THE DYNAMIC BUCKLING PROBLEM CAUSED BY PROPAGATION OF STRESS WAVE IN ELASTIC

ＨａｎＱｉａｎｇ（韩强）；ＭａＨｏｎｇｗｅｉ（马宏伟）；ＺｈａｎｇＳｈａｎｙｕａｎ（张善元）；ＹａｎｇＧｕｉｔｏｎｇ（杨桂通）；ＷｕＪｉｋｅ（武际可）（ＲｅｃｅｉｖｅｄＮｏｖ．１８．１９９４）ＴＨＥＤＹＮＡＭＩＣＢＵＣＫＬＩＮＧＰＲＯＢＬＥＭＣＡＵＳ...     

THE DYNAMIC BUCKLING OF ELASTIC-PLASTIC COLUMN SUBJECTED TO AXIAL IMPACT BY A RIGID BODY

I. INTRODUCTIONSince the 1960s the investigation on the dynamic buckling of elastic-plastic structures under impactload has been a very active subject of study in solid mechanics. In this respect the research advanceswere summarized and reviewed from di?erent aspects by some famous scholars[1??4]. The column is themost important structural element in practical engineering. So the dynamic buckling of the column hasattracted much more attention of many researchers. Lindberg H.E. carried ou…     

弹性杆在刚性块轴向撞击下的动力屈曲

基于能量关系,应用功率原理对弹性杆在刚性块轴向撞击下的动力屈曲问题进行了讨论。用幂级数解法,理论上给出了该问题的级数解,同时考虑了应力波传播及反射对屈曲的影响。通过理论分析和数值计算,得到了临界速度与冲击质量以及临界时间的关系,给出了发生屈曲时的临界条件。     

DYNAMIC BUCKLING OF ELASTIC-PLASTIC COLUMN IMPACTED BY RIGID BODY

The dynamic buckling of an elastic-plastic column subjected to an axial impact by a rigid body was discussed by using the energy law. The traveling process of elastic-plastic waves under impact action was analyzed by characteristics method. The equation of lateral disturbance used to analyze the problem was developed by taking into account the effect of elastic-plastic stress wave. The power series solution of this problem has been the power series approach. The buckling criterion of this problem was proposed by analyzing the characteristics of the solution. The relationship among critical velocity and impact mass, critical buckling length, hardening modulus was given by using theoretical analysis and numerical computation.     

The bifurcation problem of columns caused by elastic-plastic stress wave propagation

In this paper, the dynamic buckling of an elastic-plastic column is studied. Let its dynamic buckling under step load be reduced to a bifurcation problem caused by the propagation of axial elastic-plastic stress wave. The critical buckling condition is given and the reflection of the elastic-plastic stress wave is taken into consideration. In the end, numerical computation and conclusions are presented and obtained. Foundation item: the National Natural Science Foundation of China (19672038)     

冲击扭矩作用下碳纳米管动力屈曲的研究

为了研究碳纳米管在冲击扭矩作用下的动力屈曲,采用了连续模型将碳纳米管模拟成半无限长的弹性连续圆柱壳。将冲击扭矩作用下碳纳米管的动力屈曲问题归结为由于扭转应力波传播导致的分叉问题,此分叉问题被化为一个非线性方程组的求解。最后进行了数值分析,讨论了碳纳米管的不同参数对动力屈曲的影响,发现碳纳米管有极强的抗冲击性,临界屈曲剪应力可高达几百吉帕。     

刚性块轴向撞击杆的弹塑性动力屈曲

用特征线法分析了刚性块轴向撞击弹塑性直杆时应力波传播的全过程,得到了杆冲击端与固定端应力的变化规律及刚性块与杆首次分离的时间．基于能量原理,考虑了弹塑性应力波的传播与反射,建立了弹塑性杆在刚性块轴向撞击下的横向扰动方程,给出了问题的级数解,由解的稳定性得到了发生屈曲时的临界条件;通过数值计算和分析,给出了临界速度与冲击质量、线性强化模量及临界时间间的关系．     

