网状扁壳与带肋扁壳组合结构的拟三层壳分析法

本文对网状扁壳与带肋扁壳共同工作的组合结构(可简称组合网状扁壳),采用连续化的拟三层壳的计算模型,按弹性小挠度薄壳理论进行分析计算,推导建立了混合法的基本方程式。由于这种构造上的拟三层壳在一般情况下不存在中面,因而壳体的薄膜内力、弯矩与薄膜应变,弯曲应变是耦合的,存在一个耦合矩阵,使得基本方程式比单层光面的符氏扁壳方程要复杂得多。对于周边简支的组合网状扁壳可求得基本方程式的解析解。文中对三向、四向组合网状扁壳进行了详细讨论,并指出了在特定条件下,可退化为一个当量的各向同性单层扁壳。对于一般网状扁壳的拟壳分析法及带肋扁壳的拟壳分析法分别属于本文的两种特殊情况。文中附有计算例题。     

四边固支扁球壳的解析解法

以弯矩理论的单级数形式解析解为基础，应用迭加原理和将无穷级数展成无穷线性方程组的方法，得出均布荷载作用下四边固支扁球壳的闭合解。此解数学、力学模型简单、明确，使计算简化且能控制误差。     

拟壳法分析双曲率网状扁壳的竖向地震响应

本文利用粗壳法研完了双曲率网状扁壳的动力问题，以两个双重级数为函数，求得了四边简支边界条件下双曲率网状扁壳固有频率的计算公式。在考虑阻尼力的情况下，求得了双曲丰网状扁壳竖向地震响应的解，并且计算公式中的系数可从《建筑抗震设计规范(GBJll-89)》规定的设计反应谱求得，本方法计算简便，电算手算均可。     

基于扁壳理论的半解析有限条法用于冷弯构件的屈曲分析

提出了一种基于Marguerre的扁壳理论的有限条法。现有的大多数半解析有限条法都是基于基尔霍夫和Mindlin的板理论。在本文中,该板理论可以被视为扁壳理论的特殊情况。数值分析结果证实了基于扁壳理论的有限条法的有效性。     

弹性地基上扁球壳的自由振动

本文研究双参数弹性地基上扁球壳的自由振动频率和振型，推导了计及地基惯性力影响的扁壳自由振动控制方程。方程的精确解以贝塞尔函数表达。同时，分别导出了壳的经向、环向和横向位移分量的表示式。根据所得的解，文中给出了固定边扁球壳的频率方程和数值结果。同时。还给出了对应于前三个频率的振型变化曲线。     

具有初始缺陷的扁球面网壳的混沌运动

在圆形三向网架非线性动力学基本方程的基础上,用拟壳法给出了具有初始缺陷圆底扁球面网壳的大挠度方程和非线性动力学基本方程.在固定边界条件下,引入了异于等厚度壳的无量纲量,对基本方程和边界条件进行无量纲化.首先求出扁球面网壳的大挠度解,继之将大挠度解当作扁球面网壳的初始缺陷,通过Galerkin作用得到了一个含二次、三次的非线性动力学方程.通过求Melnikov函数,给出了具有初始缺陷的扁球面网壳系统可能发生混沌运动的临界条件.通过数字仿真绘出了平面相图,证实了混沌运动的存在.同时也发现考虑初始缺陷的扁球面系统固有频率增大了,从而发生混沌运动的临界载荷值减小了.     

弹性地基上中厚扁球壳的弯曲

以中厚度扁球壳的一般理论为基础,得到了极坐标系下的弹性地基上中厚度扁球壳的基本方程.该控制方程组是十阶方程组(对轴对称问题,则为八阶方程组).以应力函数、位移函数和壳体中面的法向位移为基本未知量,利用混合法对该控制方程组进行了求解,所得的解析解答则是以三角级数、Bessel函数和调和函数表示的.求解结果表明,当n=0时,中厚度扁球壳每边的边界条件为3个;当n=1时,每边的边界条件为4个;当n>1时,每边的边界条件为5个.解答还可以退化到无地基影响的中厚度扁球壳的计算以及薄扁球壳的计算.文末对位于Win-kler弹性地基上的圆底封顶中厚度扁球壳进行了数值计算,并与薄壳理论的计算结果进行了比较.     

