钢衬壳后屈曲问题分析

本文用两种方法分析了核电站预应力混凝土安全壳中的内衬壳（钢衬壳）在温度应力作用下的后屈曲问题。认为钢衬壳模型是钢衬板模型的一种特殊缺陷形式，用Ｋｏｉｔｅｒ初始后屈曲渐近分析理论研究了钢衬壳的后屈曲问题。另外，本文从大挠度偏微分方程出发导出控制钢衬壳后屈曲的带有参数的非线性方程组，且用伪弧长法追踪其后屈曲平衡路径。文中用两种方法分析了四点铆固钢衬壳的后屈曲性态，并进行了比较。     

刚粘塑性圆环受法向冲击时的动力屈曲

本文研究刚粘塑性圆环受法向冲击时的动力屈曲，文中考虑了冲击过程中圆环厚度的变化，环向力的变化以及基本变形速度的变化。通过用数值方法求解扰动运动微分方程，结果表明，当规定了临界放大函数后，仅当冲击速度位于某一范围之内时，才会发生动力屈曲。     

含轴对称初始缺陷的具有正交各向异性表层的夹层圆柱壳的非线性屈曲

夹层圆柱壳具有很高的结构效能。在许多工程结构中被广泛采用。本文研究分析了含有轴对称初始缺陷的夹层圆柱壳在轴压下的非线性屈曲问题。该夹层壳具有正交各向异性表层和各向同性可承剪的夹心．利用Stein的前屈曲一致理论得出了前屈曲挠度随轴向载荷及缺陷参数的变化情况，运用Galerkin法导出了屈曲控制方程，并进行了数值计算，得到了屈曲载荷、缺陷幅值、缺陷波数、夹心模量等参量之间的关系．结果表明与壳体实际屈曲模态相同的初始缺陷具有很大的危害性，可以通过增加壳体表层的轴向弹性模量或优化夹心的有关参数等途径来提高屈曲载荷，改善壳体屈曲性能。     

胀锚型锚栓锚固破坏及承载力研究

混凝土基材锥体受拉破坏是后锚固锚栓受拉的基本破坏形式，采用混凝土破坏准则和弹性力学方法，推导了胀锚型锚栓基于混凝土基材破坏的抗拔极限承载力简化计算公式．通过对不同混凝土强度的极限状态数值分析，发现基材锚固破坏锥面底部直径R与有效锚固深度he为近似比值关系。与试验的对比结果表明，简化计算方法精度满足工程需要，和多种试验测试结果相当吻合。     

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     

塑性屈曲理论的研究进展

本文介绍了弹塑性分支理论的最新发展,讨论了塑性角点理论对“塑性屈曲佯谬”的解释作用,概述了结构塑性屈曲后性态分析的几种近似方法以及缺陷敏感度的特点,并给出一些典型结构塑性屈曲的研究结果,最后对研究的展望提出了看法。     

周期结构后屈曲新算法及其应用

提出了周期结构后屈曲分析的一种新算法。在屈曲点附近,通过加载模型和诱导后屈曲边值问题之间的相互切换,避开屈曲点附近刚度矩阵的奇异性,并诱导结构产生预期的后屈曲变形,避免了以往后屈曲算法中引入几何初始缺陷后对系统带来的可能影响。通过对三种由超弹性材料所构成的周期孔隙结构的后屈曲分析,验证了本文所提出的后屈曲算法的有效性和灵活性。分析了周期孔隙材料多向加载对屈曲模式转换的影响,以及后屈曲变形对弹性波传播带隙的影响,为周期结构中弹性波传播的调控提供良好的基础。     

U型波纹管及相关结构环向屈曲的有限元分析(Ⅱ）--半圆环壳的屈曲

环壳不仅是U型波纹管的一个组成部分，更是一类重要的结构，在航天、核能和海洋工程中有重要的应用，其屈曲是人们关注的问题之一，其中对半圆环壳的分析还较为少见。本文采用文[7]的有限元法（考虑了屈曲前的弯曲和屈曲时载荷的转动并按线性化特征值问题处理）计算了正Gauss曲率半圆环壳在均匀外压作用下的屈曲，将所得结果与已知的近似解进行了对比、并讨论了其中的差异。本文除了给出临界载荷和子午线的屈曲模态外，还给出了前屈曲弯曲应力分布，以便仔细了解屈曲问题。     