Hamilton体系下功能梯度梁的热冲击动力屈曲分析

在Hamilton体系下,基于Euler梁理论研究了功能梯度材料梁受热冲击载荷作用时的动力屈曲问题;将非均匀功能梯度复合材料的物性参数假设为厚度坐标的幂函数形式,采用Laplace变换法和幂级数法解析求得热冲击下功能梯度梁内的动态温度场:首先将功能梯度梁的屈曲问题归结为辛空间中系统的零本征值问题,梁的屈曲载荷与屈曲模态分别对应于Hamilton体系下的辛本征值和本征解问题,由分叉条件求得屈曲模态和屈曲热轴力,根据屈曲热轴力求解临界屈曲升温载荷。给出了热冲击载荷作用下一类非均匀梯度材料梁屈曲特性的辛方法研究过程,讨论了材料的梯度特性、结构几何参数和热冲击载荷参数对临界温度的影响。     

梯度弹性基础上正交异性薄板的屈曲分析

基于双参数弹性基础模型,研究了梯度弹性基础上正交异性薄板的屈曲问题. 首先,基于能量法与变分原理,给出了梯度弹性基础上正交异性薄板的屈曲控制方程,并得到了梯度弹性基础刚度系数K₁ 与K₂的计算式;进而,通过将位移函数采用三角函数展开的方法,给出了单向压缩载荷作用下、四边简支正交异性弹性基础板屈曲载荷的计算式;在算例中,通过将该文的解退化到单纯的正交异性板,并与经典弹性解比较,证明了理论的正确性;最后,求解了弹性模量在厚度方向上呈幂律分布的梯度基础上的薄板屈曲问题,分析了基础上下表层材料弹性模量比与体积分数指数对屈曲载荷的影响.     

Dynamic torsional buckling of multi-walled carbon nanotubes embedded in an elastic medium

In this paper the dynamic torsional buckling of multi-walled carbon nanotubes （MWNTs） embedded in an elastic medium is studied by using a continuum mechanics model. By introducing initial imperfections for MWNTs and applying the preferred mode analytical method, a buckling condition is derived for the buckling load and associated buckling mode. In particular, explicit expressions are obtained for embedded double-walled carbon nanotubes （DWNTs）. Numerical results show that, for both the DWNTs and embedded DWNTs, the buckling form shifts from the lower buckling mode to the higher buckling mode with increasing the buckling load, but the buckling mode is invari- able for a certain domain of the buckling load. It is also indicated that, the surrounding elastic medium generally has effect on the lower buckling mode of DWNTs only when compared with the corresponding one for individual DWNTs.     

ELASTIC PULSE BUCKLING OF CYLINDRICAL SHELLS UNDER RADIAL IMPULSIVE LOADING

ＥＬＡＳＴＩＣＰＵＬＳＥＢＵＣＫＬＩＮＧＯＦＣＹＬＩＮＤＲＩＣＡＬＳＨＥＬＬＳＵＮＤＥＲＲＡＤＩＡＬＩＭＰＵＬＳＩＶＥＬＯＡＤＩＮＧＨｕａｎｇＣｈｅｎｇｙｉ（黄承义）ＬｉｕＴｕｇｕａｎｇ（刘土光）ＺｈｅｎｇＪｉｊｉａ（郑际嘉）（Ｄｅｐａｒｔｍｅｎｔｏ...     

基于慢动力法的受压扭管柱静力屈曲分析

钻井和螺杆泵采油等管柱,作业时同时承受轴向压力和扭矩载荷作用,提出了慢动力法计算管柱的压扭屈曲问题.利用瞬态动力学方法解决静力学问题的思想,分析了慢动力法中载荷的施加,以及阻尼和子步数的选取策略.数值结果表明:在轴向压力与扭矩单独或同时作用时,求得的有限元解均与解析解吻合较好.文章还分析了慢动力法计算效率的影响因素.     