球扁壳结构内力计算的精确方法

本文提出球形扁壳结构内力计算的精确方法——步进求和法。即将球扁壳（大、小挠度）变形划分若干段，用带有初挠度的小变形满足每段的方程。将偏微分控制方程化为三次代数方程，获得结构内力的精确解。文中用算例说明球扁壳大挠度、小挠度控制方程的步进求和算法，并与其它近似解法比较其精确性。     

带肋扁壳的拟双层壳分析法

本文把蒂肋扁壳的肋看作为一层同壳，且连续化为下层壳，并与蒂肋壳的壳板即上层壳组成件同工作的拟双层壳计算模型，进而可按弹性小挠度薄壳理论分析计算蒂肋扁壳。文中椎导建立了一般情况下带肋扁壳混台法的基本方程式。这种构造上的拟札层壳一般不存在中面，因而壳体的薄膜内力、弯矩与薄膜应变、弯曲应变是耦合的，存在一个耦合矩阵，它可充分反映肋与壳板偏心矩e的影响。对于两向正盘正放与三向带肋扁壳文中作了详细的讨论，并说明了在一定条件下，基本方程式可简化为一个构造上正史异性甚至各向同性单层扁竞的基本方程式，以方便计算和工程应用。文中附有算倒两则。     

抛物旋转扁壳的大挠度问题

本文使用积分方程理论,将旋转扁壳轴对称大挠度问题的基本微分方程化成等效的积分方程,给出了积分方程的迭代解。     

Effect of inplane edge constraints on natural frequencies of simply supported doubly curved shallow shells

Reasonably accurate natural frequencies are presented for simply supported shallow shells on rectangular planform subjected to 55 possible combinations of edge constraints. Thin shallow shell theory is used. Accurate natural frequencies of doubly curved shallow shells are presented and can be used for benchmarking by researchers as well as reference data for practicing engineers. Natural frequencies are presented for various shell curvatures including spherical, cylindrical and hyperbolic paraboloidal shells.     

预应力对柱支承扁网壳静力性能的影响

沿柱支承钢扁网壳的拉力环域施加适当预应力能降低结构在使用阶段的变形。以预应力三阶段设计为例分析预应力施加对柱支承扁网壳静力性能的影响。结果发现,预应力可以降低支座水平推力,提高结构刚度,但同时增大了结构在负风压作用时的变形,加大了支座附近杆件的轴力。预应力不能有效提高结构的临界荷载。与其他布索方案相比,折线形索-桁方案对网壳变形控制更有效。     

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.     

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.     

Stresses in thin spherical shells with imperfections. Part I: Influence of axisymmetric imperfections

A finite element model of axisymmetric geometry is used to obtain stress and moment fields in the region of an imperfection in thin, spherical shells. In Part I the studies are restricted to axisymmetric imperfections with a cosine variation along the meridian. Parametric studies are carried out to identify the main parameters controlling the response for internal pressure and gravity load. The results show that the behaviour of the shell is similar to the imperfect cylindrical shell with the same radius as in the spherical shell.     

球形网壳的优化设计

本文依据非线性球壳解为基础,对球网壳结构进行优化分析.利用Tresca屈服准则,计算满应力结构单元,将壳内力化成等效离散化构件内力之后,实现球形网壳的优化设计.     

薄壁空心球节点承载能力的非线性数值分析

现行网架规程中的焊接空心球承载力设计公式是以试验为基础的经验公式 ,对以稳定性控制的球壳 ,难以求得较为精确的屈曲临界点。应用对称旋转薄壳屈曲的非线性有限元理论 ,对空心球节点进行大位移弹塑性屈曲分析 ,得出了可供设计参考的空心球承载力数据表 ,并回归出适用于大直径空心球计算的近似公式 ,以确定空心球节点的失效状态及临界荷载。     

单点连续冲击荷载下单层球面网壳结构失效模式研究

为研究单点连续冲击荷载作用下单层球面网壳结构的失效模式,应用通用有限元软件ANSYS LS-DYNA建立了40m跨度,四种不同矢跨比的K8型单层球面网壳结构有限元模型.通过分析单层球面网壳结构在单点连续冲击荷载作用下失效全过程的冲击荷载、能量转化和杆件变形特点,总结归纳出单层球面网壳结构在单点连续冲击荷载作用下的五种失...