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1.
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。  相似文献   

2.
研究了功能梯度材料扁薄锥壳在横向非均匀升温场中的几何非线性大变形问题.基于von Kármán几何非线性理论推导出了以中面位移为基本未知量的功能梯度扁薄锥壳在横向非均匀热载荷作用下的轴对称大挠度控制方程.采用打靶法数值求解所得非线性常微分方程边值问题,得到了锥壳的大挠度弯曲变形数值解.给出了锥壳的变形与其形状参数、载荷和材料参数等变化的特征关系曲线,分析和讨论了温度参数和材料梯度变化参数对变形的影响.  相似文献   

3.
1.引言圆底扁锥壳是工程中的常见壳型结构,与扁球壳相比,对圆底扁锥壳的大挠度理论和实验研究都不多,仅有少数文献进行过研究,文献[1]和[2]用的是伽辽金方法,文献[3]用摄动法,文献[4]用修正迭代法,它们分别在壳体几何参数λ不大的范围内确定了失稳临界载荷。由于这些方法本身存在的困难,所得解答当λ稍大时就不准确了。本文利用牛顿-样条函数方法对均布压力作用下圆底扁锥壳(图1)的非线性弯曲和稳定性进行研究,获得一些有意义的结果。2.基本方程及其求解考虑均布压力作用下圆底扁锥壳的轴对称非线性方程:  相似文献   

4.
陈春红  朱卫平 《力学季刊》2002,23(2):203-209
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。  相似文献   

5.
刘东 《应用力学学报》1995,12(1):104-108
导出了双参数弹性地基上圆底扁球壳在均布荷载作用下非线性弯曲问题的初参数积分方程,并求得了数值解。  相似文献   

6.
用初参数法解C型波纹管在子午面内整体弯曲   总被引:8,自引:1,他引:7  
朱卫平 《力学季刊》2000,21(3):311-315
波纹管是一种呈波纹状的管形薄壁结构,作为弹性敏感元件、密封元件和位移补偿器,在现代工业、国防和民用设备中的应用日益广泛.波纹管的计算,特别是在非轴对称受力和变形方面亟待完善.本文讨论了C型波纹管在子午面内整体弯曲的应力分布和端面角位移.从柔性圆环壳在子午面内整体弯曲的复变量方程出发,化边值问题为初值问题,用S.Gill法,得到了该波纹管的数值解,适用于0<α<1的范围.通过3个例子,将本文的数值解和已有的细环壳一般解(解析解)作了比较.结果表明,两者基本一致,并且,当环壳较细(α较小)时,两种计算结果更为接近.  相似文献   

7.
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。  相似文献   

8.
本文在作者关于扁壳基本解的工作基础之上,以位移法建立了扁壳各物理量的边界积分方程,并讨论了边界元求解过程中的一些具体数值问题。得到了较为满意的计算结果。  相似文献   

9.
波纹壳的摄动解法   总被引:16,自引:2,他引:14  
袁鸿 《应用力学学报》1999,16(1):144-148
应用扁锥壳的非线性大挠度理论,研究了在均布载荷和中心集中载荷下,具有光滑中心的锯齿形和梯形波纹壳,采用摄动法和幂级数方法,得到了波纹壳的弹性特征。本文的解答符合实验结果。  相似文献   

10.
本文采用弹性圆锥扁壳中心无量纲振幅和壳体母线的倾角为参数,将挠度、应力函数的导数以及自由振动频率展开为双参量的幂级数形式,用直接摄动法获得各级递推线性偏微分方程,应用变分法求得各级递推方程的近似解答,从而给出弹性圆锥扁壳非线性自由振动频率的基本公式。  相似文献   

11.
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  相似文献   

12.
In this paper, a theory for non-linear thermal stability of open bimetallic shallow shells of revolution under a uniform temperature field is developed. To apply the theory to the particular case of some elastic elements in precision instruments, this paper discusses two important kinds of shells, the bimetallic shallow spherical shell with a circular hole at the center and the bimetallic truncated shallow conical shell. The more accurate solutions are obtained by the modified iteration method. All results are expressed in curves which may be applied directly to the design of the elastic elements.  相似文献   

