Nonlinear in-plane thermal buckling of rotationally restrained functionally graded carbon nanotube reinforced composite shallow arches under uniform radial loading

The nonlinear in-plane instability of functionally graded carbon nanotube reinforced composite (FG-CNTRC) shallow circular arches with rotational constraints subject to a uniform radial load in a thermal environment is investigated. Assuming arches with thickness-graded material properties, four different distribution patterns of carbon nanotubes (CNTs) are considered. The classical arch theory and Donnell’s shallow shell theory assumptions are used to evaluate the arch displacement field, and the analytical solutions of buckling equilibrium equations and buckling loads are obtained by using the principle of virtual work. The critical geometric parameters are introduced to determine the criteria for buckling mode switching. Parametric studies are carried out to demonstrate the effects of temperature variations, material parameters, geometric parameters, and elastic constraints on the stability of the arch. It is found that increasing the volume fraction of CNTs and distributing CNTs away from the neutral axis significantly enhance the bending stiffness of the arch. In addition, the pretension and initial displacement caused by the temperature field have significant effects on the buckling behavior.     

Buckling analysis of multi-walled carbon nanotubes: a continuum model accounting for van der Waals interaction

Explicit formulas are derived for the van der Waals (vdW) interaction between any two layers of a multi-walled carbon nanotube (CNT). Based on the derived formulas, an efficient algorithm is established for the buckling analysis of multi-walled CNTs, in which individual tubes are modeled as a continuum cylindrical shell. The explicit expressions are also derived for the buckling of double-walled CNTs. In previous studies by Ru (J. Appl. Phys. 87 (2000b) 7227) and Wang et al. (Int. J. Solids Struct. 40 (2003) 3893), only the vdW interaction between adjacent two layers was considered and the vdW interaction between the other two layers was neglected. The vdW interaction coefficient was treated as a constant that was not dependent on the radii of the tubes. However, the formulas derived herein reveal that the vdW interaction coefficients are dependent on the change of interlayer spacing and the radii of the tubes. With the increase of radii, the coefficients approach constants, and the constants between two adjacent layers are about 10% higher than those reported by Wang et al. (Int. J. Solids. Struct. 40 (2003) 3893). In addition, the numerical results show that the vdW interaction will lead to a higher critical buckling load in multi-walled CNTs. The effect of the tube radius on the critical buckling load of a multi-walled CNT is also examined.     

Variational principles for buckling and vibration of MWCNTs modeled by strain gradient theory

Variational principles for the buckling and vibration of multi-walled carbon nanotubes （MWCNTs） are established with the aid of the semi-inverse method. They are used to derive the natural and geometric boundary conditions coupled by small scale parameters. Hamilton＇s principle and Rayleigh＇s quotient for the buckling and vibration of the MWCNTs are given. The Rayleigh-Ritz method is used to study the buckling and vibration of the single-walled carbon nanotubes （SWCNTs） and double-walled carbon nanotubes （DWCNTs） with three typical boundary conditions. The numerical results reveal that the small scale parameter, aspect ratio, and boundary conditions have a profound effect on the buckling and vibration of the SWCNTs and DWCNTs.     

Buckling and postbuckling behavior of antisymmetrically angle-ply laminated composite plates

The buckling and postbuckling behaviors of perfect and imperfect antisymmetricallyangle-ply laminated composite plates under uniaxial compression have been studied byperturbation technique which takes deflection as its perturbation parameter.In this paper,the effects of in-plane boundary conditions,angles,total number oflayers and initial geometric imperfection on the postbuckling behavior of laminated plateshave been discussed.     

Effects of dimensional parameters and various boundary conditions on axisymmetric vibrations of multi-walled carbon nanotubes using a continuum model

Axisymmetric vibrations of multi-walled carbon nanotubes (MWCNTs) with finite length are investigated in this paper. A multi-walled carbon nanotube is modeled with multiple elastic isotropic shells. Based on a continuum model and considering van der Waals forces between tubes, a two-dimensional finite element model is developed to obtain axisymmetric natural frequencies and mode shapes of MWCNTs. First, the axisymmetric vibrational characteristics of single-walled carbon nanotubes are investigated, and then, they are compared with those of MWCNTs. The effects of van der Waals forces on radial vibration of MWCNTs are also explained. Moreover, influences of end conditions on radial and axial natural frequencies of carbon nanotubes (CNTs) with wide range of length-to-thickness ratio are studied by considering the free-free (F-F) and simply supported (S-S) end conditions. Besides, it is focused on dependence of axisymmetric mode frequencies on dimensional parameters such as length, diameter, as well as number of layers of MWCNTs. Through this, explicit expressions are found for calculating the radial breathing mode and longitudinal mode frequencies of MWCNTs.     

