Stresses in thin spherical shells with imperfections. Part II: Influence of local imperfections

The changes in stress resultants in thin spherical shells, associated with a local imperfection introducing curvature errors in all directions, are investigated. An axisymmetric finite element model of the shell and imperfection is employed to carry out the linear elastic analysis. Parametric studies have been performed, to identify the main parameters controlling the response, for the case of internal pressure. The results are compared with those obtained in Part I for axisymmetric imperfections, and bounds for maximum elastic stress resultants are established to cover the possibility of both local and axisymmetric imperfections.     

Analysis of hyperbolic cooling towers with local imperfections

Two methods to analyse hyperbolic cooling towers with local imperfections are presented. One method relies on the finite element technique. For this a specialized finite-element program, which can model any arbitrary imperfections while retaining the advantage offered by the basically axisymmetric nature of the shell, was developed. The other method is an approximate procedure, which may be implemented with a purely axisymmetric analysis capability. The two methods are compared through numerical studies. A cooling tower shell with a bulge-type imperfection is examined under dead load and wind load conditions. It is concluded that the finite-element model presented is effective for the analysis of such shells, while the equivalent-load method may be adequate for some cases. Also, it is shown that both meridional and circumferential stress resultants may be radically influenced by a small bulge imperfection.     

On the modelling of different types of imperfections in silo shells

The assessment of imperfections is most important for determining the load-bearing capacity of a thin-walled shell structure. Different ways of modelling imperfections are discussed in this paper and steel silo shells are used as an application. Buckling tests were performed on different types of model shell - standard quality and high quality with reduced heat input during welding. For the numerical studies two different approaches were used as well: an axisymmetric approach with substitute geometric imperfections and an FEM approach, where the nodal coordinates were derived from surveying the specimen. It was found that there is considerable gain in the buckling strength due to the presence of the granular solid. The larger the initial imperfections in the shell the greater the gain in strength compared to the empty cylinder. The modelling of the uneveness of the edges with uneven dead loading is also discussed.     

Finite element techniques for the analysis of cooling tower shells with geometric imperfections

Two finite element methods for analysing geometrically imperfect cooling tower shells are presented. In the first the geometry of the imperfection is modelled by the elements; in the second the imperfection is represented by an equivalent load on the shell. Axisymmetric and general shell elements have been considered.Results are given which show that the first approximation to the equivalent load is sufficiently accurate and that it is possible to represent local imperfections by axisymmetric imperfections which require less computation. It is also shown that axisymmetric elements should be used wherever possible, because of their greater efficiency, following the geometry of an axisymmetric imperfection but representing local imperfections by equivalent loads.     

Buckling of elastic cylindrical shells considering the effect of localized axisymmetric imperfections

The effect of localized axisymmetric initial imperfections on the critical load of elastic cylindrical shells subjected to axial compression is studied through analytical modeling. Some classical results regarding sensitivity of shell buckling strength with respect to distributed defects having axisymmetric or asymmetric forms are recalled. Special emphasis is placed after that on the more severe case of localized defects satisfying axial symmetry by displaying an analytical solution to the Von Kármán–Donnell shell equations under specific boundary conditions. The obtained results show that the critical load varies very much with the geometrical parameters of the localized defect. These variations are not monotonic in general. They indicate, however, a clear reduction of the shell critical load for some defects recognized as the most hazardous isolated ones. Reduction of the critical load is found to reach a level which is up to two times lower than that predicted by general distributed defects.     

Dynamics of a thin cylindrical shell under impact with limited deterministic information on its initial imperfections

This study deals with the dynamics and failure of a thin circular cylindrical shell with axisymmetric initial imperfections. In contrast to earlier studies, the uncertainty involved in the initial imperfections is described by convex modelling: a non-probabilistic, set-theoretical approach. This methodology is useful when only limited information is available on the distribution of the uncertain events. The most significant N Fourier coefficients are assumed to fall in an ellipsoidal set in N-dimensional Euclidean space. We evaluate the maximum total displacement as a function of the shape of the ellipsoid.     

基于双剪屈服准则钢筋混凝土轴对称圆球壳有矩理论的极限分析

基于双剪屈服准则,导出了钢筋混凝土轴对称圆球壳的有矩理论的屈服条件,并应用塑性理论,对钢筋混凝土圆球壳进行了极限分析,并用机动法求出壳体在竖向均布荷载下的极限载荷。计算结果与根据塑性屈服线理论计算的结果相符,可供工程技术部门参考。     

双层球面网壳的缺陷稳定分析

双层球面网壳是一种缺陷敏感型结构,影响结构稳定性的初始缺陷主要有杆件的初弯曲、杆件的残余应力和结构节点的初始安装偏差三种.本文首先利用有初始弯曲的杆件的平衡微分方程推导得到了杆单元的初始弯曲影响系数,利用CRC模型考虑了杆件残余应力的影响,并且利用有限元软件ANSYS的UPFs程序接口,开发了可以考虑残余应力和初始弯曲的杆单元;然后对原有仅能考虑节点安装偏差的随机缺陷模态法进行了改进和补充,最后提出了一种能够同时考虑三种缺陷的双层球面网壳的稳定分析方法.该法与一致缺陷模态法相比,具有更高的精度.     

