effect of torsional stiffness of inelastic hinges is studied in two shear tests for a selected fibrous metamaterial. It is shown that the stiffness of hinges can be tailored to avoid, or at least reduce, out-of-plane deformations. Moreover, it is shown that, after reaching a threshold, permanent deformations are observed. This phenomenon is treated in a simplified way, by introducing damage in the continuum model. [ABSTRACT FROM AUTHOR]

The prebuckling deformation of structures is neglected in most of the conventional buckling theory (CBT) and numerical method (CNM), because it is usually very small in conventional concepts. In the preceding paper (Su et al., 2019), we found a class of structures from the emerging field of stretchable electronics, of which the prebuckling deformation became large and essential for determining the critical buckling load, and developed a systematic buckling theory for 3D beams considering the effects of finite prebuckling deformation (FPD). For bulk structures that appear vastly in the advanced structures, a few buckling theories consider the effects of the prebuckling deformation in constitutive equations by energy method, which are significantly important but not straightforward and universal enough. In this paper, a systematic and straightforward theory for the FPD buckling of bulk structures is developed with the use of two constitutive models. The variables for the prebuckling deformation serve as the coefficients of the incremental displacements, deformation components, and stress in the buckling analysis. Four methods, including the CBT, CNM, DLU (disturbing-loading-unloading method) method and FPD buckling theory, are applied to the classic problems, including buckling of an elastic semi-plane solid and buckling of an elastic rectangular solid, respectively. Compared with the accurate buckling load from the DLU method, the FPD buckling theory is able to give a good prediction, while the CBT and CNM may yield unacceptable results (with 70% error for the buckling of an elastic semi-plane solid). [ABSTRACT FROM AUTHOR]

Buckling tests were conducted using slender specimens of western hemlock. In the tests, the slenderness ratio was varied from 132 to 418 in which elastic buckling was induced, and the values of the critical load for buckling were obtained. When the deflection of the specimen was calculated from the loading-line displacement based on elastica theory, the value of deflection/load initially decreased because the compressive deformation was more dominant than the bending deformation. In contrast, when the load increased, the bending deformation became dominant, and the deflection/load-deflection relation exhibited linearity. These tendencies indicated that the transition from compression to bending was induced around the minimum value of the deflection/load. Therefore, it was recommended to determine the critical load for buckling using the load at the minimum value of the deflection/load where the deflection was calculated from the loading-line displacement. [ABSTRACT FROM AUTHOR]

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

This present study consists to analyze the mechanical buckling and the free vibration stabilities of antisymmetric cross-ply and angle-ply laminated composite plates using a refined high order shear deformation theory of four variables against five in other high order theories. Among the advantages of this new theory it takes into consideration the shearing effect in the calculation of deformation without the need for shear correction factors and giving rise to a variation of the shear stresses along the thickness and satisfying the zero shear stresses condition in faces of the plate. The laminate resting on the Pasternak elastic foundation, including a shear layer and Winkler spring, are considered. The equations of the motion are derived from Hamilton's principal. The closed form solution of simply supported rectangular plates has been obtained by using the Navier method. In addition, the effects of various parameters of the laminated composite plate on static buckling and dynamic are presented. [ABSTRACT FROM AUTHOR]

This work aims to reveal the in-plane-compressive characteristics of Glass Fibre based single face corrugated Structure Sheet (GFSS) by developing a loading holder of the both ends of the panel of GFSS in the direction of the cross machine direction. A grooved end-support device was developed and exmined. In order to set stably and quickly a straight panel of GFSS on the compressive-testing apparatus, the width and the depth of the holder's groove were varied against the geometrical size of the panel, and the stability and reproducibility of compressive deformation of the panel was experimentally investigated. When changing the height of the panel and reinforcing the both ends of the panel by dipping instant adhesives, the deformation behavior and the buckling strength was characterized in three modes: a short height crushing without lateral deflection, a small lateral deflection mode as the intermediate state, and a triangle-like folding as a long height crushing. [ABSTRACT FROM AUTHOR]

This paper presents a large deformation Kirchhoff–Love shell model hierarchically enhanced with through-the-thickness warping functions, arbitrarily chosen by the user. Two unknowns are introduced for each of them, representing its amplitudes in two directions tangent to the shell surface. NURBS are used to approximate reference surface displacement and warping amplitudes in the weak form. The transverse shear strains are linear functions of the warping parameters only and naturally free from locking. A patch-wise reduced integration avoids membrane locking and improves efficiency. Particular attention is paid to the modeling of composites made up of multiple stiff layers coupled with soft interlayers. The alternating layup with high stiffness ratios induces a significant sectional warping with transverse shear strains concentrated in the soft layers. Two warping models are investigated: (WI) all stiff layers maintain the same director orthogonal to the deformed surface with independent transverse shear deformations of the soft layers; (WZ) a single zigzag function linking these deformations. The numerical tests confirm the great accuracy of the hierarchic shell model in reproducing the solid solution with a small number of discrete parameters, provided that the correct warping model is chosen. WI is reliable for all alternating layups. WZ reduces the unknowns to five per surface point, regardless of the number of layers, and is accurate for uniform soft layers. • The Kirchhoff–Love composite shell is enhanced with warping. • The hierarchic approach is used for large deformations. • Transverse shear strains and zigzag effects are included. • An accurate and efficient isogeometric formulation is proposed. • Two warping models are studied for stiff/soft layups. [ABSTRACT FROM AUTHOR]

