带缺口加强圈的圆柱壳屈曲特性分析

以低温液体罐车外筒体为原型,采用有限元方法研究了带缺口加强圈的圆柱壳的屈曲特性。着重考察了加强圈缺口间的夹角、加强圈之间的间距、边界条件对此类结构屈曲载荷的影响。计算结果表明:圆柱壳的屈曲载荷与加强圈缺口间夹角不是简单的线性关系,当加强圈缺口间夹角增大到一定程度后,圆柱壳的屈曲载荷几乎不再变化;加强圈布置的均匀度不但会影响到圆柱壳的屈曲载荷,同时也对其屈曲模态产生影响;在不同的边界条件下,圆柱壳也表现出不同的屈曲特性。     

Buckling of 2D-FG Cylindrical Shells under Combined External Pressure and Axial Compression

This paper presents the stability of two-dimensional functionally graded (2D-FG) cylindrical shells subjected to combined external pressure and axial compression loads, based on classical shell theory. The material properties of functionally graded cylindrical shell are graded in two directional (radial and axial) and determined by the rule of mixture. The Euler's equation is employed to derive the stability equations, which are solved by GDQ method to obtain the critical mechanical buckling loads of the 2D-FG cylindrical shells. The effects of shell geometry, the mechanical properties distribution in radial and axial direction on the critical buckling load are studied and compared with a cylindrical shell made of 1D-FGM. The numerical results reveal that the 2D-FGM has a significant effect on the critical buckling load.     

强激光辐照下预载柱壳热屈曲失效的数值分析

 采用有限元方法（ANSYS7.0）和简易的热力耦合本构关系,较系统地数值研究了预载柱壳受激光辐照时的热力响应和热屈曲失效行为,分析了几种壳体在不同预载条件下（轴压或内压）的屈曲模态和屈曲特征值,给出了屈曲模态和热屈曲失效与激光强度、辐照时间、预载条件和壳体几何尺度及形状间的定量或定性关系。计算结果表明：（1）屈曲失效行为主要集中在激光辐照区内且以径向屈曲为主。（2）在一定范围内,屈曲特征值与光斑中心点温度近似有线性关系。（3）激光辐照区内高温引起的材料软化和预载径向变形的耦合作用是柱壳发生热屈曲失效的根本原因,有效提高结构刚度,可使屈曲特征值提高。（4）壳体形状的改变对内压柱壳有更为明显的影响,其中圆柱形壳体屈曲特征值最大,因此具有较高的安全性。     

Nonlocal shear deformable shell model for thermal postbuckling of axially compressed double-walled carbon nanotubes

An investigation is reported of the thermal buckling and postbuckling of axially compressed double-walled carbon nanotubes (CNTs) subjected to a uniform temperature rise. The double-walled carbon nanotube is modeled as a nonlocal shear deformable cylindrical shell, which contains small-scale effects and van der Waals interaction forces. The governing equations are based on higher order shear deformation shell theory with a von Kármán–Donnell-type of kinematic nonlinearity and include thermal effects. Temperature-dependent material properties, which come from molecular dynamics (MD) simulations, and an initial point defect, which is simulated as a dimple on the tube wall, are both taken into account. The small-scale parameter, e ₀ a, is estimated by matching the buckling temperature of CNTs observed from the MD simulation results with the numerical results obtained from the nonlocal shear deformable shell model. The numerical illustrations concern the thermal postbuckling response of perfect and imperfect, single- and double-walled CNTs with different values of compressive load ratio. The results show that buckling temperature and postbuckling behavior of nanotubes are very sensitive to the small-scale parameter. The results reveal that temperature-dependent material properties have a significant effect on the thermal postbuckling behavior of both single- and double-walled CNTs.     

Buckling of carbon nanotubes wrapped by polyethylene molecules

The discovery of a buckling instability of a single-walled carbon nanotube wrapped by a polyethylene molecule subjected to compression is reported through molecular mechanics simulations. A decrease up to 44% in the buckling strain of the nano-structure owing to the van der Waals interaction between the two molecules is uncovered. A continuum model is developed to calculate both the interaction between the tube and the polymer and the decreased buckling strain of the structure by fitting the molecular mechanics results.     

