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     

圆柱壳稳定性问题的研究进展

圆柱壳是工程实际中广泛应用的结构,其主要破坏形式是屈曲失稳．作为力学领域的经典问题,圆柱壳稳定性问题的研究非常之多．其中,受均匀轴向压力的圆柱壳由于临界屈曲载荷的理论预测值与早期试验结果之间的巨大差异,更是推动了壳体稳定性理论的不断发展．本文简要回顾了壳体稳定性理论的发展和分类,并对轴压圆柱壳体试验结果分散且远低于理论预测值的原因及含缺陷圆柱壳体的稳定性研究方法进行了总结,然后综述了地下空间顶管、储油罐、加筋圆柱壳及脱层圆柱壳等实际工程中广泛应用的圆柱壳结构稳定性研究的现状和趋势,最后展望了将来对工程应用中圆柱壳结构的稳定性研究的难点和方向．     

Buckling behavior of compression-loaded composite cylindrical shells with reinforced cutouts

Results from a numerical study of the response of thin-walled compression-loaded quasi-isotropic laminated composite cylindrical shells with unreinforced and reinforced square cutouts are presented. The effects of cutout reinforcement orthotropy, size, and thickness on the non-linear response of the shells are described. A high-fidelity non-linear analysis procedure has been used to predict the non-linear response of the shells. The analysis procedure includes a non-linear static analysis that predicts stable response characteristics of the shells and a non-linear transient analysis that predicts unstable dynamic buckling response characteristics. The results illustrate the complex non-linear response of a compression-loaded shell with an unreinforced cutout. In particular, a local buckling response occurs in the shell near the cutout and is caused by a complex non-linear coupling between local shell-wall deformations and in-plane destabilizing compression stresses near the cutout. In general, reinforcement around a cutout in a compression-loaded shell can retard or eliminate the local buckling response near the cutout and increase the buckling load of the shell. However, results are presented that show how certain reinforcement configurations can cause an unexpected increase in the magnitude of local deformations and stresses in the shell and cause a reduction in the buckling load. Specific cases are presented that suggest that the orthotropy, thickness, and size of a cutout reinforcement in a shell can be tailored to achieve improved buckling response characteristics.     

On stability of cylindrical shells of variable thickness with initial imperfections

The paper outlines a numerical method for stability analysis of cylindrical shells with initial imperfections. We solve a nonlinear buckling problem for a cylindrical shell with variable wall thickness under surface pressure. The imperfections of the shell are modeled as the first buckling mode. A probabilistic approach is used to determine the reliability against buckling of the cylindrical shell with the probability density of initial imperfections represented by uniform distribution, triangular distribution, or Gaussian distribution     

有限长圆柱壳受径向冲击的塑性动力屈曲分析

讨论两端固定的圆柱薄壳在均布外部冲击下的塑性动力屈曲。依据实验现象对位移场作出假设，用扰动法求得屈曲的扰动控制方程组，降阶后用标准的龙格库塔法进行数值求解。其中物理关系采用Ｌｅｖｙ－Ｍｉｓｅｓ流动理论，材料为刚线性强化模型。计算结果同Ｆｌｏｒｅｎｃｅ等的Ｂｅｓｓｅｌ函数解作了比较，对边界对屈曲的影响作了讨论。本文的结果对潜艇抗水下爆炸的研究有重要意义。     

基于混合变量条形传递函数方法的圆柱壳屈曲分析

提出了一种分析交各向异性圆柱壳和阶梯圆柱壳稳定性问题的混合变量条形传递函数方法。首先基于Fluegge薄壳理论，通过定义广义位移变量和对应的广义力变量，建立了圆柱壳混合变量能量泛函；然后通过引入条形单元，定义混合状态变量和采用传递函数方法对超级壳单元求解，得到具有多种边界条件圆柱壳屈曲问题的半解析解；最后通过位移连续和力平衡条件，可以得到阶梯圆柱壳屈曲问题的解。理论解推导过程表明此方法在引入边界条件和进行阶梯圆柱壳求解时非常方便。算例分析的结果验证了本方法的正确性。     

Effects of imperfections on the buckling response of compression-loaded composite shells