Influence of elastic foundations and carbon nanotube reinforcement on the hydrostatic buckling pressure of truncated conical shells

In this study, the effects of elastic foundations(EFs) and carbon nanotube(CNT) reinforcement on the hydrostatic buckling pressure(HBP) of truncated conical shells(TCSs) are investigated. The first order shear deformation theory(FOSDT) is generalized to the buckling problem of TCSs reinforced with CNTs resting on the EFs for the first time. The material properties of composite TCSs reinforced with CNTs are graded linearly according to the thickness coordinate. The Winkler elastic foundation(W-EF) and Pasternak elastic foundation(P-EF) are considered as the EF. The basic relations and equations of TCSs reinforced with CNTs on the EFs are obtained in the framework of the FOSDT and solved using the Galerkin method. One of the innovations in this study is to obtain a closed-form solution for the HBP of TCSs reinforced with CNTs on the EFs. Finally, the effects of the EFs and various types CNT reinforcements on the HBP are investigated simultaneously. The obtained results are compared with the results in the literature, and the accuracy of results is confirmed.     

MULTI-FIELD COUPLING BEHAVIOR OF SIMPLY-SUPPORTED CONDUCTIVE PLATE UNDER THE CONDITION OF A TRANSVERSE STRONG IMPULSIVE MAGNETIC FIELD

In order to study the multi-field coupling mechanical behavior of the simply-supported conductive rectangular thin plate under the condition of an externally lateral strong impulsive magnetic field, that is the dynamic buckling phenomenon of the thin plates in the effect of the magnetic volume forces produced by the interaction between the eddy current and the magnetic fields, a FEM analysis program is developed to characterize the phenomena of magnetuelastic buckling and instability of the plates. The critical values of magnetic field for the three different initial vibrating modes are obtained, with a detailed discussion made on the effects of the length-thickness ratio a/h of the plate and the length-width ratio a/b as well as the impulse parameterτon the critical value BOcr of the applied magnetic field.     

Numerical simulation of viscous flow: Buckling of planar jets

The phenomenon of viscous fluid buckling has a long and distinguished history, dating back to Taylor (1968). This paper is concerned with demonstrating that a numerical method, GENSMAC, is capable of simulating this physical instability. A table of the parameter values (e.g. the Reynolds number, the Froude number, inlet width, inlet velocity and aspect ratio) is provided giving details of when buckling occurs and when it does not. This allows the deduction of a possible buckling condition in terms of the Reynolds number and the ratio of height of the jet to the inlet width, modifying a previous hypothesis. Visualization of jet buckling is provided. This work has been motivated by the need of industry to understand jet filling of containers; jet buckling can lead to air entrapment and this is undesirable. Copyright © 1999 John Wiley & Sons, Ltd.     

TiNi合金圆柱薄壳静压屈曲失稳特性的实验研究

对马氏体相变支配的伪弹性TiNi合金圆柱薄壳进行了准静态屈曲实验研究和分析,结果表明,TiNi柱壳的屈曲模态以非轴对称钻石型为主,卸载时可恢复,与马氏体相变和相变铰的行为相关,明显不同于传统弹塑性柱壳。还讨论了长径比和边界条件对屈曲模态、比能、临界失稳阈值等的影响。研究发现：随着长径比和边界条件的变化,TiNi圆柱薄壳呈现出多样化的屈曲模态发展。相同长径比下,两端简支的TiNi圆柱薄壳比能Se较大;随着长径比增大,边界条件的影响有逐步弱化趋势。相同边界条件下,长径比较小的TiNi圆柱薄壳比能较大。     