初始几何缺陷对网壳结构线性动力反应的影响初探

自振频率的密集分布和不可避免的初始几何缺陷,将导致网壳结构出现模态局部化现象,而模态局部化将导致结构振动呈现局部化。通过矩阵摄动理论分析并给出了模态局部化现象发生的诱因,讨论并确定了初始几何缺陷的大小和分布模式。以一个单层球面网壳为例,进行了同一地面运动激励下,50个包含不同初始几何缺陷网壳结构的线性动力反应分析,结果表明,初始几何缺陷对网壳结构线性动力反应的影响是不可忽略的,建议在网壳结构的抗震计算中予以重视。     

考虑初始几何缺陷的网壳结构整体稳定性可靠度分析

网壳结构的设计由重力荷载和初始几何缺陷共同作用下的整体稳定性控制,而结构的初始几何缺陷形状和最大值是未知的。采用联立自回归模型分别对球面网壳和柱面网壳结构的初始几何缺陷进行建模,研究空间相关初始几何缺陷对结构整体稳定极限承载力概率分布和可靠度的影响。评估杨氏模量对不同荷载工况作用下极限承载力概率分布和可靠度的影响。在永久荷载与雪荷载作用下,杨氏模量的影响可以忽略不计;如果各节点初始几何缺陷标准差的最大值等于1/2或1/3规范推荐的初始几何缺陷最大值,按规范中安全系数满足2的规定进行设计,结构的失效概率约小于6.5×10-5;若安全系数取1.5,结构失效概率约小于5.1×10-4。考虑永久荷载与活荷载的组合时,如果各节点初始几何缺陷标准差的最大值等于1/2或1/3规范推荐的初始几何缺陷最大值,安全系数取2时,网壳结构的失效概率均可忽略不计;若安全系数取1.5,球面网壳及柱面网壳的失效概率分别小于10-7和10-6。即若达到规范采用的可靠度,规范中的安全系数也许可降低至1.5且可针对不同地区确定不同安全系数值。     

Limit analysis of local failure in shallow spherical concrete caps subjected to uniform radial pressure

Many thin-walled shallow concrete shells (or caps or domes) have experienced structural collapse during or subsequent to their erection. Very few experimental investigations have been reported of shallow concrete spherical caps that allow for the effects of geometric and material non-linearities and imperfections to be identified, despite this information being essential for the validation of sophisticated numerical treatments. Classical thin-shell theories for axisymmetric domes predict a global buckling mode, but observations from experimental tests show that failure in concrete spherical caps is usually localised within a relatively small region and at a load significantly less than the classical buckling load. An investigation of the non-linear behaviour of thin-walled concrete spherical caps is currently being carried out both experimentally and theoretically at The University of New South Wales. As part of this study, an approach based on limit analysis has been developed on the basis of a local failure model and it is used for analysis of concrete/mortar spherical caps described in the published literature. The ultimate bending strength of a unit width of a spherical shell section is derived from a typical non-linear concrete stress-strain relationship and the in-plane thrust from shell membrane theory. The analytical results based on a local failure yield line model are compared with the available experimental results in the literature as well as with classical theoretical buckling results.     

Bending and stretching actions in shallow domes. Part 1. Analytical derivations

In this two-part set of articles the response of shallow axisymmetric shells with circular plan is investigated with the aid of the two-surface shell theory. Such an approach has the unique advantage of elucidating, both qualitatively, and quantitatively, the complex—and key—interaction of bending and stretching actions in such shells in a simple and direct manner. Although discussion centres upon a shallow paraboloid of revolution, the general features emerging from the study are, obviously, relevant for the generic family of shallow domes (e.g. spherical) covering the various limiting cases of support around their circumference.This first paper begins with a two-surface exposition of the set of equations describing the behaviour of the shell. Next, analytical bending solutions to the specific practical problem wherein the shell is subjected to uniformly distributed vertical loading (corresponding, say, to its self-weight) are presented; and this is followed by the working out of closed-form expressions for the distributions of bending and stretching effects in theshell under consideration.     

关于圆柱壳几何缺陷分析中傅立叶级数选取的探讨

圆柱壳屈曲一般对壳壁上微小几何缺陷的型式和幅值均十分敏感.为了能将缺陷的不同分量和圆柱壳的结构特征联系起来以及研究缺陷各分量对壳屈曲强度的影响,缺陷通常采用傅立叶级数分解.然而,大多数先前的研究选取不适当的傅立叶级数得到不正确的结果.本文首先考察傅立叶级数的数学描述基础,进而讨论不同傅立叶级数在描述不同型式几何缺陷的表现,从而得出如何选取适当的傅立叶级数用来描述圆柱壳几何缺陷的结论.采用这些适当的傅立叶级数,能更好地了解圆柱壳几何缺陷的特征分量以及这些分量对壳体屈曲强度的影响.     