考虑制作缺陷的变角度纤维复合材料层合板的屈曲

假设纤维方向角沿层合板的长度方向线性变化,研究含丝束重叠、间隙等制作缺陷的变角度纤维复合材料层合板的屈曲问题．采用ABAQUS 有限元软件建立层合板的有限元模型,选用S4 壳单元计算四边简支层合板在两端压缩荷载作用下的屈曲临界荷载及屈曲模态,并进行详细的参数分析．研究结果表明：当起始角相同时,含或不含制作缺陷的层合板的屈曲临界荷载均随着终止角的增大而逐渐提高,说明纤维的不同铺设方式对层合板的屈曲性能有很大影响．含重叠缺陷的层合板的屈曲临界荷载均大于不含缺陷层合板的值,而含间隙缺陷的层合板的屈曲临界荷载均小于不含缺陷层合板的值．当层合板的重叠、间隙缺陷共存且面积相等时,层合板的屈曲临界荷载与不含缺陷时层合板的值接近,制作缺陷对变角度纤维复合材料层合板屈曲模态的影响较小．本文研究结果可为含缺陷的变角度纤维复合材料层合板设计提供一定参考．     

U型波纹管及相关结构环向屈曲的有限元分析(Ⅰ)--基本方程及环板的屈曲

U型波纹管是现代管道系统中最常见的一种位移补偿器 ,它由环板和具有正、负Gauss曲率的半圆环壳组成 ,在管道所传输的介质的压力作用下会发生屈曲。其中环向屈曲最为复杂 ,精确的理论分析非常困难 ,有限元分析也不多见。作者在分析前人工作的基础上 ,以圆环壳段为单元 (特定的旋转壳段单元 ,能自动退化成环板单元 ) ,限于弹性范围和线性化特征值问题 ,对介质压力作用下U型波纹管及其相关结构 (圆环板、圆环壳、半圆环壳 )的环向屈曲问题进行了分析。考虑了结构屈曲前的弯曲 ,计及压力的二次势能 ,导出的应力刚度矩阵和载荷刚度矩阵是非对称的。全部工作分为三部分 :(Ⅰ )基本方程 ,环板的屈曲 ;(Ⅱ )圆环壳、半圆环壳的屈曲 ;(Ⅲ )波纹管平面失稳的机理。本文为第一部分 ,除推导公式外 ,对不同边界和不同内外径之比的环板在径向均匀压力作用下的环向屈曲进行了计算 (轴对称的径向屈曲作为特例得到 ) ,给出了前屈曲应力分布、临界载荷及相应的屈曲模态 ,并将临界压力的值与前人基于vonK偄ｒｍ偄ｎ大挠度板的精确解进行了比较 ,吻合良好。     

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.     

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.     

Lateral-torsional buckling of simply supported beams under uniform bending and axial tensile force

In this paper, the effect of a centrally applied external axial tensile load on the lateral-torsional buckling resistance of simply supported I-beams under uniform bending acting in the plane of maximum rigidity is studied. A linear and a nonlinear analysis are performed. Following the linear analysis, an expression for the critical moment of lateral-torsional buckling is presented in which the influence of the axial tensile force is included. There is an upper limit of this force over which the equilibrium in the deformed state is not possible. In the nonlinear analysis, the nature of the critical state is studied, considering the initial part of the post-buckling path. It is concluded that this critical state is associated with a stable symmetrical bifurcation point. Nevertheless, the post-buckling path is very shallow; therefore, the beam cannot exhibit practically post-buckling strength. The paper is supplemented by a representative example.     

Nonplanar post-buckling analysis of simply supported pipes conveying fluid with an axially sliding downstream end

In this study,the nonplanar post-buckling behavior of a simply supported fluid-conveying pipe with an axially sliding downstream end is investigated within the framework of a three-dimensional(3 D)theoretical model.The complete nonlinear governing equations are discretized via Galerkin’s method and then numerically solved by the use of a fourth-order Runge-Kutta integration algorithm.Different initial conditions are chosen for calculations to show the nonplanar buckling characteristics of the pipe in two perpendicular lateral directions.A detailed parametric analysis is performed in order to study the influence of several key system parameters such as the mass ratio,the flow velocity,and the gravity parameter on the post-buckling behavior of the pipe.Typical results are presented in the form of bifurcation diagrams when the flow velocity is selected as the variable parameter.It is found that the pipe will stay at its original straight equilibrium position until the critical flow velocity is reached.Just beyond the critical flow velocity,the pipe would lose stability by static divergence via a pitchfork bifurcation,and two possible nonzero equilibrium positions are generated.It is shown that the buckling and post-buckling behaviors of the pipe cannot be influenced by the mass ratio parameter.Unlike a pipe with two immovable ends,however,the pinned-pinned pipe with an axially sliding downstream end shows some different features regarding post-buckling behaviors.The most important feature is that the buckling amplitude of the pipe with an axially sliding downstream end would increase first and then decrease with the increase in the flow velocity.In addition,the buckled shapes of the pipe varying with the flow velocity are displayed in order to further show the new post-buckling features of the pipe with an axially sliding downstream end.     

