The Calculation of Semi-circular Corrugated Tube-An Application of the General Solution of Ring Shell

In this paper,the deformation and stress distribution in semi-circularcorrugated tube under axial force are calculated by means of the generalsolutions of circular ring shell given in previous paper[1].     

General solutions of axial symmetrical ring shells

This paper gives the general solutions of axial symmetrical ring shells for all values of slenderness ratio. This solution is newly brought out, and can be used to solve various practical problems, including corrugated tubes, thermal expansion joints, Borden tubes, etc.     

零曲率闭口壳的渐近解法

本文在文献[1]所得结果的基础上,建立了零曲率闭口壳当载荷沿壳表面及沿边界变化不过于急剧时,在各种边界条件下的二次近似渐近解法.将壳中的应力状态分为三种基本类型:薄膜应力状态(包括薄膜静力平衡方程的特解与齐次解)、纯弯应力状态及简单边界效应应力状态.按面向约束是否“完全”,即能否保证中心面为“不可变”的两种不同情况讨论了求解步骤.当中心面为“不可变”时,可以先解出薄膜及纯弯应力状态,然后求解简单边界效应应力状态.文中给出了在各种边界条件下各基本应力状态的相对量级关系.当中心面“可变”时,只在当载荷满足一定条件的特殊情况下才能按上述步骤求解,而在一般载荷情况下上述步骤不再适用,必须将各应力状态联立求解.     

轴对称圆环壳的一般解

本文是前文[1]的推广,它不限于细环壳a=a/R<<1的假定,其中a为环壳的截面半径,R为环壳的总体半径.提出了轴对称圆环壳在0≤a<1范围内的一般解,本文的解可以用来解决波纹壳、热膨胀器、高压容器的过渡部分和波登管等实用问题.本文的结果是前人从未求得的圆环壳的一般解.     

General Solutions of Axial Symmetrical Ring Shells

This paper gives the general solutions of axial symmetrical ring shells for all values of slender-ness ratio.This solution is newly brought out,and can be used to solve various practical nroblems,including corrugated tubes,thermal expansion joints,Borden tubes,etc.     

The Solution for Axisymmetrical Shells with Abrupt Curvature Change(Corrugated Shells)by the Finite Element Method

It has been noted in the present paper that the finite element method using linear elements for solving axisymmetrical shells cannot be applied to the analysis of axisymmetrical shells with abrupt curvature change,owing to the fact that the influence of the curvature upon the angular displace-ments has been neglected.The present paper provides a finite element method using linear elements in which the influence of curvature is considered and the angular displacements are treated as continuous parameters.This method has been applied to the calculation of corrugated shells of the type C,and compared with the experimental results obtained by Turner-Ford as well as with the analytical solution given by Prof.Chien Wei-zang.The compari-sons have been proved that this theory is correct.     

由横向稀肋加固的斜锥壳的渐近解法

在文献[1]中作者得到了具有刚性加强端的斜锥壳的渐近解法.本文在此基础上进一步讨论横向稀肋加固的斜锥壳的渐近解法.所谓“稀肋”是指相邻两肋的简单边界效应相互影响在工程精度范围内可忽略不计的肋条,例如肋间距l≥3(rh)~(1/2)时(2h——薄壳厚度,r——两肋处壳体的最大平均半径).对于本文所讨论的常用的肋条横截面尺寸,分析结果表明,作为应力状态的第一次渐近解[误差为(h/λ)~(1/2)量级,λ——壳体中心面的特征曲率半径],肋对壳体薄膜应力状态没有影响.而在求解简单边界效应时,可将肋与壳的连接处看成弹性固支边界来处理,即认为此处的壳体转角γ_1为零,而周向应变ε_2等于肋的应变值。在分析过程中,讨论了肋截面形心偏心及形心主轴偏斜等因素对壳体应力状态的影响,证明了在第一次近似时它们可忽略不计. 为了验证所得结果的精确程度,在文献[1]的试件上,进一步作了具有稀肋加强的斜锥壳的电测试验.试验结果证实,本文所得的渐近解的误差基本上在(h/λ)~(1/2)及斜锥偏度m~2的量级范围内. 为了节省篇幅,本文不再给出斜锥壳各基本应力状态的内力及位移表达式,以及它们的待定函数的确定方法,需要时可参阅文献[1].     

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。     

The Calculation of Semi-circular Corrugated Tube——An Application of the General Solution of Ring Shell

In this paper, the deformation and stress distribution in semi-circular corrugated tube under axial force are calculated by means of the general solutions of circular ring shell given in previous paper[1].     

The solution for axisymmetrical shells with abrupt curvature change (corrugated shells) by the finite element method

It has been noted in the present paper that the finite element method using linear elements for solving axisymmetrical shells cannot be applied to the analysis of axisymmetrical shells with abrupt curvature change, owing to the fact that the influence of the curvature upon the angular displacements has been neglected. The present paper provides a finite element method using linear elements in which the influence of curvature is considered and the angular displacements are treated as continuous parameters. This method has been applied to the calculation of corrugated shells of the type C, and compared with the experimental results obtained by Turner-Ford as well as with the analytical solution given by Prof. Chien Wei-zang. The comparisons have been proved that this theory is correct.