Development mechanism of local plastic buckling in bars subjected to axial impact

In order to clarify the developmental mechanism of the local plastic buckling and the interaction between axial wave and buckling deformation in an axially impacted slender-bar, the non-linear dynamic equations in the incremental form are derived and solved by use of the finite difference method, with the axial wave front treated as a moving boundary. The initial local-buckling deflection given by the characteristic-value analysis is used as the initial condition of the solution of the equations, instead of the initial imperfection that is assumed in literatures. It is found that the initial buckling deflection with one half-wave, occurring near the impacted end, develops into the higher post-buckling mode with several half-waves, as the axial compression waves propagate forward. The numerical results show that no strain reversal occurs at the early stage of post-buckling process, and the solution corresponding to the tangent-modulus theory is valid for the dynamic plastic post-buckling response of the bar at this stage. The theoretical results are in good agreement with the experimental results reported in the literature.     

Buckling and post-buckling of gradient and nonlocal plasticity columns experiencing softening

The buckling and the post-buckling behaviors of a perfect axially loaded column are analytically investigated through a global bilinear moment–curvature elastoplastic constitutive law. Three plasticity cases are studied, namely the linear hardening plasticity law, the perfect elastoplastic case and the softening case. The applications of such a study can be found in various structural engineering problems, including reinforced concrete, steel, timber or composite structures. It is analytically shown that for all kinds of elastoplastic behaviors, the plasticity phenomena lead to a global softening branch in the load–deflection diagram. The propagation of the plasticity zone during the post-buckling process is analytically characterized in case of linear hardening or softening plasticity laws. However, it is shown that the unphysical elastic unloading solution necessarily occurs in presence of local softening moment–curvature constitutive law. A nonlocal plasticity moment–curvature softening law is then used to control the localization branch in the post-buckling stage. This nonlocal plasticity law includes the explicit and the implicit gradient plasticity law. Higher-order plasticity boundary conditions are derived from an extended variational principle. Some parametric studies finally illustrate the main findings of this paper, including the plasticity modulus effect on the post-buckling behavior of these plasticity structural systems.     

Post-buckling behaviour of graphite/epoxy stiffened panels with initial imperfections subjected to eccentric biaxial compression loading

The post-buckling behaviour of anisotropic stiffened panels with initial imperfections is investigated. Since buckling of the skin between the stiffeners often occurs first, a non-linear analysis is developed for symmetric panels under biaxial compression in order to obtain the out-of-plane panel deflection in the post-buckling range. The non-linear differential equations are expressed in terms of the out-of-plane displacement and the Airy function. They are solved with the Galerkin method for various boundary conditions by imposing an edge displacement control. The theoretical and experimental results obtained by the present analysis show that the transverse load can greatly influence the buckling loads and halfwave number. Since no experimental results have been found in the literature, several tests have been carried out on graphite/epoxy blade stiffened panels 900 mm long and 620 mm wide applying simultaneously biaxial compression loads with several combined ratios. An eccentricity results between longitudinal and transverse load, because the longitudinal compression is applied along the centroidal axes of the stiffened section while the transverse compression is applied to the skin panel. The correlation between the experimental and analytical results has been quite good; the experimental results demonstrate the influence of eccentricity of the transverse load on panel deflection in the pre- and post-buckling range.     

考虑压头曲率半径和应变梯度的微压痕分析

在压头尖端曲率半径取100nm的前提下，采用Chen和Wang的应变梯度理论，对微压痕实验进行了系统的数值分析. 首先通过拟合载荷-位移实验曲线的后半段来确定材料的屈服应力和幂硬化指数值,然后用有限元方法数值模拟压痕实验，并将计算得到的整段载荷-位移曲线及硬度-位移曲线和实验结果进行了比较. 结果表明应变梯度理论所预测的计算结果和实验结果很好地符合,包括压痕深度在亚微米和微米范围内的整段曲线.     

Bifurcation and post-buckling analysis of bimodal optimum columns

A mathematical formulation of column optimization problems allowing for bimodal optimum buckling loads is developed in this paper. The columns are continuous and linearly elastic, and assumed to have no geometrical imperfections. It is first shown that bimodal solutions exist for columns that rest on a linearly elastic (Winkler) foundation and have clamped-clamped and clamped-simply supported ends. The equilibrium equation for a non-extensible, geometrically nonlinear elastic column is then derived, and the initial post-buckling behaviour of a bimodal optimum column near the bifurcation point is studied using a perturbation method. It is shown that in the general case the post-buckling behaviour is governed by a fourth order polynomial equation, i.e., near the bifurcation point there may be up to four post-buckling equilibrium states emanating from the trivial equilibrium state. Each of these equilibrium states may be either supercritical or subcritical in the vicinity of the bifurcation point. The conditions for stability of these non-trivial post-buckling states are established based on verification of positive semi-definiteness of a two-by-two matrix whose coefficients are integrals of the buckling modes and their derivatives. In the end of the paper we present and discuss numerical results for the post-buckling behaviour of several columns with bimodal optimum buckling loads.     

