Abstract
In this paper, the nonlinear stability problem of a clamped truncated shallow spherical shell with a nondeformable rigid body at the center under a concentrated load is studied by means of the singular perturbation method. When the geometrical parameter k is large, the uniformly valid asymptotic solutions are obtained.
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Liu Ren-huai, Axisymmetric stability of thin circular shallow spherical shell with a circular hole at the center under the action of an edge load,Mechanics, 3 (1977), 206–212. (in Chinese)
Liu Ren-huai, Nonlinear stability of thin circular shallow spherical shell with a circular hole at the center under the action of uniformly distributed moments along the interior edge,Science Bulletin, 3 (1965), 253–255. (in Chinese)
Liu Ren-huai, Nonlinear thermal stability of bimetailic shallow shells of revolution,Int. J. Nonlinear Mechanics,18, 5 (1983). 409–429.
Tillman, S. C., On the buckling behaviour of shallow spherical caps under a uniform pressure load,Int. J. Solids and Structures,6, 1 (1970), 37.
Jiang Fu-ru, On singular perturbations for a elliptic equation,Fudan Journal (Natural Science), 2 (1978), 29–37. (in Chinese)
Hu Hai-chang, On the snapping of a thin spherical cap,Acta Scientia Sinica,3, 4 (1954), 437–461.
Liu Ren-huai and Cheng Zhen-qiang, On the nonlinear stability of a truncated shallow spherical shell under a concentrated load,Appl. Math. and Mech.,9, 2 (1988), 95–105. (in Chinese)
Courant, R. and D. Hilbert,Methods of Mathematical Physics, Vol. I, Interscience, New York (1953).
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Communicated by Jiang Fu-ru
Dedicated to the Tenth Anniversary and One Hundred Numbers of AMM (III)
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Sheng-liane, K. Asymptotic solutions of the nonlinear stability of a truncated shallow spherical shell under a concentrated load. Appl Math Mech 12, 313–326 (1991). https://doi.org/10.1007/BF02098062
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DOI: https://doi.org/10.1007/BF02098062