The results of an experimental and analytical study of the effects of initial imperfections on the buckling and postbuckling response of three unstiffened thin-walled compression-loaded graphite-epoxy cylindrical shells with different orthotropic and quasi-isotropic shell-wall laminates are presented. The results identify the effects of traditional and non-traditional initial imperfections on the non-linear response and buckling loads of the shells. The traditional imperfections include the geometric shell-wall mid-surface imperfections that are commonly discussed in the literature on thin shell buckling. The non-traditional imperfections include shell-wall thickness variations, local shell-wall ply-gaps associated with the fabrication process, shell-end geometric imperfections, non-uniform applied end loads, and variations in the boundary conditions including the effects of elastic boundary conditions. A high-fidelity non-linear shell analysis procedure that accurately accounts for the effects of these traditional and non-traditional imperfections on the non-linear responses and buckling loads of the shells is described. The analysis procedure includes a non-linear static analysis that predicts stable response characteristics of the shells and a non-linear transient analysis that predicts unstable response characteristics.     

Imperfection sensitivity of laminated conical shells

The sensitivity of laminated conical shells to imperfection is considered, via the initial post-buckling analysis, on the basis of three different shell theories: Donnell’s, Sanders’, and Timoshenko’s. Unlike isotropic conical shells or laminated cylindrical shells, in the case of laminated conical shells the thickness and the material properties vary with the shell coordinates, which complicates the problem considerably. The main objective of the study is to investigate the influence of the variation of the stiffness coefficients on the buckling behavior and on the imperfection sensitivity of laminated conical shells. It is felt that by finding the various parameters that influence the shell’s imperfection sensitivity, it is possible to improve the behavior of the whole structure.A special Level-1 computer code ISOLCS (Imperfection Sensitivity of Laminated Conical Shells) had been developed. ISOLCS calculates the classical buckling load and the imperfection sensitivity via Koiter’s theory of laminated conical shells with consideration to the variation of the material properties in the shell’s coordinates. The range of validity of the Level-1 predictions by ISOLCS is verified by the Level-3 code STAGS-A.     

Buckling analysis of stringer-stiffened laminated cylindrical shells with nonuniform eccentricity

In this study, the influence of nonuniformity of eccentricity of stringers on the general axial buckling load of stiffened laminated cylindrical shells with simply supported end conditions is investigated. The critical loads are calculated using Love’s First-order Shear Deformation Theory and solved using the Rayleigh-Ritz procedure. The effects of the shell length-to-radius ratio, shell thickness-to-radius ratio, number of stringers, and stringers depth-to-width ratio on the buckling load of nonuniformly eccentric shells, are examined. The research demonstrates that an appropriate nonuniform distribution of eccentricity of stringers leads the buckling load to increase significantly.     

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.     

薄壁加筋肋圆柱壳稳定性分析的参数化研究

针对在轴向载荷作用下的正置、正交网格形式的薄壁加筋肋圆柱壳结构，利用有限元程序，对薄壁加筋肋圆柱壳稳定性分析进行了参数化研究，得到了进行结构优化设计的准则，对于给定的设计载荷，当结构参数位于某一个局部失稳与整体失稳的临界区域时，结构的重量最轻。提出了基于有限元分析进行结构优化设计的策略，利用优化策略，获得了一薄壁加筋肋圆柱壳结构的优化设计结果，同时给出了粘合刚度简化模型与有限元计算结果的比较。     

Propagating buckles in long confined cylindrical shells

In many practical engineering applications, relatively stiff, long, circular cavities are lined with more compliant liner shells. Pressure applied through the porous walls of the confining medium can cause buckling of the shells. Such buckling is usually local in nature and occurs at a section with the biggest geometric imperfection. The paper presents experimental evidence which demonstrates that, once such a shell has been locally dented, a buckle which propagates within the confines of the cavity can be initiated. Such a buckle has the potential of completely collapsing the liner. The lowest pressure at which this buckle will propagate is established experimentally through a parametric study of the problem. The phenomenon is found to be physically similar to the propagating buckle problem which can develop in offshore pipelines. A difference is that in the case of the confined shell, the instability is shown to have a strong geometric dependence and, as a result, it can be developed in the case of thin elastic as well as elasto-plastic shells.     

