Dynamic buckling of stiffened plates under fluid-solid impact load

A simple solution of the dynamic buckling of stiffened plates under fluid-solid impact loading is presented. Based on large deflection theory, a discretely stiffened plate model has been used. The tangential stresses of stiffeners and in-plane displacement are neglected. Applying the Hamilton‘ s principle, the motion equations of stiffened plates are obtained. The deflection of the plate is taken as Fourier series, and using Galerkin method, the discrete equations can be deduced, which can be solved easily by Runge-Kutta method. The dynamic buckling loads of the stiffened plates are obtained from Budiansky-Roth ( B-R ) curves.     

含初缺陷裂纹损伤梁的冲击动力屈曲

由Hamilton原理导出考虑初始缺陷及横向剪切变形时裂纹梁的动力屈曲控制方程;应用断裂力学中常用的线弹簧模型将裂纹引入到屈曲控制方程中;基于B-R动力屈曲判断准则,采用数值方法求解了受轴向冲击载荷作用时裂纹梁的动力屈曲;对比讨论了不同冲击速度、初始几何缺陷大小以及分布形式等因素对梁冲击动力屈曲的影响。     

Experimental studies on dynamic plastic buckling of circular cylindrical shells under axial impact

In the present paper, experimental studies on dynamic plasticbuckling of circular cylindrical shells under axial impact are carried out. Hopkinson bar and drop hammer apparatus are used for dynamic loading. Three groups of circular cylindrical shells made of copper are tested under axial impact. From the experiments, the first critical velocity corresponding to the axi-symmetric buckling mode and the second critical velocity corresponding to the non-axisymmetric buckling mode are determined. The present results come close to those of second critical velocity given by Wang Ren^[4–6]. Two different kinds of non-axisymmetric buckling modes oval-shaped and triangle shaped are founded. The buckling modes under two loading cases, viz. with small mass but high velocity and with large mass and low velocity using Hopkinson bar and drop hammer, are different. Their critical energies are also discussed. The project is supported by the National Natural Science Foundation of China (19672039) and the Foundation for Returned Scholar from Abroad of Shanxi Province     

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。     

冲击载荷作用下矩形薄板的弹性动力屈曲

为了研究冲击载荷作用下考虑应力波效应弹性矩形薄板的动力屈曲,根据动力屈曲发生瞬间的能量转换和守恒准则,导出板的屈曲控制方程和波阵面上的补充约束条件,真实的屈曲位移应同时满足控制方程和波阵面上的附加约束条件。满足上述条件,建立了该问题的完整数值解法,对屈曲过程中冲击载荷、屈曲模态和临界屈曲长度之间的关系进行研究,定量计算了横向惯性效应对提高薄板动力屈曲临界应力的贡献。研究表明：板的厚宽比一定时,临界屈曲长度随冲击载荷的增大而减小;由于屈曲时的横向惯性效应,应力波作用下薄板一阶临界力参数是相应边界板的静力失稳临界力参数的1.5倍;随着边界约束逐渐减弱,板临界力参数逐渐减小,动力特征参数逐渐增大。

     

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。     

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…     

Nonlinear dynamic buckling of a viscoelastic model under impact loading

A simple nonlinear buckling analysis is applied to a one-degree-of-freedom arch under impact loading in which viscous damping may also be included. Such a loading consists of a falling body striking centrally the joint mass of the arch in such a way that a completely plastic impact can be postulated. When there is no damping the exact dynamic buckling load for such a kind of loading-associated with an unbounded motion can be established by using a static criterion (approach). More specifically, it was shown that the dynamic buckling load corresponds to that unstable equilibrium state where the total potential energy of the system is zero. Furthermore, it was proved that the second variation of the total potential energy at the foregoing unstable equilibrium state is negative definite. This implies that the curve loading versus displacement resulting by the vanishing of the total potential energy has always a maximum on the afore mentioned unstable state. It was also found that the system may become sensitive to initial conditions. If damping is included the foregoing static criterion yields lower bound buckling estimates. These findings were verified by employing a highly efficient approximate technique as well as the numerical scheme of Runge-Kutta for solving any nonlinear initial-value problem.     

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。     

圆柱薄壳的动相变屈曲行为

利用MTS809材料试验机对TiNi圆柱薄壳进行了轴向动渐进相变屈曲实验,对轴向冲击下处于伪弹性状态的TiNi合金柱壳的动相变屈曲行为进行了数值模拟研究。结果表明,不同的加载强度将会激发出柱壳不同的动屈曲响应模态。当冲击速度较高时,柱壳两端首先形成轴对称环形相变屈曲波纹,并产生应力平台;随着马氏体含量不断增加,环形相变屈曲波纹逐渐贯穿整个壳体,名义应力缓慢抬升;当名义应变超过一定阈值时,对称环形屈曲模态突变为非轴对称块状屈曲模态,名义应力大幅下降。撞击速度为40 m/s的算例（含10％随机缺陷）与S.Nemat-Nasser等的实验结果很好吻合,说明本文中计算模型、方法和结果的有效性经过了实验的考核。结果还表明,相变耗能是TiNi柱壳吸收冲击能量的主要机制,适合制作可重复使用的高效吸能元件,并给出了相应的理想厚径比。     

