Abstract
Using a singular perturbation method, the nonlinear stability of a truncated shallow spherical shell without a nondeformable rigid body at the center under linear distributed loads along the interior edge is investigated in this paper. When the geometrical parameter k is large, the uniformly valid asymptotic solutions are obtained.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Liu Ren-huai, Nonlinear stability of thin circular shallow spherical shell with a circulr hole at the center under the action of uniformly distributed moments along the interior edge,Science Bulletin, 3 (1965), 253–255 (in Chinese)
Tillman, S. C., On the buckling behaviour of shallow spherical caps under a uniform pressure load,Int. J. Solids and Structures,6, 1 (1970), 37–45.
Kang Sheng-liang, A singular perturbation solution to nonlinear stability of a truncated shallow spherical shell with the large geometrical parameter,Journal of Tongji University,18, 4 (1990), 477–486. (in Chinese).
Kang Sheng-liang, Asymptotic solutions of the nonlinear stability of a truncated shallow spherical shell under a concentrated load,Appl. Math and Mech. (English Ed.) 12, 3 (1991), 313–326.
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.
Courant, R. and D. Hilbert,Methods of Mathematical Physics, Vol. 1 Interscience, New York (1953).
Author information
Authors and Affiliations
Additional information
Communicated by Lin Zong-chi
Rights and permissions
About this article
Cite this article
Sheng-liang, K. Singular perturbation solutions of the nonlinear stability of a truncated shallow shperical shell under linear distributed loads along the interior edge. Appl Math Mech 14, 931–944 (1993). https://doi.org/10.1007/BF02451707
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF02451707