STUDY ON AMPLIFICATION FACTOR OF FLEXURAL BUCKLING CRITICAL LOAD OF AXIAL COMPRESSION BARS1)

为了建立一般条件下轴压构件屈曲临界载荷的计算理论,首先对轴心受压构件发生屈曲时的总势能方程进行了推导,然后采用Rayleigh-Ritz法并基于势能驻值原理得到了4种不同端部约束条件下轴压构件的屈曲临界载荷,对比欧拉临界载荷,给出了临界载荷放大系数 的计算式,全面考虑了构件长细比、压缩变形、剪切变形以及截面形状系数对临界载荷的影响,推导的计算式可用于较小长细比轴压构件发生屈曲时临界载荷的计算.圆截面和双轴对称工字形截面轴压构件屈曲临界载荷的分析表明构件长细比是影响放大系数的主导因素。     

Axisymmetric compressive buckling of multi-walled carbon nanotubes under different boundary conditions

The paper studies the axisymmetric compressive buckling behavior of multi-walled carbon nanotubes (MWNTs) under different boundary conditions based on continuum mechanics model. A buckling condition is derived for determining the critical buckling load and associated buckling mode of MWNTs, and numerical results are worked out for MWNTs with different aspect ratios under fixed and simply supported boundary conditions. It is shown that the critical buckling load of MWNTs is insensitive to boundary conditions, except for nanotubes with smaller radii and very small aspect ratio. The associated buckling modes for different layers of MWNTs are in-phase, and the buckling displacement ratios for different layers are independent of the boundary conditions and the length of MWNTs. Moreover, for simply supported boundary conditions, the critical buckling load is compared with the corresponding one for axial compressive buckling, which indicates that the critical buckling load for axial compressive buckling can be well approximated by the corresponding one for axisymmetric compressive buckling. In particular, for axial compressive buckling of double-walled carbon nanotubes, an analytical expression is given for approximating the critical buckling load. The present investigation may be of some help in further understanding the mechanical properties of MWNTs.     

THE TRANSVERSE NONLINEAR FREE VIBRATION AND THE BUCKLING OF A COMPRESSIVE BAR ON AN ELASTIC FOUNDATION

基于Hamilton 原理,运用假设时间模态法,得到了弹性基础上压杆的横向非线性自由振动与屈曲的位移型常微分控制方程. 考虑一端固定另一端可移简支边界条件,采用打靶法得到了结构第一至第三阶结构频率与一阶屈曲载荷的数值结果. 结果表明：随轴心压力增加,结构频率减小;随弹性基础刚度增加,结构频率与屈曲载荷均增加;弹性基础刚度对结构频率的影响随振型阶数增加在减小;在小振幅的情形下,不同振型对一阶屈曲载荷的影响很小.     

局部径向载荷作用下外压薄壁圆筒稳定性分析

为简化真空塔器外挂件支撑区局部失稳分析,提炼出局部径向载荷作用下外压薄壁圆筒稳定性计算模型. 以易拉罐为薄壁圆筒试件,对不同外压下试件的局部径向临界载荷进行了测试. 利用有限元法对各实验模型进行了特征值屈曲分析,结果与实验数据能较好地吻合. 采用正交设计及参数化计算,得到了各结构参数及外压下的局部径向临界载荷经验公式. 实例计算表明,所得经验公式稍有保守,可用于真空塔器外挂件支撑件区的局部稳定性分析.     

THE COMPUTATIONAL METHOD FOR STABILITY OF TRUSSES WITH SMALL DEFORMATION

基于桁架结构稳定性计算的经典理论,分析了利用特征值理论开展桁架结构屈曲分析的计算方法,以及利用欧拉临界载荷屈曲理论,采取杆件撤除的静力求解确定桁架结构稳定临界载荷的计算方法. 通过理论研究和相关算例分析,论证了利用特征值理论和临界载荷屈曲理论相结合的方法,判断小变形桁架结构的失稳模态,求解桁架结构稳定临界载荷的确定性.     

TRANSVERSE BUCKLING OF STRIP

薄宽带钢的横向瓢曲是一种产生机理与解决对策都未知的板形缺陷。基于艾利应力函数和Timo-shenko 最小功原理建立了横向瓢曲前屈曲变形的力学模型,获得了其前屈曲应力场分布的表达式;运用伽辽金虚位移原理解法获得了其临界屈曲载荷。研究结果可为连退线上板带材生产过程中横向瓢曲的预测和控制提供参考依据。     

井筒内受压杆管后屈曲能量法分析与实验研究

目前不少理论力学教材都涉及刚体平面运动动力学方程的教学内容,但有些教材在叙述上有许多值得商榷之处.对这一重要的基本概念,本文提出作者的思考,供理论力学教学的教师与学过此内容的学生讨论.     