Effect of surface layer thickness on buckling and vibration of nonlocal nanowires

In this Letter, the buckling and vibration behavior of nonlocal nanowires by incorporating surface elasticity is investigated. A modified core–shell model is developed to depict the size effect of Youngʼs modulus and validated by the reported experimental data. Our results show that the buckling load and natural frequency of nanowires increase when the effect of surface layer thickness is taken into account. Moreover, as the diameter of nanowires is smaller than 50 nm, the influence of surface layer thickness becomes obvious. This work can be helpful in characterizing and predicting the buckling and vibration behavior of NWs.     

Nonlinear analysis of imperfect squarely-reticulated shallow spherical shells

Nonlinear behavior of single-layer squarely-reticulated shallow spherical shells with geometrical imperfections subjected to a central concentrated (joint) load has been studied in this paper. Using the asymptotic iteration method, an analytical characteristic relationship between the non-dimensional load and central deflection is obtained. The resulting asymptotic solution can be used readily to perform the analysis of parameters and predict the buckling critical load. Meanwhile, numerical examples are presented and effects of imperfection factor and boundary conditions on buckling of the structures are discussed. Comparisons with data based on the finite element method show good exactness of the resulting solution.     

A hybrid continuum and molecular mechanics model for the axial buckling of chiral single-walled carbon nanotubes

The purpose of this study is to describe the axial buckling behavior of chiral single-walled carbon nanotubes (SWCNTs) using a combined continuum-atomistic approach. To this end, the nonlocal Flugge shell theory is implemented into which the nonlocal elasticity of Eringen incorporated. Molecular mechanics is used in conjunction with density functional theory (DFT) to precisely extract the effective in-plane and bending stiffnesses and Poisson's ratio used in the developed nonlocal Flugge shell model. The Rayleigh-Ritz procedure is employed to analytically solve the problem in the context of calculus of variation. The results generated from the present hybrid model are compared with those from molecular dynamics simulations as a benchmark of good accuracy and excellent agreement is achieved. The influences of small scale factor, commonly used boundary conditions and chirality on the critical buckling load are fully explored. It is indicated that the importance of the small length scale is affected by the type of boundary conditions considered.     

Nonlinear dynamic buckling of shallow circular arches under a sudden uniform radial load

The structural behavior of a shallow arch is highly nonlinear, and so when the amplitude of the oscillation of the arch produced by a suddenly applied load is sufficiently large, the oscillation of the arch may reach a position at its primary unstable equilibrium path or secondary bifurcation unstable equilibrium path, leading the arch to buckle dynamically. This paper presents an analytical study of the nonlinear dynamic in-plane buckling of a shallow circular arch under a uniform radial load that is applied suddenly and with an infinite duration. The principle of conservation of energy is used to establish the criterion for dynamic buckling of the arch, and the analytical solution for the dynamic buckling load is derived. It is shown that under a suddenly applied uniform radial load, a shallow pinned–fixed arch has a unique possible dynamic buckling load, while shallow pinned–pinned and fixed–fixed arches may have two possible dynamic buckling loads: a lower dynamic buckling load and an upper dynamic buckling load. The dynamic buckling loads of a shallow arch under a suddenly applied uniform radial load with infinite duration are found to be lower than their static counterparts, and to increase with an increase of the arch included angle and slenderness. The effect of static preloading on the dynamic buckling of an arch is also investigated. It is found that the pre-applied static load decreases the dynamic buckling load of the arch, but increases the sum of the pre-applied load and the dynamic buckling load.     

Buckling induced by a topological defect in a chain

The chain buckling induced by a topological defect (anti-kink) is investigated using a generalized Frenkel–Kontorova model. Instead of a single-peak appeared in the classical Euler instability, the buckling shape induced by the topological defect is a Sine-like pattern (two-peaks) that is antisymmetric regarding the point of the maximum stress. Evolution of the unstable buckling mode is clearly characterized by two time scales: one is the lifetime of the unstable phase, the other is the growth rate of the new phase. The phase transition curve of the buckling is a linear function of the chain length.     