13.
IntroductionThetheoryofflexibleshells,establishedbyE .L .Axelrad[1,2 ]( 1 976,1 987) ,isasimplifiedtheoryforthinshells,inwhichshellsofrevolutionareformulatedinmeridionaldirectionbybendingtheoryoftheshellsandbythemembranetheoryinthecircumferentialdirection .TheAxelr…  相似文献   

14.
The overall bending of circular ring shells subjected to bending moments and lateral forces is discussed. The derivation of the equations was based upon the theory of flexible shells generalized by E.L. Axelrad and the assumption of the moderately slender ratio less than 1/3 (i.e., ratio between curvature radius of the meridian and distance from the meridional curvature center to the axis of revolution). The present general solution is an analytical one convergent in the whole domain of the shell and with the necessary integral constants for the boundary value problems. It can be used to calculate the stresses and displacements of the related bellows. The whole work is arranged into four parts: (Ⅰ) Governing equation and general solution; (Ⅱ) Calculation for Omega-shaped bellows; (Ⅲ) Calculation for C-shaped bellows; (Ⅳ) Calculation for U-shaped bellows. This paper is the first part.  相似文献   

15.
This paper follows the work of [1,2]. There are some progress in dealing with moderately small rotations (the squares of rotation angles are the order of magnitude of strains) of middle surface normals of inside and outside ring shells and compressed angle of bellows. Calculation results agree with experiments well. To bellow design, the method given in this paper is of practical value and the discussion of the influence of compressed angle on characteristic relation is helpful.  相似文献   

16.
This paper follows the work of[1,2].There are some progress in dealing withmoderately small rotations(the squares of rotation angles are the order of magnitudeof strains)of middle surface normals of inside and outside ring shells and compressedangle of bellows.Calculation results agree with experiments well.To bellow design,the method given in this paper is of practical value and the discussion of the influenceof compressed angle on characteristic relation is helpful.  相似文献   

17.
IntroductionTheplatesandtheshellswithvariablethicknessarewidelyusedinengineering .Theproblemaboutstaticshasbeenstudiedbymanyscholars;therearemanyRefs .[1 -4 ]inthisfield .Papersaboutnonlineardynamicsaremuchless[5 ,6 ].Inthispaper,selectingthemaximumamplitudeinthecenterofshallowconicalshellswithvariablethicknessasperturbationparameter,thenonlinearnaturalfrequencyofshallowconicalshellswithvariablethicknessisobtainedbymethodgiveninRef.[7] .Thenonlinearnaturalfrequencyisnotonlyconnectedwiththeva…  相似文献   

18.
Buckling of a series of thin-metal, shallow spherical shells under a uniform hydrostatic pressure has been investigated. Stress and deformation histories, as well as the critical buckling pressure and the post-buckling behavior, have been determined. Comparisons with theoretical analyses for buckling of spherical caps are given. Results are presented for an initial phase of a stability study of truncated conical sections which have been subjected to combinations of axial load and lateral pressure. A series of roll-formed and butt-welded, truncated aluminum conical shells with a 75-deg base angle have been tested. Buckle modes for axial-load condition alone, laterial-pressure load alone and combinations of these loading conditions are described. Interaction curves for the conditions investigated are given.  相似文献   

19.
Here, the nonlinear thermo-elastic buckling/post-buckling characteristics of laminated circular conical–cylindrical/conical–cylindrical–conical joined shells subjected to uniform temperature rise are studied employing semi-analytical finite element approach. The nonlinear governing equations, considering geometric nonlinearity based on von Karman’s assumption for moderately large deformation, are solved using Newton–Raphson iteration procedure coupled with displacement control method to trace the pre-buckling/post-buckling equilibrium path. The presence of asymmetric perturbation in the form of small magnitude load spatially proportional to the linear buckling mode shape is assumed to initiate the bifurcation of the shell deformation. The study is carried out to highlight the influences of semi-cone angle, material properties and number of circumferential waves on the nonlinear thermo-elastic response of the different joined shell systems.  相似文献   

20.
In this paper,the linear exact solution and nonlinear solutionfor U-shaped bellows have been obtained by using the general so-lution of circular ring shell and the method of perturbation.  相似文献   

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