Hard-to-Soft Transition in Radial Buckling of Multi-Concentric Nanocylinders

We investigate the cross-sectional buckling of multi-concentric tubular nanomaterials, which are called multiwalled carbon nanotubes (MWNTs), using an analysis based on thin-shell theory. MWNTs under hydrostatic pressure experience radial buckling. As a result of this, different buckling modes are obtained depending on the inter-tube separation d as well as the number of constituent tubes N and the innermost tube diameter. All of the buckling modes are classified into two deformation phases. In the first phase, which corresponds to an elliptic deformation, the radial stiffness increases rapidly with increasing N. In contrast, the second phase yields wavy, corrugated structures along the circumference for which the radial stiffness declines with increasing N. The hard-to-soft phase transition in radial buckling is a direct consequence of the core-shell structure of MWNTs. Special attention is devoted to how the variation in d affects the critical tube number Nc, which separates the two deformation phases observed in N -walled nanotubes, i.e., the elliptic phase for N Nc. We demonstrate that a larger d tends to result in a smaller Nc, which is attributed to the primary role of the interatomic forces between concentric tubes in the hard-to-soft transition during the radial buckling of MWNTs.

Vibration and Buckling Approximation of an Axially Loaded Cylindrical Shell with a Three Lobed Cross Section Having Varying Thickness

On the basis of the thin-shell theory and on the use of the transfer matrix approach, this paper presents the vibrational response and buckling analysis of three-lobed cross-section cylindrical shells, with circumferentially varying thickness, subjected to uniform axial membrane loads. A Fourier approach is used to separate the variables, and the governing equations of the shell are formulated in terms of eight first-order differential equations in the circumferential coordinate, and by using the transfer matrix of the shell, these equations are written in a matrix differential equation. The transfer matrix is derived from the non-linear differential equations of the cylindrical shells with variable thickness by introducing the trigonometric series in the longitudinal direction and applying a numerical integration in the circumferential direction. The natural frequencies and critical loads beside the mode shapes are calculated numerically in terms of the transfer matrix elements for the symmetrical and antisymmetrical vibration modes. The influences of the thickness variation of cross- section and radius

Post-Buckling Behavior of Laminated Composite Cylindrical Shells Subjected to Axial, Bending and Torsion Loads

In present work, post-buckling behavior of imperfect (of eigen form) laminated composite cylindrical shells with different L/D and R/t ratios subjected to axial, bending and torsion loads has been investigated by using an equilibrium path approach in the finite element analysis. The Newton-Raphson approach as well as the arc-length approach is used to ensure the correctness of the equilibrium paths up to the limit point load. Post-buckling behavior of imperfect cylindrical shells with different L/D and R/t ratios of interest is obtained and the theoretical knock-down factors are reported for the considered cylindrical shells.

Buckling analysis of functionally graded plates partially resting on elastic foundation using the differential quadrature element method

We extend the differential quadrature element method (DQEM) to the buckling analysis of uniformly in-plane loaded functionally graded (FG) plates fully or partially resting on the Pasternak model of elastic support. Material properties of the FG plate are graded in the thickness direction and assumed to obey a power law distribution of the volume fraction of the constituents. To set up the global eigenvalue equation, the plate is divided into sub-domains or elements and the generalized differential quadrature procedure is applied to discretize the governing, boundary and compatibility equations. By assembling discrete equations at all nodal points, the weighting coefficient and force matrices are derived. To validate the accuracy of this method, the results are compared with those of the exact solution and the finite element method. At the end, the effects of different variables and local elastic support arrangements on the buckling load factor are investigated.

Submarine Pipeline Lateral Global Buckling and Buckling Failure Critical State Discussion

Due to high temperature and pressure,unburied or shallow buried submarine pipelines experience lateral global buckling. Excessive bending caused by uncontrolled deformation may threaten the safety of the pipeline system. Thus,the integer of a post-buckling pipeline section should be assessed under design temperature and pressure differences. This study focuses on the post-buckling pipeline safety assessment.First,a series of model tests based on sand obtained from Bohai Gulf were proposed,and soil resistance to pipelines with different embedment are measured. A dynamic soil resistance model with varying pipeline embedment and lateral displacement was established. The influence of embedment on peak soil resistance and residual soil resistance was analyzed. Second,the critical buckling forces of pipelines with different imperfections were analyzed. A"critical force range"was proposed to evaluate whether the pipeline exhibits lateral global buckling or not. Third,the limit state of a post-buckling pipeline in an engineering case was assessed. The assessment was proposed based on both load control condition and displacement control condition. Further comparisons show that pipelines reach their limit state according to load control condition far more quickly than according to displacement control condition.