Effects of structural defects on the compressive buckling of boron nitride nanotubes

In this paper, we examined the buckling of perfect and defective armchair boron nitride nanotubes with three types of vacancy defects, i.e. B- and N- single vacancy defects and B–N- double vacancy defect, using molecular dynamics simulations. To this end, all systems were modeled with a Tersoff-type potential, which is able to accurately describe covalent bonding of BN systems. We applied external uniaxial compressive forces to the nanotubes in vacuum and derived the critical buckling loads and strains, at room temperature in an NVT-ensemble. Our results showed significant differences between the critical buckling strengths of pristine and defective nanotubes. The resistance to axial buckling decreased with the introduction of one vacancy defect, and the B–N- double vacancy was the most seriously damaged structure, followed by B-vacancy and N-vacancy defects. Furthermore, the B-vacancy was shown to have the most significant effect on the decrease of the critical buckling strain. This can be attributed to the excessive asymmetries and perturbations induced in the structure of the nanotube and the local deformations around the defective site around the B-vacancy, even before loading. Moreover, results show that reduction in the buckling strength of the nanotube due to the presence of more than one B-vacancy defect depends on their distribution. If the two or three defects are close to each other, they act as a single point of weakness and the critical buckling load is only slightly reduced (similar to the existence of only one vacancy defect). However, if the defects are at more distant points, the critical buckling load may experience a higher decrease. Results show that vacancy defects play a critical role in the compressive buckling performance of boron nitride nanotubes and special attention must be paid to the presence of structural defects when designing members against buckling, especially for micro- and nano-electro-mechanical systems. On the other hand, defect engineering is a great means for tailoring the buckling strength of boron nitride nanotubes, in cases where the nanotube is expected to absorb energy through compressive buckling deformation and is not designed against, but for buckling.     

Radial buckling of multi-walled carbon nanotubes under hydrostatic pressure

Radial buckling stresses of carbon nanotubes (CNTs) need to be studied in high-pressure resonance Raman scattering spectrum. In this work, the closed-form expression of the critical buckling stress of multi-walled carbon nanotubes (MWCNTs) under hydrostatic pressure is derived that can be conveniently employed. Using the derived formulae, the critical buckling stresses of single-walled carbon nanotubes and double-walled carbon nanotubes with different diameters are calculated. The results are in good agreement with other reported literatures. In addition, the critical buckling stresses of each layer of a quintuple-walled CNT in different buckling modes are predicted, showing that the buckling instability can occur not only in the outermost rolled layer, but also in other rolled layer of MWCNTs by considering different diameters and buckling modes.     

Buckling behaviors of open-tip carbon nanocones at elevated temperatures

This paper used molecular dynamics simulations to investigate buckling behaviors of open-tip carbon nanocones (CNCs) at elevated temperatures ranging from 300 to 700 K. Influences of cone height and apex angle on the buckling behaviors were examined. Some interesting findings, especially on the change in buckling mode shapes of the CNCs, were observed in the study. For the CNCs having an apex angle of 19.2°, the one with a lower cone height exhibited a shrinking/swelling buckling mode shape even at the higher temperature 700 K. However, as the cone height increased, the CNC displayed a deflective buckling mode shape at 300 K, but changed to a shrinking/swelling buckling mode shape when the temperature grew to 500 K. Regarding the influences of apex angle, the CNCs presented a deflective buckling mode shape even at 700 K as the apex angle expanded. This is opposite to the shrinking/swelling buckling mode shape of the CNC having the smallest apex angle of 19.2°.     

Influence of temperature change on column buckling of multiwalled carbon nanotubes

Based on theory of thermal elasticity mechanics, an elastic multiple column model is developed for column buckling of MWNTs with large aspect ratios under axial compression coupling with temperature change. In this model, each of the nested concentric tubes is regarded as an individual column and the deflection of all the columns is coupled together through the van der Waals interactions between adjacent tubes. The thermal effect is incorporated in the formulation. Following this model, an explicit expression is derived for the critical buckling strain for a double-walled carbon nanotube. The influence of temperature change on the buckling strain is investigated. It is concluded that the effect of temperature change on the buckling strain is dependent on the temperature changes, the aspect ratios, and the buckling modes of carbon nanotubes.     