JUMPING INSTABILITIES IN THE POST-BUCKLING OF A BEAM ON A PARTIAL NONLINEAR FOUNDATION

Mode jumping is an instability phenomenon in the post-buckling region, which causes a sudden change in the equilibrium configuration and is thus harmful to structure. The con- figuration of a partial elastic foundation can directly induce mode coupling from the buckling stage and through the whole post-buckling region. The mode coupling effect due to the configuration of partial foundation on mode jumping is investigated and demonstrated to be an important factor of determining mode jumping. By properly choosing the partial elastic foundation configuration, mode jumping can be avoided.     

黏弹性层合圆柱壳的临界轴压分析

基于经典屈曲理论，研究了轴向受压黏弹性复合材料层合圆柱壳的临界屈曲载荷. 利用Boltzmann线性积分型本构关系描述铺设单层的各向异性黏弹性行为. 结合解析与数值 方法，由Donnell型屈曲控制方程以及边界条件的Laplace变换导出相空间的特征方程，根 据Laplace逆变换的极值定理，获得层合圆柱壳的瞬时弹性临界载荷与持久临界载荷. 针对 多组铺设方式，通过数值算例重点分析了临界载荷随铺设角的变化特征，两种临界载荷的峰 值点差异程度与铺设方式、几何参数以及材料类型的关系，得到了一些对黏弹性层合圆柱壳 的优化设计有参考价值的结论.     

Simplified prediction of creep buckling of cylinders under external pressure. Part 1: finite element validation

In this paper, a simplified method is proposed for the prediction of creep buckling. This simplified approach relies upon a model which yields an analytical evaluation of creep buckling times for cylinders under external pressure. This model is fully developed herein, and a ‘closed-form’ solution is given for the evaluation of the critical creep collapse time. The collapse mechanism is assumed to be due to the formation of a plastic hinge which induces an unstable post-buckling of the ring. The analytical ‘closed-form’ creep collapse time is then compared to finite element buckling predictions using the quasi-axisymmetric COMU shell element in the INCA code of the CASTEM system. The model is then applied to four different cylinders under external pressure and compared to finite element predictions; the cylinders' radius-to-thickness ratio varies between 50 and 550. It is shown that the proposed model performs well for this type of prediction: in all cases, the times to failure predicted by the model are lower than the finite element predictions. These predictions prove to be rather conservative for thicker cylinders. It is shown that creep buckling is a very dangerous failure mode. If the shape of the structure is observed as a function of time, nothing seems to happen during a very long ‘incubation’ period; when the initial imperfection reaches some critical value, buckling then suddenly occurs. This phenomenon is shown by the two methods of evaluation presented herein.     

On the plastic bifurcation and post-bifurcation of axially compressed beams

The paper presents two new results in the domain of the elastoplastic buckling and post-buckling of beams under axial compression. (i) First, the tangent modulus critical load, the buckling mode and the initial slope of the bifurcated branch are given for a Timoshenko beam (with the transverse shear effects). The result is derived from the 3D J₂ flow plastic bifurcation theory with the von Mises yield criterion and a linear isotropic hardening. (ii) Second, use is made of a specific method in order to provide the asymptotic expansion of the post-critical branch for a Euler-Bernoulli beam, exhibiting one new non-linear fractional term. All the analytical results are validated by finite element computations.     

Twist buckling and the foldable cylinder: an exercise in origami

Basic mechanisms for the buckling of a thin cylindrical shell under torsional loading are reviewed from a post-buckling perspective. Deflections are considered so far into the large-deflection range that the shell is allowed to fold to a flat two-dimensional form, in a mechanism reminiscent of a deployable structure. Critical and initial post-buckling effects are explored through concepts of energy minimization and hidden symmetries. For comparisons with the final large-deflection folded shape, a truss element program is employed. It is shown that, as buckling develops, the mode shape must change to accommodate both the symmetry-breaking aspects of the predominately inwards deflection, and the rotation of peak and valley lines of the buckle pattern necessary to accommodate the geometry of the final folded shape.