A Semi-analytical Method for Vibrational and Buckling Analysis of Functionally Graded Nanobeams Considering the Physical Neutral Axis Position

In this paper,a semi-analytical method is presented for free vibration and buckling analysis of functionally graded(FG)size-dependent nanobeams based on the physical neutral axis position.It is the first time that a semi-analytical differential transform method(DTM)solution is developed for the FG nanobeams vibration and buckling analysis.Material properties of FG nanobeam are supposed to vary continuously along the thickness according to the power-law form.The physical neutral axis position for mentioned FG nanobeams is determined.The small scale effect is taken into consideration based on nonlocal elasticity theory of Eringen.The nonlocal equations of motion are derived through Hamilton’s principle and they are solved applying DTM.It is demonstrated that the DTM has high precision and computational efficiency in the vibration analysis of FG nanobeams.The good agreement between the results of this article and those available in literature validated the presented approach.The detailed mathematical derivations are presented and numerical investigations are performed while the emphasis is placed on investigating the effect of the several parameters such as neutral axis position,small scale effects,the material distribution profile,mode number,thickness ratio and boundary conditions on the normalized natural frequencies and dimensionless buckling load of the FG nanobeams in detail.It is explicitly shown that the vibration and buckling behaviour of a FG nanobeams is significantly influenced by these effects.

Buckling of filamentous actin bundles in filopodial protrusion

The mechanical behaviors of filamentous actin (F-actin) bundles play an essential role in filopodial protrusions at the leading edge of crawling cells. These bundles consist of parallel actin filaments that are hexagonally packed and interconnected via cross-linking proteins including α-actinin, filamin, and fascin. As pushing against the plasma membrane and/or external barriers, the actin bundles in filopodial protrusion inevitably encounter a compressive load. The bending stiffness and buckling stability of actin bundles are therefore important in determining the filopodia architecture and subsequent cell morphology. In this work, we employ a coarse-grained molecular dynamics model to investigate the buckling behaviors of cross-linked actin bundles under compression, which explicitly accounts for the properties of constituent filaments and the mechanical descriptions of cross-linkers. The bending stiffness of actin bundles exhibits a generic size effect depending on the number of filaments in the bundles, explicitly depending on the degree of inter-filament coupling. The distinct buckling modes are analyzed for bundles with different coupling states and strengths of cross-linkers. This study could clarify the stability and buckling mechanisms of parallelly packed actin bundles and the structure-function relations of mechanical components in filopodial protrusion.

Buckling Analysis of Tapered Continuous Columns by Using Modified Buckling Mode Shapes

Elastic critical buckling load of a column depends on various parameters,such as boundary conditions,material,and crosssection geometry.The main purpose of this work is to present a new method for investigating the buckling load of tapered columns subjected to axial force.The proposed method is based on modified buckling mode shape of tapered structure and perturbation theory.The mode shape of the damaged structure can be expressed as a linear combination of mode shapes of the intact structure.Variations in length in piecewise form can be positive or negative.The method can be used for single-span and continuous columns.Comparison of results with those of finite element and Timoshenko methods shows the high accuracy and efficiency of the proposed method for detecting buckling load.

On the Buckling of Euler Graphene Beams Subject to Axial Compressive Load

In this paper, we consider the buckling of an Euler-Bernoulli graphene beam due to an axial compressive load. We formulate the problem as a non-linear (eigenvalue) two-point boundary value problem, prove some properties of the eigenpairs and introduce a suitable numerical shooting method scheme for approximating them. We present the perturbation and the numerical approximations of the first and second buckling loads and the corresponding shapes.

Chebyshev polynomial-based Ritz method for thermal buckling and free vibration behaviors of metal foam beams

This study presents the Chebyshev polynomials-based Ritz method to examine the thermal buckling and free vibration characteristics of metal foam beams.The analyses include three models for porosity distribution and two scenarios for thermal distribution.The material properties are assessed under two conditions,i.e.,temperature dependence and temperature independence.The theoretical framework for the beams is based on the higher-order shear deformation theory,which incorporates shear deformations with higher-order polynomials.The governing equations are established from the Lagrange equations,and the beam displacement fields are approximated by the Chebyshev polynomials.Numerical simulations are performed to evaluate the effects of thermal load,slenderness,boundary condition(BC),and porosity distribution on the buckling and vibration behaviors of metal foam beams.The findings highlight the significant influence of temperature-dependent(TD)material properties on metal foam beams'buckling and vibration responses.

Buckling of Cassini Oval Pressure Hulls Subjected to External Pressure

The paper focuses on Cassini oval pressure hulls under uniform external pressure. The Cassini oval pressure hull is proposed based on the shape index of Cassini oval. The buckling of a series of Cassini oval pressure hulls with the shape index of 0.09–0.30 and one spherical pressure hull with the diameter of 2 m is devoted. Such hulls are numerically studied in the case of constant volume, material properties, and wall thickness. The results show that Cassini oval pressure hulls with the shape index of 0.10–0.11 can resist about 4% more external pressure than the spherical one. This deviates from the classical mechanics conclusion that spherical shell is the optimal shape for underwater pressure resistant structures.

