Deformation and reverse snapping of a circular shallow shell under uniform edge tension

In this paper we study the deformation and stability of a shallow shell under uniform edge tension, both theoretically and experimentally. Von Karman’s plate model is adopted to formulate the equations of motion. For a shell with axisymmetrical initial shape, the equilibrium positions can be classified into axisymmetrical and unsymmetrical solutions. While there may exist both stable and unstable axisymmetrical solutions, all the unsymmetrical solutions are unstable. Since the unsymmetrical solutions will not affect the stability of the axisymmetrical solutions, it is concluded that for quasi-static analysis, there is no need to include unsymmetrical assumed modes in the calculation. If the shell is initially in the unstrained configuration, it will only be flattened smoothly when the edge tension is applied. No snap-through buckling is possible in this case. On the other hand, if the shell is initially in the strained position, it will be snapped back to the stable position on the other side of the base plane when the edge tension reaches a critical value. Experiment is conducted on several free brass shells of different initial heights to verify the theoretical predictions. Generally speaking, for the range of initial height H < 10 the experimental measurements of the deformation and the reverse snapping load agree well with theoretical predictions.     

弹性地基梁振动特性的近似分析方法

文中介绍了用模态摄动法分析复杂情况下弹性地基梁动力特性的近似方法。这一方法中可考虑纵向钢筋以及变地基弹性系数对弹性地基梁振动特性的影响，通过算例说明了这一方法的有效性。     

Solution of axisymmetric dynamic problems for cylindrical shells on an elastic foundation

A dynamic problem for a cylindrical shell on an elastic foundation is formulated. A numerical algorithm for solving this problem is outlined. The results obtained are analyzed __________ Translated from Prikladnaya Mekhanika, Vol. 43, No. 12, pp. 103–109, December 2007.     

碎石桩复合地基若干问题的理论分析

由桩-土侧向变形及竖向变形协调条件，基于弹性理论导出了桩及桩周土的应力-应变关系、桩体材料屈服时桩-土应力比的计算式．推出了桩周土处于极限平衡状态下，碎石桩极限承载力计算式．指出了用碎石桩加固软土地基效果比较明显．但用碎石桩来加固土的变形模量大于8MPa的地基，加固效果十分有限．最后，通过工程实例，将计算结果与实验结果作了对比．     

In-plane bending of a beam resting on a rigid rough foundation

Summary The bending of a finite-length beam that lies on a rigid, rough, flat foundation and interacts with it in accordance to the dry friction law is considered. Loading by bending moments applied at the ends of the beam is studied in detail. The problem is found to be a self-similar one. For small moments, the central part of the beam remains undeflected, and the problem reduces to the solution of an infinite system of algebraic equations. Large moments deflect the entire length of the beam, and the problem partly loses its self-similarity. In this case, the problem reduces to the solution of a successively decreasing number of ordinary differential equations along with some algebraical equations. The solution for the latter case provides initial conditions for the former one. This permits to obtain a solution for any value of the moment. Received 5 November 1996; accepted for publication 27 January 1997     

大型桩基础动力特性及地震反应分析

本文针对大型桩基础的地震反应问题,以上海“东方明珠”广播电视塔桩基础为工程背景,采用梁单元模拟桩的运动,用8节点块体单元对土体进行离散,通过凝聚法消去桩（梁）节点的转动自由度,建立了“东方明珠”电视塔中央部位桩基础的三维有限元分析模型,对桩基础的动力特性进行了计算与分析。在此基础上,以文献[1]根据地震危险性分析和土层反应分析后获得的桩尖处加速度时程作为输入,对桩基础的动力反应进行时程分析,探讨了桩－土动力相互作用和上部结构等因素对地震地面运动和桩承台反应的影响,得到了一些有应用价值的结果。     

Non-linear behaviour of free-edge shallow spherical shells: Effect of the geometry

Non-linear vibrations of free-edge shallow spherical shells are investigated, in order to predict the trend of non-linearity (hardening/softening behaviour) for each mode of the shell, as a function of its geometry. The analog for thin shallow shells of von Kármán's theory for large deflection of plates is used. The main difficulty in predicting the trend of non-linearity relies in the truncation used for the analysis of the partial differential equations (PDEs) of motion. Here, non-linear normal modes through real normal form theory are used. This formalism allows deriving the analytical expression of the coefficient governing the trend of non-linearity. The variation of this coefficient with respect to the geometry of the shell (radius of curvature R, thickness h and outer diameter 2a) is then numerically computed, for axisymmetric as well as asymmetric modes. Plates (obtained as R→∞) are known to display a hardening behaviour, whereas shells generally behave in a softening way. The transition between these two types of non-linearity is clearly studied, and the specific role of 2:1 internal resonances in this process is clarified.     

基于集对分析联系数的区间数型多属性决策投影模型及其在基坑支护方案评价中的应用

多属性决策时因掌握的信息有限,加之问题本身的复杂性、不确定性以及人类思维的模糊性,其属性的精确值往往难以获取,常用区间数形式表示针对多属性决策中各指标区间数不能直接进行大小比较的问题,提出一种基于集对分析联系数的区间数型多属性决策投影模型.模型用备择方案在理想方案上的投影进行集结,根据区间数的误差分布形式,沟通区间数与联系数的关系,根据a+bi型联系数大小比较法则,综合评价方案优劣.以某大厦基坑支护拟用的4种方案优化选择为例,说明方法的应用与模糊优化理论模型和灰色物元分析优化模型进行了对比,得到的结果一致.     

样条边界元法分析圆形基础板非线性非光滑接触

本文用样条边界元法分析轴对称圆形基础板的非线性非光滑接触。除事先给出外力与地基表面位移的对应关系外,地基的模型、板的厚薄(Reissner/Kirchhoff型)和外荷载沿径向的分布均可是任意的。文中将地基反力看作板的外载,对变量沿径向采用不等距祥条插值,并用无地基效应的板基本解。算例表明本文方法只要用少量自由度,便可得到令人满意的结果。     

考虑地基-结构-散粒体相互作用时贮仓结构的静、动力研究[Ⅱ]--有限元分析

对贮仓结构的静、动力问题进行了系统的分析计算：考虑到地基—结构—散粒体间的相互作用，引入新的计算模式，对不同地基上的贮仓结构模型进行了系统的有限元静、动力分析计算，并与作者所完成的试验结果进行了比较。结果表明，所提出的计算模式及有限元计算模型是正确的。