Questions regarding the development of folds and their interactions with the seismic faults within thrust systems remain unanswered. However, estimating fault slip and earthquake hazards using surface observations and kinematic models of folding requires an understanding of how the shortening is accommodated during the different phases of the earthquake cycle. Here, we construct 16‐years of interferometric synthetic aperture radar time series across the North Qaidam thrust system (NE Tibet), where three Mw 6.3 earthquakes occurred along basement faults underlying shortened folded sediments. The analysis reveals spatio‐temporal changes of post‐earthquake surface displacement rates and patterns, which continue more than 10 years after the seismic events. The decomposition of the Sentinel‐1 ascending and descending line of sight velocities into vertical and shortening post‐earthquake components indicates that long‐term transient uplift and shortening is in agreement with the deformation that might be expected from kinematic models of folding. Long‐term uplift coincides spatially with young anticlines observed in the geomorphology, with steep gradients in the forelimbs, gentle gradients in the back‐limbs, an absence of subsidence in the footwalls, and higher gradients along interpreted bedding planes. Long‐term shortening is also different from the surface displacements expected for typical time‐varying creep on a narrow dislocation interface and shows rates higher than the average convergence across the whole region. These findings provide evidence for anelastic fold buckling during the post‐earthquake phase and highlight the contribution of distributed aseismic deformation to the growth of topography. Key Points: Sixteen years of post‐seismic transient deformations measured with interferometric synthetic aperture radarSpatio‐temporal changes of post‐seismic rates and patterns have been observedAnelastic bulk deformation of the medium in response to fault slip [ABSTRACT FROM AUTHOR]

Locomotion of an organism interacting with an environment is the consequence of a symmetry-breaking action in space-time. Here we show a minimal instantiation of this principle using a thin circular sheet, actuated symmetrically by a pneumatic source, using pressure to change shape nonlinearly via a spontaneous buckling instability. This leads to a polarized, bilaterally symmetric cone that can walk on land and swim in water. In either mode of locomotion, the emergence of shape asymmetry in the sheet leads to an asymmetric interaction with the environment that generates movement--via anisotropic friction on land, and via directed inertial forces in water. Scaling laws for the speed of the sheet of the actuator as a function of its size, shape, and the frequency of actuation are consistent with our observations. The presence of easily controllable reversible modes of buckling deformation further allows for a change in the direction of locomotion in open arenas and the ability to squeeze through confined environments--both of which we demonstrate using simple experiments. Our simple approach of harnessing elastic instabilities in soft structures to drive locomotion enables the design of novel shape-changing robots and other bioinspired machines at multiple scales. [ABSTRACT FROM AUTHOR]

Tissue paper is a thin complex nonlinear fibrous material made from fiber layers thinner (≈100 μm) than a human hair. Though it appears as a slender two‐dimensional material to our eyes, its internal microstructure reveals an intricate architected fibrous network of only 1–5 wood fibers within its thickness. The fiber network is folded in one direction giving rise to a characteristic crepe structure. Using high‐speed imaging, the crepe structure is shown to emerge from a dynamic, coupled mechanical deformation processes of fracture and buckling, occurring on a length scale of few hundred micrometer. Bending and stretching of the folds at the macroscale of the paper and at the microscale of the individual fibers are shown to govern the material's tensile properties, including the strain to rupture and the elastic modulus. Insights from this study can guide the development of strong, soft fibrous materials for biomedical and consumer products. [ABSTRACT FROM AUTHOR]

In this paper, the stability of a conical shell panel in elastic-plastic domain is considered. The shell is made of an isotropic material (316L steel) with linear work hardening behavior. The shell is placed on simply supported end constraints and the acting loads are in the form of longitudinal compressive force and lateral pressure. The incremental Prandtl-Reuss plastic flow theory and von Mises yield criterion are used in the analysis. The problem is formulated based on classical shell theory and nonlinear geometrical straindisplacement relations are assumed. The stability equations are derived using the principle of the stationary potential energy. Using Ritz method the equations are solved and the numerical results obtained for different values of semi vertex and subtended angles. The obtained results show that there is a distinct semi vertex angle in which the shell has the best stability conditions. Also, there will be a limiting condition for the semi vertex angels beyond which the instability will not occur. [ABSTRACT FROM AUTHOR]

