Doubly curved shallow shells with rectangular base elastically supported by edge arched beams and tie-rods (I)

The equations of equilibrium of shallow shells with rectangular base elastically supported with edge arched beams are obtained through the variational principle together with corresponding boundary conditions and corner conditions. It is assumed that edge arched beams are of narrow plate form, so that only the rigidities in their own planes are taken into consideration, torsional rigidities and bending rigidities out of their own planes are neglected. In this paper, two kinds of corner conditions are discussed. First of these is pinned corner conditions. Second of these is simply supported corner conditions, such that the corner can be moved freely in horizontal directions. The former corresponds to the conditions of those with heavy tension beams, in which the tension rigidities of the rods can be assumed infinite. The latter corresponds to the conditions of elastically supported edge arched beams without tension rods. In the former case, the edge tangential displacement of shallow shells is assumed to be zero everywhere, so that the vertical displacement of the edge arched beams gives the only elastic supported forces. This kind of supporting conditions is a good approximation for practical roof design.In this paper, the solutions of the problem of shallow spherical shell of square base supported elastically by edge arched beams and tie-rods under the conditions, such that the corners are restricted, are solved by the method of double trigonometric series. The edge conditions are integrated along their respective edge, and the conditions at corner are satisfied by proper choices of integral constants. The integrated edge conditions are then used to determine the unknown constants in the double trigonometric series. The result of this paper gives the tension in the tie-rods directly, which is an important quantity in the shell roof design practice.The method of integrated form of boundary conditions used in this paper in general is useful for the treatment of problem of plates and shells elastically supported by edge frames and tie-rods or by other means.This paper also gives the results of numerical calculation based upon the method of double trigonometric series on the problem of shallow spherical shell with square bases elastically supported by arched beams. The corner are pinned supported or simply supported. The calculated results for =11.5936 show that the trigonometric series converges rapidly. The effect of elastic deformation in the arched beams to the components of membrane tensions, moments, and deflections of the shell are given.     

旋转壳局部几何缺陷对其系统固有频率的影响

本文提出了分析具有几何缺陷旋转壳动力特性的初位移法,利用本方法本文对一般几何缺陷的动力影响进行了分析,並对轴对称几何缺陷的问题进行了计算。计算中考虑了两种边界条件:一种是固定支承的;一种是弹性支承的。结果表明,对于本文的特定问题,壳体局部几何缺陷使系统的基频升高。     

The effect of transverse shear deformation on stress concentration factors for shallow shells with a small circular hole

Simplified equations are derived for the analysis of stress concentration for shear-deformable shallow shells with a small hole.General solutions of the equations are obtained,in terms of series,for shallow spherical shells and shallow circular cylindrical shells with asmall circular hole.Approximate explicit solutions and numerical results are obtianed forthe stress concentration factors of shallow circular cylindrical shells with a small hole onwhich uniform pressure is acting.     

The effect local geometric imperfections of rotational shell on its natural frequencies and models

In this paper, an additional stiffness matrix of meridional geometric imperfections was formed by considering the geometric imperfections as initial displacements based on reference [7]. Then, natural frequencies and models of rotational shell with symmetric geometric imperfections were analysed by perturbation method. From the computed example, it was known that the effect of geometric imperfections of frequencies is to increase them, and the larger the range of imperfection, the more the frequencies would be increased.     

横向剪变形对具有一小圆孔的浅壳应力集中系数的影响

本文导出了分析计及横向剪变形的浅壳小孔应力集中问题的简化方程.对浅球壳和圆柱壳带一小圆孔的情况,获得了方程的级数形式通解.对均匀内压作用下的圆柱壳,求得了小圆孔边上应力集中系数的近似显式解,并计算了数值结果.     

具有弹性边拱及拉杆支承的双曲扁壳(一)

本文利用变分原理建立了具有弹性边拱及拉杆支承的双曲扁壳的平衡方程式及相应的边界条件和角点条件,这里假定边拱只在其本身平面内有刚度,边拱的扭转刚度和垂直于其平面的弯曲刚度都略去不计,本文研究了不许自由外伸的角点铰支条件,以及能够自由外伸的角点简支条件,前者相当于周边有拉杆限制角点外伸位移的情况,后者相当于周边无拉杆的情况.对于前者而言,本文近似地假定边拱沿弧方向的抗拉伸刚度为无穷大,亦即假定扁壳的边界切向位移为零,边拱只通过其垂直于扁壳平面的弯曲来产生弹性支承的作用.这些支承条件是近似地符合当前双曲扁壳屋盖的设计条件的.本文利用双三角级数解法求得具有弹性边拱及拉杆支承的方形底球面扁壳在自重载荷下的正确解.其特点在于先将边界条件积分处理使先满足角点条件,然后求解平面应力微分方程使满足积分后的边界条件.本文的结果直接给出拉杆中的拉力,对于具体设计问题是有用的.本文提出的积分形式的边界条件方法,对于弹性支承的边界问题在板壳方面的应用中是有它的普遍实用意义的.本文还给出了具有弹性边拱支承的方形底扁球壳的数值结果,角点为铰支或简支的,选取的参数值为λ=11.5936.计算结果表明级数收敛很快,并得出了边拱的弹性变形对壳体内力、内力矩及挠度分布规律的影响.     

分析土壤半无限域的一种有限层方法(Ⅱ)——几种特殊情形及算例*

本文就几种特殊情形用作者所研究的一种用于横观各向同性体动力学的有限层法作了简化分析,分别讨论了二维问题、轴对称问题以及静力问题,并推广到介质具有粘性性质的情形.对于轴对称情形,本文还给出两个算例,表明作者所研究的有限层法用于分析半无限域层状土壤介质是可行的,因而为研究土壤与结构相互作用问题提供了一条新途径.     

On the circular footing plates on two-parameters foundation under arbitrary loads

Modelling soils by two-parameter foundation model, this paper calculates the distributions of displacements of circular footing plates on soils and reactions of soils under arbitrary loads using semi-analytical finite element method. And it improves F.Z. Vlazov’s solution in the case of axisymmetry. The results agree well in comparison with those by F E M. At the same time, the boundary conditions of circular plates on soils are discussed.     

双参数地基上受任意载荷的环形基础板

本文以双参数模型模拟土壤,用半解析有限元法计算了土壤上受任意载荷的环形基础板的位移及土壤反压力分布,并在轴对称情况下改进了Vlazov的解[5],与有限元解进行对比,二者结果是一致的.同时还对土壤上环板的边界条件进行了讨论.