EFFECTS OF 2-TUNNEL AND 3-TUNNEL FIXATION ON BIOMECHANICS OF TIBIOFEMORAL JOINT

基于正常膝关节4个屈曲角度(0°, 25°, 60°, 80°)下的磁共振(MR)图像数据, 建立正常/两隧道固定/三隧道固定内侧半月板移植术后的胫股关节模型. 对各屈曲角度下的4种模型分别施加单一轴向压载和压扭组合载荷进行有限元仿真, 得到各模型在2种载荷作用下的应力及位移分布. 提取关节软骨、半月板表面的等效应力以及半月板的最大位移进行对比分析, 得到内侧半月板移植术后两/三隧道固定对胫股关节中软骨及半月板的影响. 总体上讲内侧半月板移植中的三隧道固定要优于双隧道固定, 更利于胫股关节恢复正常的应力特性.     

复合材料襟翼壁板屈曲失稳行为的栅线投影实验研究

本文利用栅线投影测量方法研究了蜂窝夹层板、工字型及T型加筋板三种不同结构形式复合材料襟翼壁板在压缩载荷下的屈曲失稳行为,得到了不同形式结构件屈曲的全场离面位移分布规律,分析了各自的屈曲失稳模式.研究结果表明,栅线投影测量方法在大尺度复合材料结构失稳变形测试中具有可行性;在相同面板尺寸条件下,工字型加筋复合材料襟翼壁板屈曲临界载荷最大,承载能力最强.本文结果可为飞机复合材料结构设计提供实验依据.     

Compressive strength of edge-loaded corrugated board panels

Postbuckling strength of simply supported corrugated board panels subjected to edge compressive loading has been studied experimentally using a specially developed test fixture. Although the load versus out-of-plane displacement response was highly sensitive to the presence of initial imperfections in the panels, the collapse loads did not vary much, which is attributed to the stable postbuckling behavior of the plates. Thin plates collapsed at nearly twice the buckling load, while thick panels collapsed at loads below the elastic critical buckling load. Local buckling of the facing on the concave side of the buckled plate was observed at load levels close to the collapse load. The plate collapse was triggered by compressive failure of the facings that initiated at the unloaded edges. A simplified design analysis was derived based on approximate postbuckling analysis and compared with an existing design formula for corrugated board panels and boxes.     

Buckling and Post-buckling Behaviour of Prismatic Aluminium Columns Submitted to a Series of Compressive Loads

The buckling and post-buckling behaviour of prismatic aluminium columns from stocky to very slender shapes is investigated. The unconventional, in terms of buckling tests, displacement control of compressive load and a series of loadings provided an enhanced insight into the buckling process. A phenomenon of buckling load drop has been detected in columns of intermediate slenderness, reaching over 20% of the load early critical value. This newly observed occurrence resembles finite disturbance instability, which until recently was commonly believed to only appear in cases of thin walled cylindrical shells, but not columns. The observation is in contradiction to predicted results from the elasto-plastic buckling models of Engesser or Shanley, with constant or growing values of load during the post-buckling process. Further tests on columns of intermediate slenderness, with strain gauges glued at node and anti-node locations of the buckled profiles, revealed that even minute buckling results in fields of highly non-symmetric residual microplastic strain. The results of the present study indicate that running column buckling tests under displacement control is worthy of being adopted as common practice. The envelope of column post-buckling states can be conveniently determined. This information will in turn allow for the quick and reliable estimation of the safety of a column, which has undergone accidental or deliberate damage in the form of limited buckling when under operational load.     

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采用Ritz近似法建立客运专线下承式系杆拱桥侧向稳定承载力实用计算公式; 假定满足拱桥侧向弯扭边界条件的位移试函数, 建立系杆拱桥的主拱肋侧倾失稳结构势能的表达式,基于最小势能原理建立了下承式系杆拱桥侧倾失稳临界载荷实用计算公式. 采用该实用计算公式计算了某客运专线下承式系杆拱桥弹性侧向稳定承载力, 并与三维有限元屈曲计算结果进行比较, 结果表明: 该方法简单实用, 可准确地预测系杆拱桥侧倾临界载荷, 便于工程应用.     

正交铺设层合板的蠕变屈曲分析

研究了正交铺设层合板的蠕变失稳问题。为了更好地模拟实际情况，在单层板的本构关系中，材料各主方向模量的松也时间均取不同值，并在建立控制方程时考虑了横向剪切变形的影响，通过理论分析，得到了粘弹性层合板的瞬时弹性临界载荷和持久临界载荷，并在算例中首次利用时间增量方法得到了有初始度层合板在长期受地的蠕变变表，计算结果表明了持久临界载荷对于粘弹性层合板的具体含义，从而使粘弹性层合板的为屈曲问题有了较为完整的     

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.     