The present manuscript is devoted to two works related to the spontaneous formation of patterns in Nature: venation in leaves and evolution of embryos. Morphogenetic processes and growth-induced instability phenomena are modelled through analogue experiments. The organization of veins in leaves is similar to what is expected from growth in a tensorial stress field that governs the formation of fractures, while the change in the shape of embryos is related to the deformation of a shell-like membrane whose properties evolve with time. The approaches resulting from analogue experiments is a way to explore specific properties of the media at a macroscopic scale. Thus the manuscript aims to focus on the analogue experiments, their adaptability to reproduce specific patterns and the relation between both growth-induced instability and mechanical behaviour of the matter. [ABSTRACT FROM AUTHOR]

Microtubule is the most rigid component of eukaryotic cytoskeleton that plays pivotal roles in many important cellular events. Microtubules are known to undergo bending or buckling in cells which often results in breaking of this cytoskeletal protein filament. Various cellular events such as cell migration, chromosome segregation, etc. are dependent on the buckling induced breaking of microtubules. However, the reason behind the breaking of buckled microtubules in cell has remained obscure yet. In this work, we have demonstrated breaking of microtubules on a 2D elastic medium by applying compressive stress. The applied compressive stress caused buckling of the microtubules which ultimately resulted in their breaking. We show that breaking of the buckled microtubules cannot be accounted for by considering the changes in curvature of the microtubules due to mechanical deformation. Our results confirm that, it is the interaction of kinesin, a microtubule-associated motor protein, with microtubules which plays the key role in breaking of the buckled microtubules on the 2D elastic medium. The breaking of buckled microtubules is ascribed to decrease in rigidity of microtubules upon interaction with kinesins. This work for the first time confirms the involvement of a microtubule-associated motor protein in breaking of microtubules under compressive stress, which will help further clarify the mechanism of breaking of buckled microtubules in cells and its significance in the cellular events. Biomolecular motor kinesin mediates breaking microtubules (MT) under compressive stress by decreasing the rigidity of microtubules. Image 1 • Breaking of buckled microtubules is demonstrated in a simple vitro condition. • A reason behind the breaking of buckled microtubules is unveiled. • Kinesin, a microtubule-associated motor protein, is found to play a critical role in breaking of buckled microtubules. • Frequency of breaking of buckled microtubules depends on the extent of interaction of microtubules with kinesins. • Presence of microtubule severing proteins is not a requirement for causing breaking of buckled microtubules. [ABSTRACT FROM AUTHOR]

In this article, bending, buckling, and free vibration of viscoelastic sandwich plate with carbon nanotubes reinforced composite facesheets and an isotropic homogeneous core on viscoelastic foundation are presented using a new first order shear deformation theory. According to this theory, the number of unknown's parameters and governing equations are reduced and also the using of shear correction factor is not necessary because the transverse shear stresses are directly computed from the transverse shear forces by using equilibrium equations. The governing equations obtained using Hamilton's principle is solved for a rectangular viscoelastic sandwich plate. The effects of the main parameters on the vibration characteristics of the viscoelastic sandwich plates are also elucidated. The results show that the frequency significantly decreases with using foundation and increasing the viscoelastic structural damping coefficient as well as the damping coefficient of materials and foundation. [ABSTRACT FROM AUTHOR]

Butterfly dampers dissipate energy through the flexural, shear, or axial response of the strips when the device is subjected to inelastic cyclic deformation. The buckling response, elastic stiffness, and cyclic performance of non-uniform steel butterfly dampers have been studied in this paper. Validated material and geometric nonlinear finite element models in the ABAQUS has been used to perform a comprehensive parametric study on a wide range of geometrical parameters to evaluate the response of non-compact butterfly dampers. The results showed that although the low-cycle-fatigue response of butterfly dampers can be improved by altering the side edge shapes, the buckling capacity and elastic stiffness of non-uniform strips would decrease in comparison with uniform ones. Hence several analytical equations were provided to quantitative prediction of the buckling capacity and elastic stiffness of butterfly dampers. [ABSTRACT FROM AUTHOR]

Abstract The prebuckling deformation of structures is usually very small in conventional concepts, and is always neglected in the conventional buckling theory (CBT) and numerical method (CNM). In this paper, we find a class of structures from the emerging field of stretchable electronics, of which the prebuckling deformation becomes large and essential for determining the critical buckling load. Although great progress has been made for the buckling theory in the past hundred years, it is still challenging to analyze the buckling problems with finite prebuckling deformation (FPD buckling) straightforwardly. Here, the experimental stretch of a series of serpentine interconnects was firstly conducted as a representative example to show the FPD buckling behaviors and inapplicability of the CBT and CNM. The CNM can yield a huge error of 50% on the critical buckling load for the case with thickness-to-width ratio of the cross section h / b = 0.6. Most importantly, a systematic and straightforward theory (FPD buckling theory) is developed to analyze the FPD buckling behaviors of beams with the coupling of bending, twist and stretch/compression. As a comparison, various theoretical and numerical methods are applied to three classic problems, including lateral buckling of a three-point-bending beam, lateral buckling of a pure bending beam and Euler buckling. Our FPD buckling theory for beams is able to give a good prediction, while the CBT (by Timoshenko et al.) and CNM (by commercial program packages) yield unacceptable results (with 70% error for a three-point-bending beam with h / b = 0.8, for example). Discussion on the FPD buckling of bulk structures is deferred to a following paper. [ABSTRACT FROM AUTHOR]

