波纹管在子午面内整体弯曲的半解析有限元法

波纹管是一类子午线呈波纹状的旋转壳，作为弹性敏感元件和柔性连接件在航空仪表和管道工程中起着重要的作用。长期以来基于壳体理论的分析多限于轴对称变形问题。最近，虽然出现了以柔性旋转壳理论为基础的解决波纹管整体弯曲问题的解析解和数值解，但仍有必要通过别的途径加以验证和补充。为些，本文提出了波纹管在子午面内整体弯曲的半解析有限元解。把波纹管近似成有限个截顶锥壳的组合体，每个截顶锥为一个单元。将位移分量沿纬线用Fourier级数展开，沿子午线用多项式插值，截锥单元因此化为2节点的直线单元，每节点为4个自由度。显然，对于同等的RAM和CPU，线单元可比其他单元划得更小。于是，利用小单元条件，将一个单元内的壁厚和平行圆半径近似地当作不变量，给出了用显式表示的单元刚度矩阵，为直观分析结构参数对波纹管力学性能的影响提供了方便。在此基础上，计算了Ω型，C型和U型波纹管在纯弯矩作用下的变形和应力分布，所得结果和已有的解析解，数值解相符。本法不限于波纹管的计算分析。     

用传递矩阵法求解组合壳轴对称变形

本文用细环壳,锥壳的一般解构成传递矩阵,可以求解波纹管一个单元内的内力与位移.运用这一方法使解变得更加简洁.     

波纹管在内压作用下柱失稳临界压力的计算

 讨论了波纹管在内压作用下的柱失稳问题，将波纹管等效成圆 柱壳，证明了该柱壳在内压作用下失稳的临界压力与在轴向均布压力 作用下失稳的临界压力相等，利用作者对波纹管整体弯曲问题的研究 成果确定等效柱壳的抗弯刚度，给出了波纹管在内压作用下柱失稳临 界压力的计算公式. 由对前人实验的观察分析得出波纹管呈弹性柱失 稳的条件为其长细比大于1，在此条件下本文的计算结果和前人的实 验结果相一致.     

U型波纹管及相关结构环向屈曲的有限元分析(Ⅰ)--基本方程及环板的屈曲

U型波纹管是现代管道系统中最常见的一种位移补偿器 ,它由环板和具有正、负Gauss曲率的半圆环壳组成 ,在管道所传输的介质的压力作用下会发生屈曲。其中环向屈曲最为复杂 ,精确的理论分析非常困难 ,有限元分析也不多见。作者在分析前人工作的基础上 ,以圆环壳段为单元 (特定的旋转壳段单元 ,能自动退化成环板单元 ) ,限于弹性范围和线性化特征值问题 ,对介质压力作用下U型波纹管及其相关结构 (圆环板、圆环壳、半圆环壳 )的环向屈曲问题进行了分析。考虑了结构屈曲前的弯曲 ,计及压力的二次势能 ,导出的应力刚度矩阵和载荷刚度矩阵是非对称的。全部工作分为三部分 :(Ⅰ )基本方程 ,环板的屈曲 ;(Ⅱ )圆环壳、半圆环壳的屈曲 ;(Ⅲ )波纹管平面失稳的机理。本文为第一部分 ,除推导公式外 ,对不同边界和不同内外径之比的环板在径向均匀压力作用下的环向屈曲进行了计算 (轴对称的径向屈曲作为特例得到 ) ,给出了前屈曲应力分布、临界载荷及相应的屈曲模态 ,并将临界压力的值与前人基于vonK偄ｒｍ偄ｎ大挠度板的精确解进行了比较 ,吻合良好。     

细环壳钱伟长方程的精确解

1979年钱伟长对细环壳进行了非常系统的研究,推导出一个细环壳复变量方程,并给出了一个用连分式表达的级数精确解,但没有提及这个级数解是否可以化成为已知的特殊函数.本文利用一个线性变换,把细环壳的钱伟长方程变换成Mathieu方程,用Mathieu函数表示了问题的解,这样就把钱伟长的连分式解与Mathieu函数联系了起来.由于Mathieu函数是已知的特殊函数,这里的工作可为今后有关的细环壳具体计算带来方便.     