Torsional buckling of spherical shells under circumferential shear loads

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具有复合正交异性铺层和偏心加筋的圆柱壳体的屈曲问题

本文导出了具有正交异性复合铺层和偏心加筋的圆柱壳体在轴压、横向压力或它们的任意组合作用下的屈曲问题的近似解,文中提出的方法使壳中不同铺层及偏心加筋引起的弯曲与拉伸间的耦合研究成为可能。以前的研究方法表明由于忽略了弯一拉耦合效应,所予测的屈曲结果是不完全正确的。     

THE CREEP EFFECTS ON THE BUCKLING OF SHALLOW SHELLS

An analysis of the creep effects on the buckling of concreteshallow shells is presented in this paper.Based on the non-linear theory of thin elastic shells.it is found that forthose of the elliptical paraboloidal type.the upper cri-tical load of the load-deflection curve will decrease whilethe lower limit Will increase with time.As to the problemof local buckling of the shell.the critical load is de-pendent only upon the modulus of elasticity at the instantit occurs.     

Nonlinear buckling of torsion-loaded functionally graded cylindrical shells in thermal environment

Based on the nonlinear large deflection theory of cylindrical shells, this paper deals with the nonlinear buckling problem of functionally graded cylindrical shells under torsion load by using the energy method and the nonlinear strain–displacement relations of large deformation. The material properties of the functionally graded shells vary smoothly through the shell thickness according to a power law distribution of the volume fraction of the constituent materials. Meanwhile, on the base of taking the temperature-dependent material properties into account, various effects of external thermal environment on the critical state of the shell are also investigated. Numerical results show various effects of the inhomogeneous parameter, the dimensional parameters and external thermal environment on nonlinear buckling of functionally graded cylindrical shells under torsion. The present theoretical results are verified by those in literature.     

Torsional,flexural, and torsional-flexural buckling modes of a cylindrical shell under combined loading

Stability problems for cylindrical shells under various loading modes were considered in numerous papers. A detailed analysis of such problems can be found, e.g., in the monograph [1]. We refer to the solutions presented in this monograph as classical.For long cylindrical shells in axial compression, one of the buckling modes is the purely beam flexural mode similar to the classical buckling mode of a straight rod. It is well known that it can be studied by using the nonlinear or linearized equations of the membrane theory of shells. In [2], it was shown that, on the basis of such equations constructed starting from the noncontradictory version of geometrically nonlinear elasticity relations in the quadratic approximation [3], under the separate action of the axial compression, external pressure, and torsion, there are also previously unknown nonclassical buckling modes, most of which are shear ones.In the present paper, we show that the use of the above equations for cylindrical shells under compression and external pressure with simultaneous pure torsion or bending permits revealing the earlier unknown torsional, beam flexural, and beam torsional-flexural buckling modes, which are nonclassical, just as those found in [2]. The second of these buckling modes is realized when axially compressing forces are formed in the shell with simultaneous torsion, and the third of them is realized under compression combined with pure bending.It was found that, earlier than the classical buckling modes, the torsional buckling modes can be realized for relatively short shells with small shear rigidity in the tangent plane, while the second and third buckling modes can be realized for relatively long shells.     

Repeated buckling and its influence on the geometrical imperfections of stiffened cylindrical shells under combined loading

The present experimental study aims at providing better inputs for improvement of the buckling load predictions of stiffened cylindrical shells subjected to combined loading. The work focuses on two main factors which considerably affect the combined buckling load of stiffened shells, namely geometric imperfections and boundary conditions. Six shells with nominal simple supports were tested under various combinations of axial compression and external pressure. The vibration correlation technique is employed to define the real boundary conditions. The geometric imperfections of the integrally stiffened shells are measured in the present experiments in situ and are used as inputs to a multimode analysis which yields the corresponding “knockdown” factor for various combinations of loading. Thus, when employing the repeated buckling procedure for obtaining interaction curves, each point on the curve is adjusted (using the multimode analysis) for the measured “new” surface of the shell and this results in more realistic interaction curves. The geometrical imperfections of the preloaded shells can also serve as an input to the International Imperfection Data Bank for future studies on the correlation between the manufacturing method of the shell and their geometric imperfections.     

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。     

Experimental investigation of the buckling of shallow spherical shells

In the present paper, the buckling behavior of clamped thin shallow spherical shells under external pressure is studied. Seventy-nine plastic shells formed by thermovacuum process were tested. The distributions of initial geometrical imperfections and vertical displacements were minutely measured with a differential transformer. It was possible to control the symmetrical initial geometrical imperfection of each specimen.Results indicate that the buckling phenomena of shallow spherical shells vary greatly with the symmetrical initial imperfection parameter η. In the case of the geometrical parameter λ larger than 5.5, the amplitude of the asymmetrical displacement component with the bifurcation buckling wave calculated by Huang becomes large immediately before buckling. The validity of Huang's theory for an initially perfect shell is experimentally demonstrated.