Highlights • Incompressible functionally graded rectangular thick plates are studied. • Material properties vary through the thickness based on the power law function. • Higher order shear and normal deformable plate theory is developed. • Legendre polynomials are used in the expansion of displacement field components. • Bending, buckling and free vibration are investigated for simply supported plates. Abstract In the present study, higher order shear and normal deformable plate theory is developed for analysis of incompressible functionally graded rectangular thick plates. Also, The effect of incompressibility is studied on the static, dynamic and stability responses of thick plate. It is assumed that plate is incompressible and the incompressibility condition is considered in addition to the governing equations for determining the unknowns. Since the plate is thick, higher order shear and normal deformable theory is applied so that the Legendre polynomials are used for expansion of displacement field components in the thickness direction. Also, it is supposed that material properties vary through the thickness based on the power law function. Utilizing the variational approach, governing equations for static, stability and dynamic analysis of plate are derived. Resulted equations are solved analytically for simply supported plates. Finally, the effects of material properties and dimensions on the response of incompressible plates are investigated in details. [ABSTRACT FROM AUTHOR]

Buckling analysis of a functionally graded (FG) nanobeam resting on two-parameter elastic foundation is presented based on third-order shear deformation beam theory (TOSDBT). The in-plane displacement of TOSDBT has parabolic variation through the beam thickness. Also, TOSDBT accounts for shear deformation effect and verifies stress-free boundary conditions on upper and lower faces of FG nanobeam. The twoparameter elastic foundation model including linear Winkler's springs along with Pasternak's shear layer is in contact with the beam in deformation. Material properties of FG nanobeam are supposed to vary gradually along the thickness according to both power-law and Mori-Tanaka laws. Small-scale effect of Eringen's nonlocal elasticity theory has been considered. Nonlocal equilibrium equations are obtained based on the minimum potential energy principle and solved analytically. The accuracy of current method is examined by comparing current results with the available ones in literature. Effects of foundation parameters, gradient index, nonlocal parameter and slenderness ratio on buckling behavior of FG nanobeams are examined. [ABSTRACT FROM AUTHOR]

Inorganic stretchable electronics based on the island-bridge layout have attracted great attention in recent years due to their excellent electrical performance under the extreme condition of large deformations. During the mechanics design of interconnects in such devices, the major task is not only to maximize the elastic stretchability of device but also to smoothen the whole deformation process of interconnects. In this work, a novel design strategy is proposed for free-standing fractal serpentine interconnects to improve their elastic performance comprehensively without reducing the areal coverage of functional/active components of device. By modifying the classical design slightly, the new strategy can achieve a larger elastic stretchability, a smaller maximum out-of-plane displacement, and most strikingly, a smoother post-buckling deformation. This study will provide helpful guidance to the mechanics design of stretchable electronics with free-standing interconnects. [ABSTRACT FROM AUTHOR]

Abstract A finite strip method was developed for buckling and free vibration analysis of piezoelectric laminated composite plates based on various plate theories such as Zigzag, Refined plate and other higher order shear deformation theory by variation of transverse shear strains through plate thickness in the form of parabolic, sine and exponential. The plate edge conditions are considered to be simply supported and the polynomial shape functions are used to evaluate the in–plane and out–of–plane deflection and rotation of the normal cross section of plates in transverse direction. Numerical results were obtained based on various shear deformation plate theories to verify the proposed method. The effects of length to thickness ratio and fiber orientation of cross–ply and angle–ply laminate were presented. Also, the effect of different electrical conditions on the critical buckling load under in–plane forces and strains is investigated and electrical buckling load and natural frequency of piezoelectric laminate composite plates are calculated through numerical examples. In addition, the new results on the effect of piezoelectric layers thickness, placement of piezoelectric layers and also the effect of length to thickness ratio in the interaction of biaxial in–plane loading on critical buckling load were studied. Highlights • The buckling load of CC electrical conditions, unlike of OC, is close to elastic solutions. • The rate of decreasing in buckling load of OC is higher than CC with locating piezoelectric layers close to mid-surface. • In anti-sym angle-ply with locating the piezoelectric layers closer to the mid-surface the buckling load would increase. • The natural frequency would be increased or decreased with locating pzt in mid-surface for different thickness of plate. • The linear behavior is obtained for all electric boundary conditions and length to thickness ratio for biaxial loading. [ABSTRACT FROM AUTHOR]

