CALCULATION OF STRESSES AND DEFORMATIONS OF BELLOWS BY INITIAL PARAMETER METHOD OF NUMERICAL INTEGRATION

摘要/Abstract

摘要： 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.

关键词: radiation, optically dense fluid, transient natural convection, thermophorestic particle deposition

Abstract: 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.

Key words: radiation, optically dense fluid, transient natural convection, thermophorestic particle deposition

黄黔. CALCULATION OF STRESSES AND DEFORMATIONS OF BELLOWS BY INITIAL PARAMETER METHOD OF NUMERICAL INTEGRATION[J]. Applied Mathematics and Mechanics (English Edition), 1982, 3(1): 99-112.

Hwang Chien. CALCULATION OF STRESSES AND DEFORMATIONS OF BELLOWS BY INITIAL PARAMETER METHOD OF NUMERICAL INTEGRATION[J]. Applied Mathematics and Mechanics (English Edition), 1982, 3(1): 99-112.

参考文献

[1] Chien Wei-zang and Zheng Si-liang.Equations of symmetrical ring shells in complex quantities and their general solutions for slender ring shells,(in Chinese) J.of Qinghua University.19(1979),27-47.
[2] Chien Wei-zang.Calculations for semi-circular arc type corrugated tube--Applications of the theorg of slender ring shells.(in Chinese) J.of Qinghua University.19(1979),84-99.
[3] Chien Wei-zang and Zheng Si-liang.General solutions of axial symmetrical.ring shells.Applied Mathematics and Mechanics.1,3. (1980. 11).
[4] Chien Wei-zang and Zheng Si-liang.Calculations for semi-circular arc type corrugated tube--Applications of general solutions of ring shell equation.Applied Mathematics and Mechanics.2. 1,(1981),103-116.
[5] Shieh Chih-cheng,Fu Cheng-song and Zheng Si-liang.The solution ofaxisym-metrical shells with abrupt curature change(Corrugated shells) by the finite element method,Applied Mathematics and Mechanics.2,1,(1981) 117-136.
[6] Chen Shan-lin.Stress and deflection of s-shaped bellows under symmetrical load (to be published).(in Chinese).
[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] Numerical Solution Methods in Ordinary Differential Equations.(in Chinese) edited by Division of Computational Mathematics.Department of Aathematics.Nanking University.(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] Numerical Approximation.(in Chinese),edited by Division of Computational Mathematics.Department of Mathematics.Nanking University,(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] Andrewa,L.E.,Beceda,A.I.and etc.,Bellowe,Calculation and Projection,Moscow,(in Russian),Moscow,(1975).
[19] Reissner,E.,On the theorg of thin elastic shells,Reissner Anniversarg Volume,Contributions to Applied Mechanics,Ann Arbor,Edwards(1949),231-247.