U型波纹管及相关结构环向屈曲的有限元分析(Ⅲ)--波纹管平面失稳的机理

波纹管无论是在内压还是在外压作用下都会发生环向屈曲或平面失稳,问题很复杂至今未得到妥善解决。本文首先指出了现行的有关“塑性铰”概念的某些不足之处,然后按文[8]的有限元法(考虑了屈曲前的弯曲和屈曲时载荷的转动并按线性化特征值问题处理)对波纹管的环向屈曲进行了计算,并与前人的有关实验进行了对比分析,在此基础上解释了波纹管平面失稳的原因和发展过程。     

线载荷作用下圆柱壳环向弯曲变形的研究

通过引入单三角级数形式的位移函数, 求解了法向任意分布载荷作用下对 边简支时圆柱壳的环向弯曲问题, 把线载荷近似为微元矩形区的分布载荷, 推导出了线 载荷作用下圆柱壳的环向弯曲变形计算式, 并给出了线载荷为均布和线性变化时的具体解. 计算表明, 该种边界约束条件下圆柱壳的环向弯曲变形位移分布场的理论计算结果与有限元 分析结果基本吻合.     

正交各向异性功能梯度圆柱壳的应力分析及材料剪裁

假设正交各向异性功能梯度材料的弹性系数沿圆柱壳的径向按照任意连续函数变化,采用应力函数法和加权残值法导出了圆柱壳在非轴对称载荷作用下应力分析的一种新的数值解.建立了圆柱壳内部应力状态给定时材料剪裁问题的基本方程,提出了实现圆柱壳内部一种特殊的应力分布时所需要的材料弹性系数沿径向变化的解析解.通过数值算例验证了本文所导出的应力分析的数值解的正确性和收敛性,分析了弹性系数沿径向的变化对圆柱壳内部应力分布的影响.数值算例还给出了实现圆柱壳内部环向应力和切应力沿径向均匀分布时功能梯度材料的弹性系数沿径向的三种不同变化形式.所得研究结果可为正交各向异性功能梯度材料圆柱壳的设计提供一定的参考,同时材料剪裁的解析结果也可作为其他数值方法计算结果验证的考题.     

U型波纹管及相关结构环向屈曲的有限元分析(Ⅱ）--半圆环壳的屈曲

环壳不仅是U型波纹管的一个组成部分，更是一类重要的结构，在航天、核能和海洋工程中有重要的应用，其屈曲是人们关注的问题之一，其中对半圆环壳的分析还较为少见。本文采用文[7]的有限元法（考虑了屈曲前的弯曲和屈曲时载荷的转动并按线性化特征值问题处理）计算了正Gauss曲率半圆环壳在均匀外压作用下的屈曲，将所得结果与已知的近似解进行了对比、并讨论了其中的差异。本文除了给出临界载荷和子午线的屈曲模态外，还给出了前屈曲弯曲应力分布，以便仔细了解屈曲问题。     

以环肋加强的圆柱壳在液压作用下的总体稳定

本文给出了以环肋加强的圆柱壳在液压作用下屈曲形态和临界载荷的计算方法.根据组合结构的方法,建立了一组肋和肋间壳段的稳定微分方程组.在肋的截面高度、偏心距、截面总面积ΣF_r、总抗弯刚度ΣE_rI_(G_ra)不变的前提下,而使环肋的数目趋于无穷大,从而得到了作为组合的环肋加强壳的初次近似的正交各向异性壳模型及其弹性关系.可以进一步寻求方程组的级数解,其首项代表零阶近似解,亦即上述等效正交各向异性壳的解,其余各项代表逐次渐近的修正解,或等效壳和真实的环肋加强组合壳解的误差.根据误差的估计可以给出简化为等效各向异性壳的判据.最后给出了算例并与其它作者的方法进行了比较.计算结果表明与实验符合得很好.     

Calculation of stresses and deformations of bellows by initial parameter method of numerical integration

By reducing the boundary value problem in stress analysis of bellows into initial value problem, this paper presents a numerical solution of stress distribution in semi-circular arc type bellows based upon the toroidal shell equation of V. V. Novozelov^[8]. Throughout the computation, S. Gill’s method^[1O] of extrapolation is used. The stresses and deformations of bellows under axial load and internal pressure are c-alculated, the results of which agree completely with those derived from the general solution of Prof. Chien Wei-zang^[1-4]. The extrapolation formula presented in this paper greatly promotes the accuracy of discrete calculation.The computer program in BASIC language of Wang 2200 VS computer is included in the appendix.     