Shock initiated instabilities in underwater cylindrical structures

An experimental investigation to understand the mechanisms of dynamic buckling instability in cylindrical structures due to underwater explosive loadings is conducted. In particular, the effects of initial hydrostatic pressure coupled with a dynamic pressure pulse on the stability of metallic cylindrical shells are evaluated. The experiments are conducted at varying initial hydrostatic pressures, below the critical buckling pressure, to estimate the threshold after which dynamic buckling will initiate. The transient underwater full-field deformations of the structures during shock wave loading are captured using high-speed stereo photography coupled with modified 3-D Digital Image Correlation (DIC) technique. Experimental results show that increasing initial hydrostatic pressure decreases the natural vibration frequency of the structure indicating loss in structural stiffness. DIC measurements reveal that the initial structural excitations primarily consist of axisymmetric vibrations due to symmetrical shock wave loading in the experiments. Following their decay after a few longitudinal reverberations, the primary mode of vibration evolves which continues throughout later in time. At the initial hydrostatic pressures below the threshold value, these vibrations are stable in nature. The analytical solutions for the vibration frequency and the transient response of cylindrical shell are discussed in the article by accounting for both (1) the added mass effect of the surrounding water and (2) the effect of initial stress on the shell imposed by the hydrostatic pressure. The analytical solutions match reasonably well with the experimental vibration frequencies. Later, the transient response of a cylindrical shell subjected to a general underwater pressure wave loading is derived which leads to the analytical prediction of dynamic stability.     

Postbuckling of pressure-loaded shear deformable laminated cylindrical panels

IntroductionInrecentyears,fiber_reinforcedcompositelaminatedpanelshavebeenwidelyusedintheaerospace,marine ,automobileandotherengineeringindustries .Theproblemofbucklingandpostbucklingofcylindricalpanelsunderaxialcompressionortorsionhasbeenextensivelystudied .Incontrast,theliteratureoncylindricalpanelsunderpressureloadingisrelativelyspares.Thesestudiesincludealinearbucklinganalysis (Singeretal.[1]) ,anonlinearbucklinganalysi(YamadaandCroll[2 ]) ,anelastoplasticbucklinganalysisusingreducedstif…     

微尺度金属薄膜屈曲稳定性的实验研究

微尺度金属薄膜的脱粘和屈曲严重影响着膜基结构的性能和使用寿命。本文对微尺度的金属铜薄膜在残余应力和外部压力共同作用下的脱粘屈曲和后屈曲模式进行了研究,用自行设计的单轴对称加载装置进行压力加载,用一台光学显微镜观察薄膜表面的屈曲形貌。在外力作用下薄膜会出现垂直于加载方向的直线型屈曲,但在外力卸载过程中该屈曲并不稳定,会演化成电话线型屈曲,完全卸载后形成泡状屈曲。再次加载后,恢复到直线型屈曲。研究表明:直线型屈曲的不稳定现象主要与薄膜的残余应力、基底的泊松比以及薄膜沿纵向与横向的应力比有关。     

夹层FGM圆柱壳在扭转载荷作用下的弹性稳定性

采用半解析方法研究了两端简支的功能梯度夹层圆柱壳在端部扭转载荷作用下的弹性稳定性.考虑圆柱壳的里外表层为均匀材料,中间层为材料性质沿厚度方向连续变化的功能梯度材料,并且在界面处的材料性质保持连续. 基于Flügge薄壳理论,建立了位移形式的结构静态屈曲控制方程.根据边界条件将位移表示为三角级数形式,获得包含柱壳端部扭转载荷参数的近似线性代数特征值问题,并通过数值方法求得了表征结构失稳特征的临界载荷. 数值结果表明,临界载荷随着半径与厚度比的增加而减小,随着功能梯度中间层的弹性模量的平均值的增加而增加.      

BUCKLING AND POSTBUCKLING ANALYSIS OF ELASTO-PLASTIC FIBER METAL LAMINATES

The elasto-plastic buckling and postbuckling of fiber metal laminates （FML） are studied in this research. Considering the geometric nonlinearity of the structure and the elasto- plastic deformation of the metal layers, the incremental Von Karman geometric relation of the FML with initial deflection is established. Moreover, an incremental elasto-plastic constitutive relation adopting the mixed hardening rule is introduced to depict the stress-strain relationship of the metal layers. Subsequently, the incremental nonlinear governing equations of the FML subjected to in-plane compressive loads are derived, and the whole problem is solved by the iterative method according to the finite difference method. In numerical examples, the effects of the initial deflection, the loading state, and the geometric parameters on the elasto-plastic buckling and postbuckling of FML are investigated, respectively.     

