Hwang Chien. Calculation of Stresses and Deformations of Bellows by Initial parameter Method of Numerical Integration[J]. Applied Mathematics and Mechanics, 1982, 3(1): 101-112.
 Citation: Hwang Chien. Calculation of Stresses and Deformations of Bellows by Initial parameter Method of Numerical Integration[J]. Applied Mathematics and Mechanics, 1982, 3(1): 101-112.

# Calculation of Stresses and Deformations of Bellows by Initial parameter Method of Numerical Integration

• Publish Date: 1982-02-15
• 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[10] 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.
•  [1] 钱伟长、郑思梁,轴对称圆环壳的复变量方程和轴对称细环壳的一般解,清华大学学报,19(1979).27-9 7. [2] 钱伟长,半圆弧波纹管的计算-一细环壳理论的应用,清华大学学报,19(1979).84-99. [3] 钱伟长、郑思梁,轴对称圆环壳的一般解,应用数学和力学,1,3(1980) [4] 钱伟长、郑思梁,半圆弧波纹管的计算-一环壳一般解的应用,应用数学和力学,2,1(1981). [5] 谢志成、付承诵、郑思梁,有曲率突变的轴对称壳(波纹壳)的有限元解.应用数学和力学,2,1(1981). [6] 陈山林,S型波纹管的轴对称应力和位移,(未发表). [7] Turner.C.E.and Ford,H.,Stress and deflection of pipeline expansion bellows.P.T.I.M.E.,171,(1957),526-552. [8] Новожнлов В.В.,Теория Тонких оболочек,(1951 ),(V.V.Novozelov,Theorg of thin shell.in Russian). [9] 南京大学数学系计算数学专业编,《常微分方程的数值解法》(1979). [10] Gill.S.,A process for step-by-step integration of differential equations in automatic digital computing machine.Proc.Cambridge Phil.Soc.,47.(1951),96-108. [11] 南京大学数学系计算数学专业编,《数值逼近方法》(1978). [12] Clark.R.A.,On the theory of thin elastic toroidal shells.J.of Math.and Phys.,29,(1950),146-178. [13] Osipova.L.N.and Tumakin.S.A.,Tables for the Computation of Toroidal Shells.(in Russian),Moscow(1963). [14] Turner.C.E.,Study of the symmetrical elastic loading of some shells of revolution.With special reference to toroidal elements.J.of Mech.Engg.Sci.1,(1959).113-129. [15] Turner,C.E.,stress and deflection studies of flat-plate and toroidal expansion bellows,subJected to axial.eccentric or internal pressure loading.J.Mech.Engng.Sci.,1,(1959),130-143. [16] Hamada.M.and Takezoho.S.,Strength of U-shaped bellows(lst Report.Case of Axial Loading),Bull.JSME.8.32.(1965),525-531. [17] Hamada,M.and Takezoho,S.,Strength of U-shaped bellows,(3rd Report,Case of Load of Internal Pressure),Bull.JSME.9,35,(1966),513-523. [18] Андреена,Л.Е.,Беседа,А.И.и Силъфоны,ДР.,Расчет и Проектирование,М.Машиностроение,(1975). [19] Reissner,E.,On the theorg of thin elastic shells,Reissner Anniversarg Volume,Contributions to Applied Mechanics,Ann Arbor,Edwards(1949),231-247.

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