轴向应力波作用下圆柱壳塑性轴对称动力屈曲

运用有限元特征值分析方法对应力波作用下圆柱壳塑性轴对称动力失稳问题进行了研究。基于应力波理论和相邻平衡准则导出了圆柱壳轴对称动力失稳时的特征方程,在分析中同时考虑了应力波效应及横向惯性效应,把圆柱壳塑性动力失稳问题归结为特征值问题。通过引入圆柱壳动力失稳时的波前约束条件实现了此类问题的有限元特征值解法。计算结果揭示了圆柱壳塑性轴对称动力屈曲变形发展的机理,以及轴向应力波和屈曲变形的相互作用规律。     

充满液体弹塑性圆柱壳轴向冲击屈曲的数值模拟

基于对充满液体的弹塑性圆柱壳轴向冲击屈曲的实验观察 ,建立了相应的计算模型 ,借用 LS-DYNA软件包 ,在 HP-C36 0工作站上完成了数值模拟 ,得到了动画显示 ,给出的屈曲模态及一些特征量的时程曲线与实验结果相当一致。文中对壳的几何、物理参数对屈曲性能的影响进行了较详细的讨论     

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。     

Elasto-plastic analysis for the buckling and postbuckling of rectangular plates under uniaxial compression

Full-range analysis for the buckling and postbuckling of rectangular plates under in-plane compression has been made by perturbation technique which takes deflection as itsperturbation parameter.In this paper the effects of initial geometric imperfection on the postbuckling behaviorof plates have been discussed.It is seen that the effect of initial imperfection on the inelasticpostbuckling of plates is sensitive.By comparison,it is found that the theoretical results ofthis paper are in good agreement with experiments.     

Dynamic large deformation response of rigid plastic arches under impact

This paper presents a theoretical analysis of the dynamic large deformation response of highly circular arches under impact. By the Instantaneous Configuration Method (ICM), the solutions of the entire large deformation response process of the problem are obtained. The influences of the mass ratio, the energy ratio and the supported condition on the final deformation, the response time and the occurrence of plastic deformation are discussed in detail. The necessary condition for occurrence of the local reverse bending phenomenon has been found. An approximate method is provided to describe the phenomenon. The numerical results are in good agreement with experimental data.     

A numerical calculation of dynamic buckling of a thin shallow spherical shell under impact

Assuming the deformation of the shell has an axial symmetrical form, we transform Marguerre's equations into difference equations, and use these equations to discuss the buckling of an elastic thin shallow spherical shell subjected to impact loads. The result shows when impact load acts on the shells, a jump of the shell takes place dependent on the values λ and the critical buckling load increases with the enlargement of the loading area.     

The impact torsional buckling for the rigid plastic cylindrical shell

By using the energy criterion in[3],the impact torsional buckling for the rigid plastic cylindrical shell is studied.The linear dynamic torsional buckling equations for the rigid plastic shell is drived,and the critical impact velocity is given.     

Mechanism of buckling development and strain reversal occurrence in elastic–plastic cylindrical shells under axial impact

In order to clarify the mechanism of loading and unloading, buckling growth, and strain-reversal occurrence in elastic–plastic cylindrical shells that are impacted axially, non-linear dynamic equations in incremental form are derived and solved by using the finite difference method. The validity of the developed theory is verified by comparing theoretical and experimental results. From the calculation results, it is found that, at the initial stage of the impact process, the effective stress related to the middle-surface stresses in the part near the impacted end rises with time, and exhibits plastic loading. The radial restraints on the impacted end have obvious influence on the strain reversal occurrence at an early stage of the impact process. The effective modulus controls the post-buckling deformation of the shell, which contrasts with the situation for the bar to be impacted axially.     

An experimental study on the static and impact torsional buckling of cylindrical shells

In this paper, experimental studies are carried out on the buckling of circular cylindrical thin shells under impact torque. Experiments of impact buckling are made on a Hopkinson torsional bar. The torsional bar gives a step torque on the shells. Through an analysis of the strain-time curve obtained in experiment, the dynamic buckling critical torqueM _er and buckling waves numbern of the shell with different geometric data and some qualitative results are obtained. The buckling behavior of circular cylindrical thin shells under static and impact torque is compared.     

Two-dimensional analyses of delamination buckling of symmetrically cross-ply rectangular laminates

The conventional approach to analysis the buckling of rectangular laminates containing an embedded delamination subjected to the in-plane loading is to simplify the laminate as a beam-plate from which the predicted buckling load decreases as the length of the laminate increases. Two-dimensional analyses are employed in this paper by extending the one-dimensional model to take into consideration of the influence of the delamination width on the buckling performance of the laminates. The laminate is simply supported containing a through width delamination. A new parameter β defined as the ratio of delamination length to delamination width is introduced with an emphasis on the influence of the delamination size. It is found that (i) when the ratio β is greater than one snap-through buckling prevails, the buckling load is determined by the delamination size and depth only; (ii) as the ratio β continues to increase, the buckling load will approach to a constant value. Solutions are verified with the well established results and are found in good agreement with the latter.