Free vibration and buckling analysis of polymeric composite beams reinforced by functionally graded bamboo fbers

Natural fibers have been extensively researched as reinforcement materials in polymers on account of their environmental and economic advantages in comparison with synthetic fibers in the recent years.Bamboo fibers are renowned for their good mechanical properties,abundance,and short cycle growth.As beams are one of the fundamental structural components and are susceptible to mechanical loads in engineering applications,this paper performs a study on the free vibration and buckling responses of bamboo fiber reinforced composite(BFRC)beams on the elastic foundation.Three different functionally graded(FG)layouts and a uniform one are the considered distributions for unidirectional long bamboo fibers across the thickness.The elastic properties of the composite are determined with the law of mixture.Employing Hamilton’s principle,the governing equations of motion are obtained.The generalized differential quadrature method(GDQM)is then applied to the equations to obtain the results.The achieved outcomes exhibit that the natural frequency and buckling load values vary as the fiber volume fractions and distributions,elastic foundation stiffness values,and boundary conditions(BCs)and slenderness ratio of the beam change.Furthermore,a comparative study is conducted between the derived analysis outcomes for BFRC and homogenous polymer beams to examine the effectiveness of bamboo fibers as reinforcement materials,demonstrating the significant enhancements in both vibration and buckling responses,with the exception of natural frequencies for cantilever beams on the Pasternak foundation with the FG-◇fiber distribution.Eventually,the obtained analysis results of BFRC beams are also compared with those for carbon nanotube reinforced composite(CNTRC)beams found in the literature,indicating that the buckling loads and natural frequencies of BFRC beams are lower than those of CNTRC beams.

Dynamic Buckling of Column Impacted by a Rigid Body

The dynamic buckling of an elastic column subjected to axial impact by a rigid body is discussed in accordance with the energy law in this paper. The equation of lateral disturbance used to analysis the problem is developed by taking into account the effect of stress wave. The power series solution of this problem has been obtained by using the power series approach. The buckling criterion of this problem is proposed by analyzing the characteristics of the solution. The relationships between critical velocity and impacting mass as well as critical velocity and critical length are given by using theoretical analysis and numerical computation.

Twist deformation and buckling behavior of veins

Introduction Twisted arteries and veins disrupt normal blood flow and elevate the risk for clinical complications such as thrombosis,heart attack,stroke,and organ dysfunction.Veins should remain mechanically stable for normal function.However,compared to arteries,veins are more vulnerable to collapse because they are thin-walled and under lower lumen pressure.Twisted veins have been shown to occur with head turning or after inadvertent twist during various vascular surgeries.In vivo and cadaver studies have demonstrated that turning the head to one side can result in torsion and compression of the internal jugular vein and can compromise cranial drain-

An Efficient Method for Local Buckling Analysis of Stiffened Panels

The local buckling of stiffened panels is one of possible failure modes and concerned by engineers in the preliminary design of lightweight structures. In practice,a simplified model,i.e.,a rectangular plate with elastically restrained along its unloaded edges,is established and the Ritz method is usually employed for solutions. To use the Ritz method,however,the loaded edges of the plate are usually assumed to be simply supported. An empirical correction factor has to be used to account for clamped loaded edges. Here,a simple and efficient method,called the quadrature element method(QEM),is presented for obtaining accurate buckling behavior of rectangular plates with any combinations of boundary conditions, including the elastically restrained conditions. Different from the conventional high order finite element method(FEM),non-uniformly distributed nodes are used,and thus the method can achieve an exponential rate of convergence. Formulations are worked out in detail. A computer program is developed. Improvement of solution accuracy can be easily achieved by changing the number of element nodes in the computer program. Several numerical examples are given. Results are compared with either existing solutions or finite element data for verifications. It is shown that high solution accuracy is achieved. In addition,the proposed method and developed computer program can allow quick analysis of local buckling of stiffened panels and thus is suitable for optimization routines in the preliminary design stage.