黏弹性薄板蠕变屈曲的载荷-时间特性研究

通过对黏弹性薄板压屈的稳定性分析,着重讨论了蠕变屈曲载荷－时间的特性,理论分析表明：黏弹性薄板蠕变屈曲与材料的力学性能密相关,屈曲载荷不像弹性薄板为一定值,而是与时间相关的;在一定载荷下,经过一段时间后出现延迟屈曲,相关的实验研究也证实这一重要结论;这种延迟失稳问题在工程中有其重要的意义。     

碳纳米管在简单荷载作用下的变形屈曲行为研究

采用分子动力学方法研究了不同螺旋性的单壁碳纳米管在轴压、扭转和外压分别作用下的变形屈曲行为。针对每种加载形式，给出了宏观形式的内力一变形曲线来反映碳原子间相互作用力的变化与碳管变形量之间的关系。对碳管在这三种不同荷载作用下的失稳特性、微观结构和应变能的变化进行了详细的分析。结合经典弹性理论和本文的模拟结果，得出了单壁碳纳米管的等效壁厚、弹性模量和Poisson比。另外，通过对比不同螺旋性碳管的模拟结果，讨论了螺旋性对碳纳米管力学行为的影响。文中采用的势能函数为Brenner多体势。     

Engineering measures for preventing upheaval buckling of buried submarine pipelines

In-service hydrocarbons must be transported at high temperature and high pressure to ease the flow and to prevent the solidification of the wax fraction.The high temperature and high pressure will induce the additional stress in the pipeline,which results in the upheaval buckling of the pipeline.If such expansion is resisted,e.g.,by the frictional effects of the foundation soil over a kilometer or of a pipeline,the compressive axial stress will be set up in the pipe-wall.When the stress exceeds the constraint of the foundation soil on the pipeline,suddenly-deforming will occur to release the internal stress,similar to the sudden deformation of the strut due to stability problems.The upheaval buckling may jeopardize the structural integrity of the pipeline.Therefore,effective engineering measures against this phenomenon play an important role in the submarine pipeline design.In terms of the pipeline installation and protection measures commonly used in Bohai Gulf,three engineering measures are investigated in great details.An analytical method is introduced and developed to consider the protection effect of the anti-upheaval buckling of the pipeline.The analysis results show that the amplitude of the initial imperfection has a great effect on the pipeline thermal upheaval buckling.Both trenching and burial and discrete dumping are effective techniques in preventing the pipeline from buckling.The initial imperfection and operation conditions of the pipelines determine the covered depth and the number of layers of the protection measures.     

Stress and buckling analysis of a thick-walled micro sandwich panel with a flexible foam core and carbon nanotube reinforced composite(CNTRC) face sheets

In this paper, the stresses and buckling behaviors of a thick-walled micro sandwich panel with a flexible foam core and carbon nanotube reinforced composite(CNTRC) face sheets are considered based on the high-order shear deformation theory(HSDT) and the modified couple stress theory(MCST). The governing equations of equilibrium are obtained based on the total potential energy principle. The effects of various parameters such as the aspect ratio, elastic foundation, temperature changes, and volume fraction of the canbon nanotubes(CNTs) on the critical buckling loads, normal stress,shear stress, and deflection of the thick-walled micro cylindrical sandwich panel considering different distributions of CNTs are examined. The results are compared and validated with other studies, and showing an excellent compatibility. CNTs have become very useful and common candidates in sandwich structures, and they have been extensively used in many applications including nanotechnology, aerospace, and micro-structures. This paper also extends further applications of reinforced sandwich panels by providing the modified equations and formulae.     

Scale effects on nonlocal buckling analysis of bilayer composite plates under non-uniform uniaxial loads

Scale effects are studied on the buckling behavior of bilayer composite plates under non-uniform uniaxial compression via the nonlocal theory. Each isotropic plate is composed of a material that is different from others, and the adhesive between the plates is modeled as the Winkler elastic medium. According to the symmetry, effects of the Winkler non-dimensional parameter, the thickness ratio, the ratio of Young''s moduli, and the aspect ratio are also considered on the buckling problem of bilayer plates, where only the top plate is under the uniaxial compression. Numerical examples show that the Winkler elastic coefficient, the thickness ratio, and the ratio of Young''s moduli play decisive roles in the buckling behavior. Nonlocal effect is significant when the high-order buckling mode occurs or the aspect ratio is small.     

圆柱形薄壳冲击扭转屈曲的实验研究

本文对受冲击扭矩作用下的圆柱形簿壳扭转屈曲进行了实验研究，利用Ｈｏｐｋｉｎｓｏｎ扭杆使圆柱受阶跃扭矩作用，分析所得到的应变－时间曲线，得到了不同几何参数的圆柱壳的冲击临界扭矩Ｍｄｅｒ和屈曲波数ｎ及几条定性结论，同时找出了圆柱壳静力扭转屈曲行为和冲击扭转屈曲行为之间的异同。