辛方法和弹性圆柱壳在内外压和轴向冲击下的动态屈曲

针对有内压或外压的弹性圆柱壳在轴向冲击载荷耦合作用下的动态屈曲问题,构造哈密顿体系,在辛空间中将临界载荷和动态屈曲模态归结为辛本征值和本征解问题,从而形成一种辛方法。该方法直接得到非轴对称的屈曲模态。数值结果给出了圆柱壳问题的临界载荷和屈曲模态以及一些规律。     

轴向冲击载荷作用下弹性圆柱壳横向弯曲动态屈曲

研究在轴向冲击载荷下弹性圆柱壳动态屈曲问题.通过构造哈密顿体系,在辛空间中将临界载荷和动态屈曲模态归结为辛本征值和本征解问题.辛本征解反映了局部的压缩屈曲模态和整体的弯曲屈曲模态,特别是在冲击端为自由支承边界时的特殊屈曲方式.数值结果给出了具体的临界载荷和屈曲模态规律.     

受轴向冲击有限长弹性直杆中应力波引起的分叉问题

研究了有限长理想直杆受阶跃载荷作用的弹性动力屈曲问题。将直杆的屈问题归结为由轴向应力波传播而导致的杆的分叉问题，并考虑了应力波反射的影响。给出了分叉发生的临界条件并对具体实例进行了计算。最后对阶跃载荷及脉冲载荷对杆的动力屈曲的影响进行了讨论。     

弹性圆柱壳在轴向冲击载荷和温度耦合作用下的屈曲

通过引入哈密顿体系,将临界载荷和临界温度及它们所对应的屈曲模态归结为辛体系下的广义本征值和本征解问题。根据辛本征解的正交性和完备性,给出了全部的且独立存在的屈曲模态。数值结果表明,在轴向冲击载荷和温度耦合作用下,弹性圆柱壳的屈曲呈现出复杂的模式,温度直接影响冲击临界载荷的大小。随着温度的增加,冲击临界荷载降低,最后,文中给出各种条件下的屈曲模态。     

轴向冲击圆柱壳非弹性响应

简要论述承受轴向冲击载荷圆柱壳非弹性动屈曲响应的研究进展。采用Ｋａｒｍａｎ－Ｄｏｎｎｅｌｌ运动方程研究轴向流固冲击载荷作用下的圆柱壳轴对称弹塑性动屈曲问题。本构关系采用增量理论，借助增量数值方法求解动力方程组。研究不同边界条件对屈曲的影响，以及径向外压力在不同边界条件下对屈曲的影响。     

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)     

直杆塑性动力屈曲的双特征参数解

在关于轴向弹塑性压缩波下直杆塑性动力屈曲的研究中,将临界应力和屈曲惯性项指数参数作为一对特征参数求解．由动力屈曲发生瞬间的能量转换和守恒准则,导出波阵面上的屈曲变形补充约束条件．失稳控制方程、边界条件、塑性波阵面上的连续条件和补充约束条件构成定量求解两个特征参数和动力屈曲模态的完备条件。     

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 asymptotic solution of a dynamic buckling problem in elastic columns

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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。     

含脱层损伤复合材料层合梁的冲击动力屈曲

针对含初始缺陷和脱层损伤的复合材料层合梁的轴向冲击动力屈曲问题进行了分析。基于Hamilton原理导出了考虑初始缺陷、轴向和横向惯性、横向剪切变形以及转动惯性影响时含脱层损伤复合材料梁的非线性动力屈曲控制方程;基于B-R准则,采用有限差分方法求解了受轴向冲击载荷作用下含脱层损伤复合材料梁的动力屈曲问题;讨论了冲击速度、初始几何缺陷、铺层角度以及脱层长度等因素对复合材料层合梁动力屈曲的影响。     

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。     

Impact bifurcation of semi-infinite elastic thin bars

The dynamic buckling problem of elastic bars subjected to axial impact has been investigated by many authors in different ways. In this paper the problem, in which the elastic bars are assumed to be ideally straight, is reformulated in connection with the bifurcation due to the stress wave propagation. The example of a semi-infinite elastic bar is used for illustration.     