Highlights • The differential system is solved with low computational cost. • The numerical results indicate a very good performance of the 6DE model proposed. • The 6DE model allows to obtain the equivalent properties for the beam-column model. • Practical expressions for the buckling loads exhibit an excellent agreement. Abstract Lattice towers and guyed masts are frequently used in the telecommunication industry, particularly to support antennas. These structural systems comprise a large number of elements (mainly, legs and diagonals) and for this reason, their representation by equivalent models is quite common and convenient. In a previous study, the authors derived a continuous model of a spatial lattice governed by nine differential equations (9DE). The legs trace forms a triangle and the diagonals with a zig-zag pattern are contained in three planes that join each two legs, defined as Pattern 1. Here and starting from an energy statement, the structural behavior of a 1D continuous model governed by six differential equations (6DE) which leads to a simpler representation of the lattice structure, is stated. This formulation considers the shear flexibility and the second order effect due to axial loads. Also, the inertial forces due to the legs and diagonals masses are taken into account. Numerical examples dealing with deflections, critical buckling loads and natural frequencies are solved with this 1D model. The results are compared with the outcomes found with finite element methods. A very good performance is attained with the proposed model. Finally, the equivalent properties for other patterns of diagonalization (Patterns 2, 3 and 4) different to the studied as well as the formulas to find the critical loads are included in Appendices. [ABSTRACT FROM AUTHOR]

This paper presents an experimental study of the compressive response of hexagonal honeycomb core from the initial elastic regime to a fully crushed state. To understand the crushing mechanism, aluminum honeycomb core was compressed quasi-statically between rigid platens under displacement control. Honeycomb test specimens made of aluminum alloy with different configurations such as cell size, cell number, core density, and specimen size have been tested. During the crushing, the cells buckle elastically and collapse at a higher stress due to inelastic action, after the cells crush by progressive formation of folds on cell walls. The response densifies when folds consume the whole panel height. The peak load recorded during tests corresponded to the buckling of honeycomb cells. The different specimens showed similar load/displacement curves, and the differences observed were only due to the influence of the core density, number of cells, and specimens size on mechanical behavior of hexagonal honeycomb core which has a very important role in the energy absorption capacity. In addition, this study allowed us to build a database of experimental tests for various configurations and allowed us to know the precise energy absorption capacity. [ABSTRACT FROM AUTHOR]

Highlights • In situ study on the buckling and post-buckling of Cu–Zr amorphous films. • A unique buckling and post-buckling behavior is observed. • A buckling map has been developed, including four buckling modes. • Formation of buckling modes are related to the size-dependent deformation. Abstract The buckling and post-buckling behavior of the Cu–Zr amorphous films is highly dependent on film thickness (h) and applied strain (ε). A buckling map has been developed with h and ε as axes, where four buckling modes are detected, including uncracked triangular buckle, cracked rectangular buckle, cracked triangular buckle, and patches. Formation of the four buckling modes will be discussed in terms of the film thickness and size-dependent deformation. [ABSTRACT FROM AUTHOR]

Abstract This paper is dedicated to study the elastic buckling behavior of isotropic, laminated composite and sandwich beams subjected to various axially varying in-plane loads and boundary conditions (BCs). The formulation of the problem is derived by using the Ritz method with the displacement field based on a shear and normal deformable beam theory (SNDBT). Polynomial functions are employed to present the displacement field. The convergence studies are performed and then obtained results are compared with those of reported works. Results from extensive analysis are presented for different BCs, aspect ratios, orthotropy ratios, fiber angles and loading conditions. It is observed that the type of the axially variable in-plane load significantly affects the critical buckling loads and mode shapes of the beams depending on the BCs. The normal deformation effect depends on not only the aspect ratio but also BCs and the fiber orientation angles. [ABSTRACT FROM AUTHOR]

Abstract The result of an experimental programme investigating a novel technique to strengthen web plates of steel plate girders against breathing fatigue due to shear buckling deformations is presented. An experimental test series is present in which six specimens were manufactured to simulate the end panel of a plate girder; these were strengthened with an optimized FRP retrofit panel that was developed in an earlier phase of the research project, and tested for plate girder web shear buckling deformation mitigation under repeated cyclic loading, as well as ultimate load capacity enhancement. Test results and non-linear finite element modelling demonstrated the efficiency of this technique for stiffening the web against these deformation and thus reducing the critical stresses, consequently increasing the fatigue life of the girders by a factor ranging between three and seven, depending on the applied stress range and the fatigue resistance assessment method. The research demonstrates the applicability of this novel FRP strengthening technique to prolong and extend the fatigue life of existing plate girder bridges. [ABSTRACT FROM AUTHOR]