ON THE ORIENTATION OF BUCKLING DIRECTION OF ANISOTROPIC ELASTIC PLATE UNDER UNIAXIAL COMPRESSION

The theory of small deformation superimposed on a large deformation of an elastic solid is used to investigate the buckling of anisotropic elastic plate under uniaxial compression. The buckling direction (the direction of buckling wave) is generally not aligned with the compression direction. The equation for determining the buckling direction is obtained. It is found that the out-of-plane buckling of anisotropic elastic plate is possible and both buckling conditions for flexural and extensional modes are presented. As a specific case of buckling of anisotropic elastic plate, the buckling of an orthotropic elastic plate subjected to a compression in a direction that forms an arbitrary angle with an elastic principal axis of the materials is analyzed. It is found that the buckling direction depends on the angle between the compression direction and the principal axis of the materials, the critical compressive force and plate-thickness parameters. In the case that the compression direction is aligned with the principal axis of the materials, the buckling direction will be aligned with the compression one irrespective of critical compressive force and plate-thickness. Project supported by the National Natural Science Foundation of China (No. 19772032).     

理想直杆中轴向应力波的传播和反射导致的分叉问题

对阶跃载荷作用下弹性理想完善直杆中应力波的传播及其反射引起民的分叉问题进行了理论分析和数值计算，讨论了此类动力屈曲问题中横向惯性效应的影响；给出了一种进行后分叉分析的近似方法，得到了一些结论，在各类结构由于应力波的传播及反射引起的分叉问题具有指导意义。     

A nondestructive dynamic method for the determination of the critical load of elastic columns

A dynamic method for predicting the buckling load of an elastic column is formulated. The method is based on the integral-equation representation of a column with varying cross section and elastic springs at the boundaries. The experimental inputs are the dynamic properties of the unloaded column (trequencies, mode shapes and masses). The buckling loads predicted for three tested configurations agreed well with loads defined by other static and dynamic methods.     

径向余弦冲击的长圆柱壳弹性脉冲屈曲

根据已有的实验现象假定变形模态，采用Ｌａｇｒａｎｇｅ方法分析了单位长度薄圆环在余弦冲击载荷作用下的弹性脉冲动屈曲。导出了动力屈曲方程组，借助数值方法求解方程，并与已有的计算进行了比较，得出结论     

On out-of-plane buckling of anisotropic elastic plate subjected to a simple shear

Out-of-plane buckling of anisotropic elastic plate subjected to a simple shear is investigated. From exact 3-D equilibrium conditions of anisotropic elastic body with a plane of elastic symmetry at critical configuration, the eqution for buckling direction (buckling wave direction) parameter is derived and the shape functions of possible buckling modes are obtained. The traction free boundary conditions which must hold on the upper and lower surfaces of plate lead to a linear eigenvalue problem whose nontrivial solutions are just the possible buckling modes for the plate. The buckling conditions for both flexural and barreling modes are presented. As a particular example of buckling of anisotropic elastic plate, the buckling of an orthotropic elastic plate, which is subjected to simple shear along a direction making an arbitrary angle of θ with respect to an elastic principal axis of materials, is analyzed. The buckling direction varies with θ and the critical amount of shear. The numerical results show that only the flexural mode can indeed exist. Project supported by the National Natural Science Foundation of China (No. 19772032).     

弹性圆柱壳在轴向应力波传播过程中的非对称屈曲

讨论弹性圆柱壳端部受冲击载荷作用，在应力波传播过程中的非对称屈曲问题。通过求解扰动方程得到了动态屈曲的分叉条件、临界载荷和屈曲模态。数值结果表明，当壳壁厚不很薄时，轴对称屈曲临界载荷比非对称临界载荷高；反之，轴对称临界载荷会比非对称临界载荷低。不同的冲击载荷，屈曲模态也将不同。     

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.      

A simplified over-stress analytical model of the dynamic buckling of a perfectly plastic column under axial impact

I.Introduction-Tllet1niaxiaIyieldingstrengthofastrain-raterelativemateriaIvariesobviuoslyunderdynamicloadstll.Sotheslrain-rateeffectshou1dbeincludedintheanalysisofplasticdynamicbucklingofacolumnl:J.ThispaperappliesMalvern'sover-stressmodell3jtoperfectplasticn'aterialsinthepIasticdynamicbucklinganalysisofacolumn.ThedifferentialequationofdynaI11icsaboutthenexuraIdeflectionofthecolumnisdeduced.Thedominantbucklingmode.thecriticalloadandthebucklingtimeissolvedviatheamplifyingfunctionmethodl4l.F…