Modelling the flexural buckling failure of stratified rock slopes based on the multilayer beam model

The buckling failure of stratified rock slopes intersected by a set of steep discontinuities that are approximately parallel to the slope surface is frequently encountered while constructing railways and roadways in mountainous areas. In this study, an analytical approach based on the energy equilibrium principle is presented to solve the flexural buckling stability of stratified rock slopes within the framework of multilayer beam theory. The generalized HoekBrown failure criterion is introduced to reflect the influences of slope size(scale effects) on the buckling stability. Subsequently, numerical and physical modellings from previous literatures are employed to validate the proposed approach. Furthermore, a practical case of Bawang Mountain landslide is also used for the comparative analysis. The study shows that the present analytical approach is capable to provide a more reasonable assessment for the buckling failure of stratified rock slopes, compared with several existing analytical approaches. Finally, a detailed parametric study is implemented, and the results indicate that the effects of rock strength, rock deformation modulus, geological strength index, layer thickness and disturbance degree of rock mass on the buckling failure of stratified rock slopes are more significant than that of rock type and slope angle.

Scleral buckling combined with internal cyclopexy for severe traumatic cyclodialysis cleft in open globe injuries

This study aimed to evaluate the effect of scleral buckling combined with internal cyclopexy on the treatment of severe traumatic cyclodialysis cleft in open globe injuries(OGIS). This retrospective study recruited 10 patients of 10 eyes. With our surgical intervention, all the 10 eyes achieved retinal and ciliary body anatomic re-attachment. The choroidal ruptures in nine eyes were closed with complete choroidal reattachment. Postoperative best-corrected visual acuity of nine eyes had various improvements. The mean intraocular pressure was increased from 8.9±2.6 mm Hg to 13.4±4.4 mm Hg. Eventually, six eyes underwent silicone oil(SO) removal without complications, two eyes still had SO tamponade and two eyes became SO-dependent eyes. The result shows that internal direct cyclopexy combined with scleral buckling is an effective treatment for severe traumatic cyclodialysis cleft in OGIS.

Thermal buckling analysis of ceramic-metal functionally graded plates

Thermal buckling response of functionally graded plates is presented in this paper using sinusoidal shear deformation plate theory (SPT). The material properties of the plate are assumed to vary according to a power law form in the thickness direction. Equilibrium and stability equations are derived based on the SPT. The non-linear governing equations are solved for plates subjected to simply supported boundary conditions. The buckling analysis of a functionally graded plate under various types of thermal loads is carried out. The influences of many plate parameters on buckling temperature difference will be investigated. Numerical results are presented for the SPT, demonstrating its importance and accuracy in comparison to other theories.

Dynamic buckling mechanism of pillar rockbursts induced by stress waves

Rockbursts are sudden and violent rock failures that can lead to huge production and equipment losses,injury or death of mining workers.Buckling has been regarded as one of the key mechanisms of rockbursts,which are often induced by dynamic loads from mining excavations,such as drilling and blasting in underground mining.The paper attempts to investigate the dynamic buckling mechanism of pillar rockbursts in underground mining,by considering rockbursts as a dynamic stability problem of underground rock structures.The results include:(1)A new explanation of the“sudden and violent”phenomenon of rockbursts,characterized by exponential growth of the amplitudes of transverse displacement responses,even in the presence of rock damping;(2)Identification of the critical role in inducing rockbursts of dynamic loads that bear frequencies approximately double the natural pillar frequency;(3)The greater influence on rockburst occurrence of the amplitude of dynamic component relative to the static component of loads;and(4)Quantification of the relative effects of stress waveform of dynamic loads on pillar rockbursts,which are in decreasing order if other parameters remain constant:rectangular,sinusoidal,and exponential waveforms.Application examples are provided and limitations of the approach are discussed.This research is motivated by the on-going and ubiquitous occurrence of rockbursts in underground excavations all around the world.In contrast to conventional methods that use rock specimens or rock materials to study rockbursts,this investigation emphasizes the structural effects on rockbursts,which has potential applications in hard rock mining engineering.

A non-probabilistic reliability topology optimization method based on aggregation function and matrix multiplication considering buckling response constraints

A non-probabilistic reliability topology optimization method is proposed based on the aggregation function and matrix multiplication.The expression of the geometric stiffness matrix is derived,the finite element linear buckling analysis is conducted,and the sensitivity solution of the linear buckling factor is achieved.For a specific problem in linear buckling topology optimization,a Heaviside projection function based on the exponential smooth growth is developed to eliminate the gray cells.The aggregation function method is used to consider the high-order eigenvalues,so as to obtain continuous sensitivity information and refined structural design.With cyclic matrix programming,a fast topology optimization method that can be used to efficiently obtain the unit assembly and sensitivity solution is conducted.To maximize the buckling load,under the constraint of the given buckling load,two types of topological optimization columns are constructed.The variable density method is used to achieve the topology optimization solution along with the moving asymptote optimization algorithm.The vertex method and the matching point method are used to carry out an uncertainty propagation analysis,and the non-probability reliability topology optimization method considering buckling responses is developed based on the transformation of non-probability reliability indices based on the characteristic distance.Finally,the differences in the structural topology optimization under different reliability degrees are illustrated by examples.