基于非局部弹性理论的单壁碳纳米管轴向受压屈曲研究

基于非局部弹性理论，在考虑小尺度效应影响的情况下，建立了单壁碳纳米管在均匀轴向外 部压力下的壳体模型. 得到了单壁碳纳米管的轴向受压屈曲的临界条件，验证了小尺度效应 对纳米管轴向受压屈曲的影响. 经典的壳体模型理论由于没有考虑小尺度效应影响而导致碳 纳米管轴向屈曲临界压力值偏高. 关键词： 非局部弹性理论 碳钠米管 小尺度效应 轴向受压     

Effect of small length scale on elastic buckling of multi-walled carbon nanotubes under radial pressure

A nonlocal multiple-shell model is developed for the elastic buckling of multi-walled carbon nanotubes under uniform external radial pressure on the basis of theory of nonlocal elasticity. The effect of small length scale is incorporated in the formulation. An explicit expression is derived for the critical buckling pressure for a double-walled carbon nanotube. The influence of the small length scale on the buckling pressure is examined. It is concluded that the critical buckling pressure for a carbon nanotube could be overestimated by the classic (local) shell model due to ignoring the effect of small length scale.     

Buckling instability of circular double-layered graphene sheets

In this paper, we study the buckling properties of circular double-layered graphene sheets (DLGSs), using plate theory. The two graphene layers are modeled as two individual sheets whose interactions are determined by the Lennard-Jones potential of the carbon-carbon bond. An analytical solution of coupled governing equations is proposed for predicting the buckling properties of circular DLGSs. Using the present theoretical approach, the influences of boundary conditions, plate sizes, and buckling-mode shapes on the buckling behaviors are investigated in detail. The buckling stability is significantly affected by the buckling-mode shapes. As a result of van der Waals interactions, the buckling stress of circular DLGSs is much larger for the anti-phase mode than for the in-phase mode.     

Dynamic column buckling of multi-walled carbon nanotubes under axial impact load

This paper studies the dynamic column buckling of multi-walled carbon nanotubes (MWNTs) under axial impact load. The analysis is based on the continuum mechanics model and a simplified model for the van der Waals forces between adjacent layers. By introducing initial imperfections for MWNTs and applying the method of preferred mode, a buckling condition is derived for the buckling load and associated buckling mode. In particular, explicit expressions are obtained for double-walled carbon nanotubes (DWNTs). Finally, numerical calculations are worked out for a DWNT and a five-layer MWNT with different length-to-radius ratios.     

Axial instability of double-nanobeam-systems

This Letter considers the axial instability of double-nanobeam-systems. Eringen's nonlocal elasticity is utilized for modelling the double-nanobeam-systems. The nonlocal theory accounts for the small-scale effects arising at the nanoscale. The small-scale effects substantially influence the instability (or buckling) of double-nanobeam-systems. Results reveal that the small-scale effects are higher with increasing values of nonlocal parameter for the case of in-phase (synchronous) buckling modes than the out-of-phase (asynchronous) buckling modes. The increase of the stiffness of the coupling elastic medium in double-nanobeam-system reduces the small-scale effects during the out-of-phase (asynchronous) buckling modes. Analysis of the scale effects in higher buckling loads of double-nanobeam-system with synchronous and asynchronous modes is also discussed in this Letter. The theoretical development presented herein may serve as a reference for nonlocal theories as applied to the instability analysis of complex-nanobeam-system such as complex carbon nanotube system.     

Force chain buckling,unjamming transitions and shear banding in dense granular assemblies

Force chain buckling, leading to unjamming and shear banding, is examined quantitatively via a discrete element analysis of a two-dimensional, densely-packed, cohesionless granular assembly subject to quasistatic, boundary-driven biaxial compression. A range of properties associated with the confined buckling of force chains has been established, including: degree of buckling, buckling modes, spatial and strain evolution distributions, and relative contributions to non-affine deformation, dilatation and decrease in macroscopic shear strength and potential energy. Consecutive cycles of unjamming–jamming events, akin to slip–stick events arising in other granular systems, characterize the strain-softening regime and the shear band evolution. Peaks in the dissipation rate, kinetic energy and local non-affine strain are strongly correlated: the largest peaks coincide with each unjamming event that is evident in the concurrent drops in the macroscopic shear stress and potential energy. Unjamming nucleates from the buckling of a few force chains within a small region inside the band. A specific mode of force chain buckling, prevalent in and confined to the shear band, leads to above-average levels of local non-affine strain and release of potential energy during unjamming. Ongoing studies of this and other buckling modes from a structural stability standpoint serve as the basis for the formulation of internal variables and associated evolution laws, central to the development of thermomicromechanical constitutive theory for granular materials.