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。     

两参数轴向冲击载荷作用下圆柱壳弹塑性动力屈曲

研究圆柱壳在两参数轴向冲击载荷下的弹塑性动力屈曲问题，基本控制方程由弹塑性连续介质中关于加速度的最小原理获得，本构关系采用增量理论。研究表明：屈曲过程可划分为两相，两相之间由临界时间ｔ表征，并分别讨论了应力波对屈曲的影响，压缩波与弯曲波的相互作用及几何尺寸，材料参数，初始缺陷，载荷峰值及持续时间等诸多因素与动力屈曲的关系。     

INVESTIGATION OF THE DYNAMIC BUCKLING OF DOUBLEWALLED CARBON NANOTUBE SUBJECTED TO AXIAL PERIODIC DISTURBING FORCES

IntroductionThediscoveryofthefirstcarbonnanotubes[1]hasattractedwideattentionandstimulatedextensivestudies[2 - 5 ].Thestudiesshowedthatthecarbonnanotubesexhibitsuperiormechanical,electronicandchemicalproperties.Onthemechanicalbehavior,thecarbonnanotubespossessexceptionallyhighstrength ,stiffnessandelasticmodulus.Theestimatemodulusofthecarbonnanotubemayreachashighas 1TPa.Itisthelargestofallknownmaterials.Thestrengthorstiffnessishigherthananyknownfiber[3].Thecarbonnanotubeareusedascompositemat…     

Dynamic buckling analysis of composite cylindrical shells using a finite element based perturbation method

In this paper a finite element formulation of a reduction method for dynamic buckling analysis of imperfection-sensitive shell structures is presented. The reduction method makes use of a perturbation approach, initially developed for static buckling and later extended to dynamic buckling analysis. The implementation of a single-mode dynamic buckling analysis in a general purpose finite element code is described. The effectiveness of the approach is illustrated by application to the dynamic buckling of composite cylindrical shells under axial and radial step loads. Results of the reduction method are compared with results available in the literature. The results are also compared with full model finite element explicit dynamic analysis, and a reasonable agreement is obtained.     

Twin-characteristic-parameter solution of axisymmetric dynamic plastic buckling for cylindrical shells under axial compression waves

In the present investigation on the dynamic plastic buckling of cylindrical shells under axial compression waves, the critical axial stress and the exponential parameter of inertia terms in stability equations are treated as a couple of characteristic parameters. The criterion of transformation and conservation of energy in the process of buckling initiation is used to derive the supplementary restraint equation of buckling deformation at the fronts of axial elastic and plastic compression waves. The supplementary restraint equation, stability equations, boundary conditions and continuity conditions constitute the necessary and sufficient conditions of determining the two characteristic parameters. Two characteristic equations are derived for the two characteristic parameters. The critical axial stress or the critical buckling time, the exponential parameter of inertia terms and the initial modes of buckling deformation are calculated quantitatively from the solution of the characteristic equations.     

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.     

Dynamic buckling and plastic collapse of rectangular strips under axial slamming impact

The dynamic buckling and plastic collapse of elastic-plastic rectangular strips under axial slamming impact are investigated experimentally. The dynamic response of the specimens is measured by several back-to-back paris of strain gages located at different positions. According to the experimental records, the compressive and bending motions of the rectangular strips are analyzed. The strips exhibit three different critical dynamic conditions: buckling, plastic incipience and plastic collapse. Based on the response characters, three criteria are proposed which completely define the elastic-plastic dynamic behavior of rectangular strips under axial slamming impact with loading durations ranging from 14 to 18 milliseconds. These conditions are estimated by introducing three critical axial compressive strains. Moreover, the effect of geometric imperfection on the dynamic behavior of the strips is discussed.