Abstract A bio-inspired concept of non-uniform curved grid-stiffened composite structures with embedded stiffeners (embedded NCGCs) is proposed in the paper. Shallow curved stiffeners are embedded in the laminate skin to form an integrated structure to improve the skin–stiffener deformation compatibility. A method named streamline stiffener path optimization (SSPO) based on multiscale modeling is proposed for curved stiffener layout design of embedded NCGCs. Firstly, the homogenization-based global/local analysis is used to calculate structural responses on a global unstiffened model with the equivalent material properties obtained from local representative cell configurations (RCCs). Secondly, the discrete distribution of 2D curved stiffener paths is transformed into a continuous distribution of the streamline function values (SFVs) on a 3D level set surface. The stiffener path description using the streamline function is similar as the level set method with specific constraints. Projections of points with the same integral SFVs will form one stiffener path. Thirdly, optimal curved stiffener layout is achieved using shape design of local parallelogram representative cell configurations with analytical sensitivities calculated using the affine mapping from the square master domain to the parallelogram RCCs. Fourthly, stiffener spacing and angle constraints are added for manufacturing considerations and local buckling resistance, and optimization design is implemented to maximize the buckling load within a given weight. Finally, numerical examples of a square laminated panel under uniaxial and biaxial compressions validate the effectiveness of the proposed SSPO method and indicate the significant improvement of the buckling loads by steering the stiffener paths. Highlights • Bio-inspired shallow stiffeners embedded inside the laminate skin is proposed. • Curved stiffener layout optimization is solved based on multiscale modeling. • Curved stiffener paths are interpreted using the streamline functions. • Parallelogram representative cell configurations provide analytical sensitivities. [ABSTRACT FROM AUTHOR]

Abstract Empirical expressions for estimating the maximum induced strain on buried steel pipelines crossing strike-slip faults are proposed. These expressions have been obtained through parametric studies involving finite element analyses of 18 different case loads of buried pipelines. The pipe and its soil surrounding were modeled in Abaqus software with shell and solid elements, respectively. Pipelines with different values of diameter, thickness, yielding strain and ultimate stress were analyzed under different values of fault displacement and pipe-fault crossing angle. The obtained response databank was used to develop empirical relations providing the maximum pipe strain in terms of geometrical, material and faulting characteristics of the problem. These expressions describe both the tensile and compressive modes of deformation and can be used in practice for the estimation of the maximum induced strain during the seismic design and/or evaluation of pipelines. It was found that the pipe type, bending angle and fault offset have pronounced effects on the behavior of the fault-crossing pipeline. On the other hand, the response of the pipeline was shown to be insensitive to the crossing angle due to the large strain caused by the section deformation, which occurs at any crossing angle. Highlights • The pipe-fault crossing problem is studied. • Empirical expressions for the prediction of maximum induced stain in pipe body are proposed. • Pipe type, bending angle, and fault offset have crucial effect on the induced strain in pipe body. • Pipe-fault crossing angle is less influential on the induced strain in pipe body. [ABSTRACT FROM AUTHOR]

The non-linear hygrothermal and mechanical buckling responses of FG sandwich plates resting on two-parameter elastic foundations are presented in this study. Non-linear Fourier temperature distribution is considered as a special case. A hyperbolic displacement model is proposed in the present investigation. The present model involves four unknown variables, and the shear stresses on the bottom and top of the plate surfaces are equal to zero. The effective material properties of the FG sandwich face sheets are presumed to be varied in the direction of the thickness using a simple power law distribution, while the core is supposed to be purely ceramic. The stability equations are deduced by the principle of virtual work, containing the effect of foundations interaction and hygrothermal effects based on the present model. The hygrothermal effects are considered as non-linear, linear and uniform distribution through the plate thickness. Comparison examples are presented to verify the accuracy of the present model. The effects played by the temperature rise, moisture concentration, parameters of elastic foundation, side-to-thickness ratio, aspect ratio of the plate, the inhomogeneity parameter on the critical buckling of FG sandwich plates are investigated. [ABSTRACT FROM AUTHOR]

Purpose The purpose of this paper is to assess different five variables shear deformation plate theories for the buckling analysis of FGM plates.Design/methodology/approach Governing differential equations (GDEs) of the theories are derived by employing the Hamilton Principle. A polynomial radial basis function (RBF)-based Meshless method is used to discretize the GDEs, and a MATLAB code is developed to solve these discretize equations.Findings Numerical results are obtained for buckling loads. The results are compared with other available results for validation purpose. The effect of the span-to-thickness ratio and grading index is observed. It is observed that some theories underpredict the deflection for thick plates, while at the same time they seem to be in good agreement with other theories for thin plates.Originality/value This paper assesses the different theories with the same method to determine their applicability. [ABSTRACT FROM AUTHOR]

Buckling is one of the main challenges in thickening the sidewall of a deep drawn cup. To overcome this problem, a novel sheet-bulk forming method, upsetting with a controllable deformation zone, was developed in this study to prevent the buckling during sidewall thickening. In this method, the material from the protective cavity of the die is pushed into the forming cavity under a counter force to establish a stabilised deformation zone, which can eliminate the limitation of the initial slenderness ratio in conventional upsetting methods. The experimental and simulated results reveal that the occurrence of buckling can be successfully avoided through upsetting with a controllable deformation zone. The forming load tends to remain unchanged because of the existence of a stable deformation zone. Additionally, the forming quality can be improved, and a uniform distribution of hardness in the cross section can be obtained, thereby improving the performance-in-service. [ABSTRACT FROM AUTHOR]

