壳体简史

壳体可以简单地看作成弯曲的板,它具有比较优越的力学特性,本文简单介绍了薄壳壳体和旋转壳理论的发展历史,同时评述了壳体解析理论的复变量方法和位移场方法.     

轴对称圆环壳的基本解的完全渐近展开

1.序言轴对称圆环壳的复变量方程有多种形式,经[1]修改的Tlke 方程为x″+x(iμq_1+q_2)=τ(1)式中,非齐项τ()的表达式取决于载荷沿小圆的分布形式     

环壳屈曲的渐近解

本文提出分析圆环壳屈曲的一种渐近解析方法,由Sanders非线性平衡方程和壳中面变形协调方程推导出静水外压下环壳的稳定方程,求出了方程的渐近解,理论计算的临界压力值与Fishlowitz的实验结果符合良好,并研究了屈曲前非线性变形对临界载荷的影响。     

旋转薄壳稳定性的数值分析

用数值方法求解旋转薄壳稳定性问题的主要困难在于:对任意应力状态下的旋转壳进行稳定性分析,各谐波间彼此耦合,致使方程推导的复杂性和计算量都增大,本文采用[3]所提供的单元及经典的能量判据,在最一般的提法下构造了有限元列式,详细讨论了耦合情况,利用本文方案编制程序并进行了许多算例分析,结果令人满意。同时表明在某些情况下边界条件对临界载荷的影响很大,这可以部分地解释古典稳定性分析结果与实验偏差较大以及实验数据分散的原因。     

双曲扭壳力学性能分析

本文从扁壳的挠度和内力函数混合方程出发,得到了双曲扭壳的重三角级数表示的解析结果.分析了扭率对该扭壳的刚性影响,提出关于扭率判别条件上界和下界的概念:当扭壳扭率小于判别值的下界时,扭壳可视为矩形平板;当扭率大于判别值的上界时,则可忽略扭壳的平板效应,视其为无矩状态.对于这两种情况计算误差控制在百分之一以内.     

一种大变形曲壳单元

本文用壳中面节点的位移矢量和节点处壳中面单位法线矢量的矢端位移矢量构造了一种大变形曲壳单元,它是大变形曲壳单元的一般形式,能包括已有的大变形曲壳单元,且公式最简单,计算中采用的载荷增量或位移增量可以很大。     

任意叠层球壳内的应力波传播

提出一种有效求解方法,求解了任意叠层球壳在动载荷作用下的应力波传播。首先,利用有限Ｈａｎｋｅｌ变换和Ｌａｐｌａｃｅ变换求解了每一单层的弹性动力学解。然后,利用叠层球壳的内、外边界条件和层与层之间的连接条件确定每一单层解中的待定常数。从而,我们可以得到应力波在叠层球壳内传播的精确解。最后,我们计算了在一个突加内压作用下的两层球壳（Ｓｔｅｅｌ／Ａｌ）和三层球壳（Ｓｔｅｅｌ／Ａｌｌｏｙ／Ａｌ）内的应力波传播。求解过程和计算结果表明文中提出的求解方法是简便可行的。     

板壳非线性问题的曲壳有限单元法

本文基于总体Lagrange坐标描述法,采用Kirchhoff应力张量定义和Green应变张量定义,导出了分析板壳非线性问题的曲壳有限单元法。通过引入新的单元几何非线性关系,本文方法可用于分析板壳的大挠度大转角情况。由于采用了材料本构关系的修正子增量形式,提高了有限单元的分析计算精度。本文采用增量—拟牛顿—子增量迭代技术求解板壳的荷载一位移曲线,与传统迭代方法相比大大提高了计算效率。此外,对于板壳任意边界条件的形成和任意初始形状的考虑问题,本文分别导出了罚单元法和局部坐标转换法予以处理。经计算比较,证明本文方法可以有效地用于板壳的弯曲、屈曲及屈曲后性态和极限强度等问题的非线性分析。     

球面扁壳的比拟解法

在扁壳的工程实用理论中,除薄壳一般理论中所采用的基本假设外,还采用了下列两个假定:(1)曲面上线素的二次式ds~2=A~2dα~2+B~2dβ~2与高斯曲率无关;(2)壳体上的切向荷载可不予考虑.对于中曲面为部分球面而覆盖平面为圆形或环形的球面扁壳,引用上述假设,能满足工程实用上的要求。文中限于讨论这一类球面扁壳,并建议一个较为有效的实用解法--比拟法,因而,使问题的求解大为简化. ...     

Equation in complex variable of axisymmetrical deformation problems for a general shell of revolution

In this paper, the equation of axisymmetrical deformation problems for a general shell of revolution is derived in one complex variable under the usual Love-Kirchhoff assumption. In the case of circular ring shells, this equation may be simplified into the equation given by F.Tölke(1938)^[3], R.A.Clark(1950)^[4]and V.V.Novozhilov(1951)^[5]. When the horizontal radius of the shell of revolution is much larger than the average radius of curvature of meridian curve, this equation in complex variable may be simplified into the equation for slander ring shells. If the ring shell is circular in shape, then this equation can be reduced into the equation in complex variable for slander circular ring shells given by this author (1979)^[6]. If the form of elliptic cross-section is near a circle, then the equation of slander ring shell with near-circle ellipitic cross-section may be reduced to the complex variable equation similar in form for circular slander ring shells.     