The conception of quasi-collapse-affine imperfections: A new approach to unfavourable imperfections of thin-walled shell structures

Despite of the intensive research effort of the last decades there are considerable gaps of knowledge concerning the imperfection sensitivity of steel shell structures, even with regard to the basic buckling cases. It is explained in the presented paper why the most unfavourable imperfection pattern does not exist for shell structures but only different unfavourable patterns depending on the imperfection amplitude. This amplitude-depending pattern cannot be determined with certainty because of the substantial influence of the material non-linearity and because of the numerous post-buckling paths which cross each other. However, the method of quasi-collapse-affine imperfections allows a reasonable approximation to the most unfavourable imperfection pattern. The basic thoughts of this concept are presented. The application of the concept to slender wind-loaded shells illustrates its capability.     

基于SMA—橡胶支座和碟形弹簧的球面网壳结构多维隔震

球面网壳结构是典型的大跨度空间结构,地震时水平和竖向地面运动分量对其地震响应的影响均十分显著。为了提高其抗震性能,采用SMA—橡胶支座和碟形弹簧形成分段隔震机制以降低结构的多维地震响应。本文建立了SMA—橡胶支座和碟形弹簧的隔震计算模型。进而,根据球面网壳结构多维隔震的动力方程,针对某单层球面网壳结构,开展了其在不同地震作用下的多维隔震控制研究。由时程响应的数值模拟结果可见,多维隔震网壳结构的杆件内力、加速度响应和位移响应较无控结构有了显著的降低,从而验证了所提出的多维隔震技术对于保护球面网壳结构免遭地震灾害破坏的有效性。     

K6型单层球面网壳的自振特性分析

选用实际工程中应用较为普遍的K6型单层球面网壳作为重点研究对象，计算了多种工况（不同的矢跨比、荷载、支座条件）对网壳结构自振特性的影响，对K6型网壳结构的自振特性做了较为系统的研究，以得到K6型网壳结构的自振规律。     

Effects of geometric imperfections on stress distributions in cooling towers

The effect of geometric imperfections on the static stress distributions in cooling towers is investigated. The antisymmetric imperfections as well as the axisymmetric ones are assumed to be localized band imperfections at some height in a tower. Analyses are carried out for the self weight, seismic lateral load and wind load. Hoop stress and meridional bending moment are strongly influenced and the quantitative effects are summarized in simple figures.     

球节点刚度对单层柱面网壳地震响应影响随PGA变化的规律

已有研究发现单层柱面网壳焊接空心球节点刚度对结构的地震响应有一定影响,为了解此影响随PGA(地震动峰值加速度)变化的规律,对相同尺寸的单层柱面网壳精细化模型和常用模型进行了地震响应对比分析。其中精细化模型是按照空心球节点和钢管杆件的实际尺寸建立的壳单元模型;常用模型采用梁单元建模,不考虑球节点。改变PGA后,对比2种模型相同位置节点的位移时程曲线可以看到:随着PGA的增加,精细化模型与常用模型的节点位移响应差值越来越大;PGA超过结构的失稳临界值后,随着PGA的增加,加大精细化模型节点壁厚对提高结构抗失稳能力的作用越来越小。     

Effect of the presence of fluid on the dynamic response of buried orthotropic cylindrical shells under a moving load

This paper deals with the theoretical analysis of the axisymmetric steady state dynamic response of a buried fluid-filled orthotropic cylindrical shell subjected to a radial line load moving along the axis of the shell. A thin shell is assumed to be perfectly bonded to the surrounding medium of infinite extent, and only the axisymmetric response has been included. A linear acoustic equation has been used for the wave propagation in fluid. The nature of variation of differences between the results of the empty and fluid-filled shells has been studied for varying soil conditions. Changes in results due to variation in the orthotropy parameters have been compared with the difference in results due to the presence of fluid inside the shell.     

有多条轴对称焊接凹陷的钢圆柱薄壳在内压力和轴压力共同作用下的强度

钢筒仓中圆柱薄壳承受内压力和轴压力共同作用:在轴压和低内压作用下,壳可发生弹性失稳;在轴压和高内压作用下,壳可发生塑性破坏.内压轴压共同作用下的圆柱薄壳对几何缺陷比较敏感:单条轴对称焊接凹陷可使壳的承载力降低;而多条轴对称凹陷由于相邻凹陷的相互作用,可使壳的强度进一步降低;对于小间距的凹陷,这种相互作用更为明显.本文首次对有多条小间距轴对称凹陷轴压圆柱薄壳的整体结构在不同水平内压作用下的强度进行了有限元分析,并将计算结果与欧洲规范EC3的设计曲线进行比较,对EC3的设计曲线提出了修改意见,从而达到安全设计的目的.