Highlights • A coupled mechanochemical model is proposed for buckling simulation. • The buckling behavior is strongly dependent on SOC & electrochemical process. • Lithiation-soften of active material remarkably reduces the buckling stability of cell system. • Design insights into enhancing the buckling resistance of electrode are provided. Abstract This work has proposed a coupled mechanochemical model to investigate the buckling performance of electrode and thereby enhance the mechanical integrity of lithium-ion batteries. This method based upon finite deformation theory is capable to simulate the state of charge (SOC) and path dependent buckling phenomenon of the layered structure. It is revealed that the buckling behavior of an electrochemical loaded electrode depends not only on the material properties and the electrode geometry but also on the charging/discharging process, SOC as well as the operation current rate. Moreover, with regarding to the lithiation stiffening active material, the results show that increasing the current density in lithiation while decreasing it upon delithiation can increase the relatively critical buckling load, and contribute the electrode to withstand buckling failure. As for the lithiation softening one, it is disclosed that the bucking resistance would be impaired in lithiation and recovered upon full delithiation. In addition, to eliminate the adverse effect of lithiation soften on the electrode buckling resistance, design insights into the current collector have been provided. [ABSTRACT FROM AUTHOR]

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

In this paper, the effect of the homogenization models on buckling and tree vibration is presented for simply supported functionally graded plates (FGM) resting on elastic foundation. The majority of investigations developed in the last decade, explored the Voigt homogenization model to predict the effective proprieties of functionally graded materials at the macroscopic-scale for FGM mechanical behavior. For this reason, various models have been used to derive the effective proprieties of FGMs and simulate thereby their effects on the buckling and free vibration of FGM plates based on comparative studies that may differ in terms of several parameters. The refined plate theory, as used in this paper, is based on dividing the transverse displacement into both bending and shear components. This leads to a reduction in the number of unknowns and governing equations. Furthermore the present formulation utilizes a sinusoidal variation of displacement field across the thickness, and satisfies the stress-free boundary conditions on the upper and lower surfaces of the plate without requiring any shear correction factor. Equations of motion are derived from Hamilton's principle. Analytical solutions for the buckling and free vibration analysis are obtained for simply supported plates. The obtained results are compared with those predicted by other plate theories. This study shows the sensitivity of the obtained results to different homogenization models and that the results generated may vary considerably from one theory to another. Comprehensive visualization of results is provided. The analysis is relevant to aerospace, nuclear, civil and other structures. [ABSTRACT FROM AUTHOR]

Amorphous carbon probably is the most-known and widely used carbon allotrope. However, unlike crystalline carbon such as graphene or carbon nanotubes, amorphous carbon generally is brittle and unable to sustain large mechanical deformation due to the inherent lack of long-rang order. In this work, we demonstrate a significant delay of failure on an amorphous carbon hollow nanosphere due to the buckling and post-buckling deformation of the spherical shell. Both in situ experiments and finite element analyses are conducted to probe deformation mechanism of buckling and post-buckling, suggesting a strong dependence of the shell thickness on the buckling process. A unified deformation energy-based mechanics model is developed to extract the critical buckling and post-buckling force, and shows good agreement with in situ experiments and finite element analyses. Extension of the model to inhomogeneous hollow nanospheres is also discussed and confirmed with finite element analyses. [ABSTRACT FROM AUTHOR]

This work investigates the interplay between viscoelasticity and instabilities in soft particulate composites undergoing finite deformation. The composite is subjected to in-plane deformation at various constant strain rates, and experiences microstructural buckling upon exceeding the critical strain level. We characterize the dependence of the critical strain and wavelength on the applied strain rate through our numerical analysis. In the simulations, we employ the single and multiple-branch visco-hyperelastic models. We find that the critical strain and wavelength – characterized by the single-branch model – show a non-monotonic dependence on the strain rate, reaching a maximum at a specific strain rate. Remarkably, different buckling patterns (with different critical wavelengths) can be activated by changing strain rates. The space of admissible buckling modes widens in composites with higher instantaneous shear modulus. In the composites characterized by the multiple-branch model, the critical strain function exhibit multiple local maxima following a superposition of the single-branch responses. Typically, the branch with a larger relaxation time has a more significant effect on the critical strain. Moreover, the local maximum (of the critical strain function) is amplified by increasing the strain–energy factor of the corresponding branch term. Finally, we perform the experiments on the 3D-printed particulate soft composite characterized by a broad spectrum of relaxation times. The comparison of the experimental and simulation results demonstrates the ability of the numerical model to predict the critical buckling characteristics. [ABSTRACT FROM AUTHOR]

The buckling capacity of uniformly compressed flat plates has been investigated in this study. Material properties were characterized based on parameterization of the stress-strain curves using a simple and novel mathematical expression. Idealized stress-strain relationships were developed using the proposed material model and extensive parametric numerical analyses were conducted to investigate the effect of the material stress-strain properties on the buckling capacity of flat plates. For stress-strain curves with a yield plateau, the results of the parametric study showed a minimal influence of the material properties on the buckling capacity of the plates whereas a significant effect of the strain-hardening properties was observed in plates with round-house curves. Ultimately, the proposed stress-strain model was shown to be remarkably useful for capturing the relevant intricacies associated with material nonlinearity when predicting the buckling capacity and post-buckling behavior of uniformly-compressed flat plates. [ABSTRACT FROM AUTHOR]

