Qian Wei-zhang. Equation in Complex Variable of Axisymmetrical Deformation Problems for a General Shell of Revolution[J]. Applied Mathematics and Mechanics, 1990, 11(7): 565-579.
Citation: Qian Wei-zhang. Equation in Complex Variable of Axisymmetrical Deformation Problems for a General Shell of Revolution[J]. Applied Mathematics and Mechanics, 1990, 11(7): 565-579.

Equation in Complex Variable of Axisymmetrical Deformation Problems for a General Shell of Revolution

  • Received Date: 1989-11-10
  • Publish Date: 1990-07-15
  • In this paper,the equation of axisymmetrical deformation problems for a general shell of revolution is derived in one complex variable under the usual Love-Kirchhoff assumption.In the case of circular ring shells,this equation may be simplified into the equation given by F.Tdlke(1938)[3].R.A.Clark(1950)[4] and V.V.Novozhilov(1951)[5].When the horizontal radius of the shell of revolution is much larger than the average radius of curvature of meridian curve,this equation in complex variable may be simplified into the equation for slander ring shells.If the ring shell is circular in shape,then this equation can be reduced into the equation in complex variable for slander circular ring shells given by this author(1979)[6].If the form of elliptic cross-section is near a circle,then the equation of slander ring shell with near-circle ellipitic cross-section may be reduced to the complex variable equation similar in form for circular slander ring shells.
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    Reissner.H.,Muller-Breslau-Festschrift,Leipzig(1912),181.
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    Meissner,E.,Physik.Zeits.,14(1913),343;Vieteljahrsschr Naturforsch Gas,Zurich,60,23(1915).
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    Tölke,F.,Ingenieur Archiv.,9(1938),282.
    [4]
    Clark,R.A.,J.of Nath.and Physics,29(1950),146-178.
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    Novozhilov,V.V.,Thin Shell Theory,Translated from Russian by Beijing Institute of Petroleum,Science Publisher(1951).(Chinese version).
    [6]
    钱伟长,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.19,1(1979).27-47.
    [7]
    钱伟长,细环壳极限方程的非齐次解及其在仪器仪表上的.应用,仪器仪表学报,创刊号(1980),89-112.
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