阶跃扭矩作用下弹性圆柱壳冲击屈曲

本文首先基于Koiter初始后屈曲理论和Thompson离散坐标方法,给出了受扭圆柱壳的缺陷敏感性分析及冲击扭转屈曲渐近分析,并指出它对应于对称失稳的情形。然后通过求解受扭圆柱壳的非线性动力学方程,指出在阶跃扭矩作用下的后屈曲阶段,壳体的振动幅值剧增,周期变大。     

Post-buckling analysis of a thin stiffened plate with uncertain initial deflection via interval analysis

The post-buckling behavior of the thin stiffened plates with uncertain initial deflection under uni-direction compression load is investigated based on Von-Karman large deflection theory. The uncertain initial deflections are considered to be unknown except that they belong to a given set in the interval range. Interval analysis model for computing the bounds of curves of the post-buckling deflection versus load of the plate is presented. Interval analysis model is compared with the stochastic model, which is taken as the benchmarks of accuracy for judgment. The results indicate that the non-probabilistic and stochastic methods will produce similar results for a large deviation of uncertainty. If the probabilistic information is unavailable, one should not propose the probabilistic method based on an arbitrary assumption on the distribution of the deflection coefficients. Rather, one should use the non-probabilistic method to uncertainty.     

受均布载荷压杆后屈曲形态的数值计算

对受均布载荷压杆的屈曲及后屈曲行为进行了分析.基于杆的大变形理论,考虑杆的轴向伸长,建立了受均布载荷作用下细长压杆的几何非线性平衡方程.采用打靶法和解析延拓法数值求解非线性两点边值问题,得到了杆的后屈曲平衡路径和平衡构形.     

刚体碰撞下直杆的塑性屈曲和后屈曲

研究了受刚体轴向碰撞直杆中塑性屈曲变形发展的机理.推导了增量形式的非线性动力方程,并用差分法求解,将特征值分析给出的初始局部屈曲位移作为方程解的初始条件.数值结果说明:随着轴向压缩波的传播,碰撞端附近发生的局部屈曲变形增长和向前传播,由半波形的初始模态发展成后屈曲高阶模态;在后屈曲变形的早期阶段无应变率逆转发生,切线模量理论适用于该阶段弯曲变形的计算.     

Post-buckling of cantilever columns having variable cross-section under a combined load

Post-buckling of a cantilever column is examined under a combined load consisting of a tip-concentrated load and a distributed axial load, through dynamic formulation. The formulation of the problem is based on the moment–curvature relationship. The two-point boundary value problem described by the governing equations is dependent on the frequency parameter and the two load parameters. The buckling loads are those loads at which the eigencurve, namely, the load versus frequency curve of the column meets the load axis. A simple and reliable iterative procedure to convert the two-point boundary value problem into an initial value problem is followed and solved the non-linear differential equations utilizing a fourth-order Runge–Kutta integration scheme. To demonstrate the potentiality of the adopted numerical scheme, linear vibration frequencies of truncated, tapered cantilever wedges and cones are determined and compared with the published analytical and test results. Buckling and post-buckling loads of a simply supported stepped column are obtained and compared with the published test results. The loads and deflections of non-uniform cantilever columns are obtained for various slopes at the tip. The interaction of load parameters for a free–free truncated conical column has also been examined. The numerical results indicate that the path represented by the two load parameters turns out to be nearly a straight line.     

Buckling and post-buckling of long pressurized elastic thin-walled tubes under in-plane bending

The present paper focuses on the structural stability of long uniformly pressurized thin elastic tubular shells subjected to in-plane bending. Using a special-purpose non-linear finite element technique, bifurcation on the pre-buckling ovalization equilibrium path is detected, and the post-buckling path is traced. Furthermore, the influence of pressure (internal and/or external) as well as the effects of radius-to-thickness ratio, initial curvature and initial ovality on the bifurcation moment, curvature and the corresponding wavelength, are examined. The local character of buckling in the circumferential direction is also demonstrated, especially for thin-walled tubes. This observation motivates the development of a simplified analytical formulation for tube bifurcation, which considers the presence of pressure, initial curvature and ovality, and results in closed-form expressions of very good accuracy, for tubes with relatively small initial curvature. Finally, aspects of tube bifurcation are illustrated using a simple mechanical model, which considers the ovalized pre-buckling state and the effects of pressure.     

Post-buckling behavior of a point-supported cylindrical liner shell of concrete pressure vessels

Using W. T. Koiter's initial post-buckling theory, this paper deals with the critical load and post-buckling behavior of a point-supported cylindrical liner shell encased in a concrete pressure vessel while the liner shell is subjected to axial and lateral compressions. The reasonable spacing of anchors is given. The results show that the point-supported cylindrical liner shell has a relatively complicated post-buckling behavior. The behavior is subject to the change of anchor spacing in both axial and circumferential directions. When the ratio of the anchor spacing in the two directions satisfies a certain condition, the liner shell will carry the maximum load.     