THERMAL BUCKLING ANALYSIS OF CIRCULAR PLATE EMBEDDED IN AN INFINITE ELASTIC PLATE 1)

分析了嵌入无限大弹性板中的圆板在变温时的热屈曲问题。由于圆板的热膨胀系数与无限大弹性板的热膨胀系数不同，温度变化时圆板中会产生压应力。当压应力达到其临界值时，圆板会发生热屈曲。首先，基于弹性力学平面应力问题的基本理论，得到圆板和无限大弹性板的应力和位移；然后建立圆板热屈曲的控制微分方程，求得临界屈曲温度的解析解和数值解，着重讨论圆板和无限大弹性板的材料物性参数的关系对圆板临界屈曲温度的影响。     

联合载荷作用下简支矩形板的屈曲和过屈曲

本文研究了简支正交各向异性矩形板在两对板受中面压力作用下的屈曲和过屈曲性态,得到了载荷的稳定性区域,证明了临界载荷最多为二重的。利用多参数摄动方法求得临界载荷附近板的过屈曲状态的渐近解,分析了在二重临界载荷附近,当载荷按比例变化时,板的可能的过屈曲状态及其与参数的依赖关系。     

含铰接杆系结构几何非线性分析子结构方法

将细长杆系结构按长度方向划分为多个子结构,由于在子结构坐标系下的节点位移均是小位移,可以将子结构内部自由度凝聚到边界. 考虑到子结构端面在变形过程中保持为刚性截面,将端面节点自由度进一步凝聚到端面形心点,这样每一个子结构就减缩成形式上只有两个节点的广义梁单元,大大减缩了自由度. 大位移大转动是细长杆系结构产生几何非线性效应的一个重要原因,基于共旋坐标法,建立了随单元一起运动的随动坐标系,推导了子结构单元的节点力平衡方程及其切线刚度阵. 同时,考虑到工程机械中细长杆系结构含有相互铰接的刚体加强块,给出了非独立自由度节点力转换到独立参数下的广义节点力及其导数. 最后,通过履带式起重机的副臂工况算例,给出了其在不同载荷下的臂架结构位移,验证了方法的正确性.      

Dynamic stability analysis of composite plates including delaminations using a higher order theory and transformation matrix approach

A refined higher order shear deformation theory is used to investigate the dynamic instability associated with composite plates with delamination that are subject to dynamic compressive loads. Both transverse shear and rotary inertia effects are taken into account. The theory is capable of modeling the independent displacement field above and below the delamination. All stress free boundary conditions at free surfaces as well as delamination interfaces are satisfied by this theory. The procedure is implemented using the finite element method. Delamination is modeled through the multi-point constraint approach using the transformation matrix technique. For validation purposes, the natural frequencies and the critical buckling loads are computed and compared with three-dimensional NASTRAN results and available experimental data. The effect of delamination on the critical buckling load and the first two instability regions is investigated for various loading conditions and plate thickness. As expected, the natural frequencies and the critical buckling load of the plates with delaminations decrease with increase in delamination length. Increase in delamination length also causes instability regions to be shifted to lower parametric resonance frequencies. The effect of edge delamination on the static and dynamic stability as well as of delamination growth is investigated.     

端部切向载荷作用下的压杆失稳分析及其应用

细直杆件在压应力作用下会产生横向屈曲即失稳．直杆撞击刚性平面或拉断卸载后将形成压缩波，因承载压缩载荷的长度增加可以引起失稳．冲击速度转换的压应力沿着杆件切线方向，该处弯矩和剪力为零；而众多文献设定的失稳段固支边界条件并不准确．基于精确的杆件变形曲率方程得到端部载荷指向杆件中固定点时的受压失稳条件，得到其极限状态即载荷沿杆端切向作用时失稳长度相当于两端简支的1.5 倍．对于钢丝绳拉断形成的冲击失稳，载荷恒定而长度增加，可以产生高阶屈曲即在侧向出现多次曲折，并基于尼龙-橡胶带的模拟试验给出了定性说明．     

Edge-compression fixture for buckling studies of corrugated board panels

A test fixture, developed for evaluating the preand postbuckling response of simply supported, nearly flat, rectangular corrugated board panels subjected to edge compression is evaluated. The test fixture enables loading of panels into the postbuckling regime until collapse. The shadowmoiré method verified that buckling in the first mode occurred, and that there was symmetry of the adge-boundary conditions. Through an iterative regression model, experimental curves of load versus out-of-plane displacement for isotropic panels were fitted to an equation governing the nonlinear postbuckling response. This method provides the critical buckling load, a postbuckling parameter and the amplitude of initial imperfection of the panel. Comparison with analytical results revealed that simply supported boundary conditions were closely achieved. Examination of compressively loaded corrugated board panels showed that collapse occurred due to compressive failures of the facings in the highly stressed edge regions without severe influence from stress concentrations at load introduction and edge supports.