Closed-form solution for the contact problem of reinforced pin-loaded joints used in glass structures

In a typical pin-loaded joint used to assemble glass plates, the hole in a glass plate is reinforced by a steel ring glued to the glass plate via a soft resin layer. Thus, the ring is in direct contact with the steel bolt and prevents the glass plate from high stress concentration. This paper proposes an analytical approach to solving the resulting conforming contact problem. The strain and stress fields inside the resin layer are first determined by exploiting the fact that the stiffness of the material constituting it is much smaller than the stiffness of steel and glass. After finding the relevant Green functions for the ring and pin, the frictionless contact between them is then formulated in terms of an integral equation with a Fourier series as the kernel. This integral equation is solved by neglecting the terms of high orders and transforming it into the Cauchy singular integral equation. The derived analytical results for the contact pressure and angle are finally compared to and validated by those obtained by the finite element method.     

Flow stability of a flat plastic ring with free boundaries

The problem of two-dimensional unstable flow of an ideally plastic ring acted upon by internal pressure is formulated. The determination of the law of motion for the boundaries and of the time change of pressure is reduced to an ordinary nonlinear differential equation of the second order. For this equation a particular solution of the Cauchy problem is determined; this corresponds to a widening of the ring boundaries with a negative acceleration. For the field of initial velocities an estimate from above is available, expressed in terms of the original parameters. The very particular unstable flow obtained for an ideally plastic ring is also investigated with respect to stability to small harmonic perturbations of the velocity vector, the pressure, or the boundaries of the ring. It is shown that the fundamental flow is stable irrespective of the wave number. This result has been obtained by assuming that the inertial forces in the perturbed flow are small compared to the lasting ones.Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, No. 2, pp. 94–101, March–April, 1975.     

Axisymmetry problems of ring shells under arbitrary distributed loads

Extending Novozhilov's transformation, this paper simplifies successfully the axisymmetry problems of ring shells under arbitrary distributed loads, and the equation of the problems in complex form which is similar to Novozhilov's is obtained. The particular solution is obtained. Combining with Chien's general solution of homogeneous equation, this paper gives the general solution for the general symmetry problems of ring shells. Various examples of useful loads and closed ring shells are discussed respectively.     

Evolution of a Viscous Vortex Ring

The velocity field inside a viscous vortex ring and its overall velocity are obtained on the basis of an existing solution of the Stokes equation for the vorticity in a moving coordinate system. It is shown that these characteristics of the motion relate the results obtained earlier for limiting times and are confirmed by the experimental data. The effect of the initial Reynolds number on the development of the vortex ring is analyzed by constructing entrainment diagrams.     

Natural frequencies and modes of out-of-plane vibrations a fixed ring

The natural frequencies and modes of a flexible elastic ring fixed at one point are determined numerically by solving an eigenvalue problem for the differential operator of the equation of its motion. The ring models a large circular antenna that slowly expands under zero gravity. Bending and torsional vibrations in a plane perpendicular to the antenna plane are studied     

Long-wave instability of a vortex ring

The instability of barrel-shaped vibrations of a vortex ring in an ideal fluid is investigated. These vibrations, stable for a vortex ring with a piecewise-uniform vorticity profile, appear to be unstable for a vortex ring with a smooth vorticity profile. The instability growth rate is found on the basis of the energy balance equation determining the energy transport from perturbations with negative energy in the critical layer to perturbations with positive energy in the rest of the flow. The curvature of the vortex ring, by virtue of which the perturbations with energies of different signs appear to be connected, plays a prominent role in the mechanism under consideration.Moscow. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 6, pp. 72–78, November–December, 1995.     

Slope modulation of ring waves governed by two-dimensional sine–Gordon equation

A theory of slope modulation of waves governed by the two-dimensional sine–Gordon equation is proposed. A large time asymptotic solution describing the slope modulation of trains of ring kinks is obtained. The comparison with the numerical solution of two-dimensional sine–Gordon equation shows excellent agreement.     

刚粘塑性圆环受法向冲击时的动力屈曲

本文研究刚粘塑性圆环受法向冲击时的动力屈曲，文中考虑了冲击过程中圆环厚度的变化，环向力的变化以及基本变形速度的变化。通过用数值方法求解扰动运动微分方程，结果表明，当规定了临界放大函数后，仅当冲击速度位于某一范围之内时，才会发生动力屈曲。     

The region of possible motion of the planar circular restricted three-body problem under the influence of a ring

This paper discusses the region of possible motion of planar cir-cular restricted three-body problem that one primarg in them has aring and it gives the equation of motion of the third body.Some re-sults are as follows:(1)The location of equilibrium points depends on the parameter μof the system;inner radius a and outer radius b of the ring;the dis-tance l between two primaries;and the ratio θ of the mass of the ringwith the sum of masses of the primary which has the ring and the ringitself.when α,b,l,θare constant.the number of the equilibriumpoints varies with μ,it is five at most and three at least.Besideseach triangular point and two primaries form an isosceles triangle.(2)When α.b.l.θ are constant,we give a range of μ.If μ isin this range.the structure of the region of possible motion of thethird body is the same as that of general planar circular restrictedthree-body problem.