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.     

Bending instabilities of elastic tubes

The present paper examines instabilities of long thin elastic tubes. Both initially straight and initially bent tubes are analyzed under in-plane bending. Tube response, a combination of ovalization instability and bifurcation instability (buckling), is investigated using a nonlinear finite element (FE) technique, which employs polynomial functions in the longitudinal tube direction and trigonometric functions to describe cross-sectional deformation. It is demonstrated that the interaction between the two instability modes depends on the value and the sign of the initial tube curvature. The ovalization of initially bent tubes is examined in detail and, in particular, the case of opening moments. Furthermore, the paper emphasizes on bifurcation instability. It is shown that buckling may occur prior to or beyond the ovalization limit point, depending on the value of the initial curvature. Using the nonlinear FE formulation, the location of bifurcation on the primary path is detected, post-buckling equilibrium paths are traced, and the corresponding wavelengths of the buckled configurations are calculated. Moreover, results over a wide range of initial curvature values are presented, extending the findings of previous works. Finally, several analytical approaches, introduced in previous research works, are also employed to estimate the moments causing ovalization and bifurcation instability. These approaches are based on nonlinear flexible shell theory or simplified ring analysis. The efficiency and accuracy of those analytical methods with respect to the nonlinear FE formulation are examined.     

Post-bifurcation behavior in the plastic range

In the first part of the paper a simple model is used to introduce some of the analytical and physical features of post-bifurcation phenomena in continuous elastic-plastic systems. An analysis is presented for the initial post-bifurcation behavior of a class of elastic-plastic solids subject to loads characterized by a single load parameter. Bifurcations which occur at the lowest possible load are singled out for attention. The theory makes connection with Hill's general theory of bifurcation and uniqueness in elastic-plastic solids and Koiter's general approach to the initial post-buckling behavior of conservative elastic systems. Buckling of an axially compressed column in the plastic range is used to illustrate the theory.     

Theoretical and Experimental Results on the Post-Buckling of Ring-Stiffened Cylinders

ABSTRACT

The post-buckling behavior of ring-stiffened cylinders subjected to lateral pressure is studied theoretically and experimentally. The theoretical analysis uses the energy method and terms of up to and including fourth order of the buckling displacements are considered. The results of experiments on ten machined ring-stiffened cylinders subjected to lateral pressure and used to verify the theoretical analysis. The theory shows the post-buckling behavior to be stable-symmetric for both the shell and general instability modes. The experimental results are in reasonable agreement with the theory, although they indicate, in general, a lower post-buckling stiffness. For the range of parameters considered, no instability or imperfection sensitivity is found in either the theoretical or the experimental studies.     

受圆形表面单面约束的点锚固圆环热屈曲分析

应用Ｗ．Ｔ．Ｋｏｉｔｅｒ的初始后屈曲理论，研究了受圆形混凝土表面单面约束的点锚固圆环的热屈曲问题，根据混凝土容器壁的几何约束条件，假设了圆环的合理屈曲模状，得出了圆环在两锚固点之间发生屈曲的临界温度，并研究了其后屈曲性态和缺陷敏感性。结果表明，临界点和后屈曲路径的平衡均为稳定的，圆环对于与屈曲模态形状相同的缺陷是不敏感的。     

网格湍流微结构的实验研究

本文试验研究了网格湍流从前期到后期整个连续衰变过程即湍能和Taylor微尺度随时间的变化规律,以及高阶速度相关系数的变化规律,试验结果是在一个低湍流度、低速风洞内,用TSI热线风速仪测得的,而拟均匀各向同性湍流是用在风洞试验段入口处加网格产生的,本文的试验结果与文献[1]提出的涡旋结构理论的计算结果做了比较,发现理论计算的和曲线与本文实测值非常吻合,本文的实测结果与Townsendt早年的试验以及Beanett七十年代末的试验也做了比较。结果表明,这些试验结果彼此也很一致,因而,所有这些试验结果与理论计算值都相互获得了验证。     

安全壳中钢衬壳热屈曲问题理论与实验研究(I)———理论分析部分

钢衬壳热屈曲问题是核工程安全壳设计中的主要问题把铆固之间的钢衬壳视为钢衬板的特殊缺陷形式，利用Ｋｏｉｔｅｒ初始后屈曲理论分析了完善和具有初始缺陷钢衬壳的弹性热后屈曲性态给出了用挠度－温度载荷表示的钢衬壳的后屈曲平衡路径表达式和屈曲临界载荷表达式具体分析了三种钢衬壳模型：四点铆固钢衬壳、四边固支钢衬壳和五点铆固钢衬壳给出了钢衬的初始缺陷、锚钉间距、钢衬厚度等参数对钢衬热屈曲载荷的影响结果对安全壳中钢衬壳的设计有很好的参考价值