The paper presents an analysis of critical buckling forces and critical lengths for drilling wells and weight on bit. Buckling leads to increased frictional forces and rotational moments as a result of the contact pressures of the drilling string with the walls of the well holes. [ABSTRACT FROM AUTHOR]

Studies on buckling of steel tubular truss arches are lacking in contrast to steel arches with solid web sections, although they have been widely applied in long-span structures. This paper deals with the in-plane elasto-plastic buckling and strength design of circular steel tubular truss arches with triangular sections by using finite element analyses (FEA). Firstly, the in-plane buckling failure modes are explored to reveal the buckling mechanics of truss arches. By introducing the normalized slenderness of the entire arch and the chord tube, as well as the interactive coefficient that accounts for the effect of chord tube buckling, the unified buckling curve for truss arches in uniform compression are obtained. Lastly, an interactive equation is proposed for in-plane buckling resistance of steel tubular truss arches under combined compressive and bending actions. It is found that, the buckling of diagonal web tubes greatly reduces the load-carrying capacity and deformation ability of truss arches hence should be prevented in design. The chord tube deformation always exists during the buckling failure of the truss arch and its effect on the buckling resistance is inevitable. The buckling curve b in the codes can used for truss arches in uniform compression, and the interactive equation can provide satisfactory lower bound predictions for truss arches under general loading. [ABSTRACT FROM AUTHOR]

This paper presents a two-variable first-order shear deformation theory considering in-plane rotation for bending, buckling and free vibration analyses of isotropic plates. In recent studies, a simple first-order shear deformation theory (S-FSDT) was developed and extended. It has only two variables by separating the deflection into bending and shear parts while the conventional first-order shear deformation theory (FSDT) has three variables. However, the S-FSDT provides incorrect predictions for the transverse shear forces on the insides and the twisting moments at the boundaries except simply supported plates since it does not consider in-plane rotation. The present theory also has two variables but considers in-plane rotation such that it is able to correctly predict the responses of plates with any boundary conditions. Analytical solutions are obtained for rectangular plates with two opposite edges that are simply supported, with the other edges having arbitrary boundary conditions. Numerical results of deflections, stress resultants, buckling loads and natural frequencies are presented with the FSDT, the S-FSDT and the present theory. Comparative studies demonstrate the effects of in-plane rotation and the accuracy of the present theory in predicting the bending, buckling and free vibration responses of isotropic plates. [ABSTRACT FROM AUTHOR]

To reveal the atomistic scale mechanism of buckling of single-walled carbon nanotubes (SWCNTs) under axial compression, we carried out molecular dynamics (MD) simulation and atomistic structural instability (ASI) analysis. The ASI analysis enables us to reveal the development of ‘latent’ instability modes until buckling of structure, which cannot be clarified with MD alone. Euler-type buckling was found in relatively thin and long nanotube models, while buckling triggered by change of cross-sectional shape (i.e., radial buckling) was found in thick and short models. With growing radius, a crossover between the Euler-type and radial buckling modes was clearly found in the ASI analysis. Even when the deformation behavior was apparently the same, the buckling can be triggered by different instability modes. We also analyzed the structural instability using the Flügge theory based on linear continuum mechanics (LCM) to compare the results with the ASI analysis. Initial eigenvalues and development of instability modes were different between the ASI and LCM results, leading to a significant deviation of buckling strain and instability crossover points. We investigated the effect of chirality of CNT which is difficult to explain by LCM. [ABSTRACT FROM AUTHOR]

Highlights • Axial buckling of taxol- and MAP-stabilized microtubules is investigated. • Both surface and nonlocal effects are taken into consideration. • SLS model is used to describe the viscoelastic surrounding cytoplasm. • A good agreement is found between the results and available experimental data. • Stabilizing microtubules with taxol reduces the critical buckling load. Abstract In this paper, an orthotropic elastic shell model is developed for the buckling analysis of protein microtubules subjected to an axial force in living cells. Surface effects are taken into consideration based on the Gurtin–Murdoch elasticity theory. To incorporate the small scale effects, the nonlocal elasticity theory is also used. The influences of the viscoelastic surrounding cytoplasm are taken into account employing standard linear solid model. The governing differential equations are derived using the first-order shear deformation theory and the principle of virtual work. A numerical solution is obtained for the governing equations by employing differential quadrature method. To verify the accuracy of the numerical results, the present results for the axial buckling of microtubules stabilized with microtubule-associated proteins and taxol are compared with those of experimental observations in the literature. It is found that the orthotropic shell model with both surface and nonlocal effects can describe the buckling behavior of microtubules accurately, while the nonlocal shell model without surface effects fails to predict the buckling loads. [ABSTRACT FROM AUTHOR]