轴对称载荷下正交异性圆环壳的一般解

本文导出了在Kirchhoff假设下受轴对称载荷时、材料正交异性的圆环壳的复变量方程,给出了该方程的一般解,该解可用于α=a/R<1,其中a为环壳截面的半径,R为环壳的总体半径,文中并举例说明其应用,结果表明本文所提出的解是很有效的。     

环壳弹性静力及自由振动问题的弱形式求积元分析

基于旋转薄壳理论, 采用求积元法, 建立了求积元法求解环壳问题的单元列式, 并对圆环壳、椭圆环壳的静力及自由振动问题进行了分析. 数值算例与精确解及有限元结果相对比, 证明了求积元法分析此类连续环壳问题的准确和高效性. 同时, 分析结果表明, 椭圆环壳长短轴的比值k对壳体的受力特性及求积元法的收敛率有显著的影响.     

On second order asymptotic solutions of axial symmetrical problems ofr>0 thin uniform circular toroidal shells with a large parametera 2/R0h

According to the classical shell theory based on the Love-Kirchhoff assumptions, the basic differential equations for the axial symmetrical problems of r>0 thin uniform circular toroidal shells in bending are derived, and the second order asymptotic solutions are given for r>0 thin uniform circular toroidal shells with a large parameter a²/R₀h. In the resent paper, the second order asymptotic solutions of the edge problems far from the apex of toroidal shells are given, too. Their errors are within the margins allowed in the classical theory based on the Love-Kirchhoff assumptions.     

Nonlinear deformation analysis of a U-shaped bellows with varying thickness

Summary The nonlinear integral equations for a U-shaped bellows with compressed angle and varying wall-thickness are derived according to the simplified Reissner theory of large deflection for revolution shells and integral-equation method. The iteration procedure for nonlinear analysis is developed by means of the integral equation iteration in conjunction with the gradient method. Numerical solutions for a U-shaped bellows under the action of axial compression force and internal pressure are obtained, which are compared with previous theories and experiments. The present results are shown to have a good accuracy, and may be applied directly to the design of bellows. Received 13 November 1997; accepted for publication 6 July 1999     

Vibrations of Reinforced Cylindrical Shells with Initial Deflections under Nonstationary Loads

The paper addresses dynamic problems for discretely reinforced shells with initial deflections. Timoshenko theory is used. A numerical method of solving such problems is developed and theoretically justified. Numerical results for a specific problem are presented__________Translated from Prikladnaya Mekhanika, Vol. 41, No. 1, pp. 60–68, January 2005.     

An approximation to red blood cells with a model of three-center-combined shells

Red blood cells present a biconcave shape and bear an inner pressure (osmotic pressure) when they are in the static state. In this paper, a model of “three-center-combined shells”, which consists of two spherical shells and a toroidal shell, is employed to describe the geometric shape of red blood cells. Surface area and volume of the combined shells model are very close to those measured from experiment. The stress distribution in the cell membrane is formulized as a closed form according to the Novozhilov's theory of the three-center-combined shells. Calculating results in terms of Novozhilov's formula give a good agreement with the numerical results given by ABAQUS when using actual measurements. It is concluded that the combined shells model can well approximate to the biconcave structure of red blood cells. In addition, stress calculation shows that the membrane of biconcave red blood cells can carry bending moments, and the moments reach a maximum value in the vicinity of joint line of the spherical shell and the toroidal shell in the combined shells model.     

FINITE ELEMENT DISPLACEMENT PERTURBATION METHOD FOR GEOMETRIC NONLINEAR BEHAVIORS OF SHELLS OF REVOLUTION OVERALL BEDING IN A MERIDIONAL PLANE AND APPLICATION TO BELLOW (Ⅱ)

The finite-element-displacement-perturbation method (FEDPM)for the geometric nonlinear behaviors of shells of revolution subjected to pure bending moments or lateral forces in one of their meridional planes (Ⅰ) was employed to calculate the stress distributions and the stiffness of the bellows. Firstly, by applying the first-order perturbation solution (the linear solution)of the FEDPM to the bellows, the obtained results were compared with those of the general solution and the initial parameter integration solution proposed by the present authors earlier, as well as of the experiments and the FEA by others.It is shown that the FEDPM is with good precision and reliability, and as it was pointed out in (Ⅰ) the abrupt changes of the meridian curvature of bellows would not affect the use of the usual straight element. Then the nonlinear behaviors of the bellows were discussed. As expected, the nonlinear effects mainly come from the bellows ring plate,and the wider the ring plate is, the stronger the nonlinear effects are. Contrarily, the vanishing of the ring plate, like the C-shaped bellows, the nonlinear effects almost vanish. In addition, when the pure bending moments act on the bellows, each convolution has the same stress distributions calculated by the linear solution and other linear theories, but by the present nonlinear solution they vary with respect to the convolutions of the bellows. Yet for most bellows, the linear solutions are valid in practice.