Abstract
Numerical solutions of the relevant boundary value problem suggest that the first bifurcation from the basic solution for a spherical cap under a class of meridionally nonuniform loading is to a dimple state. Delicate asymptotic analysis of the linearized buckling problem confirm this observation.
Deceased
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
K.O. Friedrich, On the minimum buckling load for spherical shells, Th. von Karman Anniversary Volume, Caltech (Pasadena), 1941, 258–272.
D.G. Ashwell, On the large deflexion of a spherical shell with an inward point load, Proc. IUTAM Symp. on Thin Shells (Delft), Ed. W.T. Koiter, North-Holand, Amsterdam, 1960, 43–63.
C.V. Ranjan and C.R. Steele, Large deflection of deep spherical shells under concentrated load, Proc. AIAA/ASME 18th Structures, Struc. Dynamics and Materials Conf. (San Diego), 1977, 269278.
F.Y.M. Wan, The dimpling of spherical caps, Mechanics Today 5 (The Eric Reissner Anniversary Volume), 1980, 495–508.
F.Y.M. Wan, Polar dimpling of complete spherical shells, Proc. (3rd) IUTAM Sym. on Thin Shells (Tibilisi): Theory of Shells,Ed. W.T. Koiter and G.K. Mikhailov, North-Holland, 1980, 589–605.
F.Y.M. Wan and U. Ascher, Horizontal and flatpoints in shallow shell dimpling, Proc. BAIL I Conf. Ed. J. Miller, Boole Press, Dublin, 1980, 659–679.
L.A. Taber, Large deflection of a fluid-filled spherical shell under a point load, J. Appl. Mech., 49, 1982, 121–128.
F.Y.M. Wan, Shallow caps with a localized pressure distribution centered at the apex, Proc. EUROMECH Colloq. (No. 165) on Flexible Shells (Munich), Ed. E. Axelrad and F. Emmerling, Springer-Verlag, Berlin-New York-Heidelberg, 1984, 124–145.
D.F. Parker and F.Y.M. Wan, Finite polar dimpling of shallow caps under sub-buckling pressure loading, SIAM J. of Appl. Math., 44 1984, 301–326.
E. Reissner, On axisymmetric deformations of thin shells of revolution, Proc. Symp. in Appl. Math., Vol.III, Amer. Math. Soc., Providence, 1950, 27–52.
E. Ressner, Symmetric bending of shallow shells of revolution, J. Math Mech., 1, 1958, 121–140.
U. Ascher, J. Christiansen and R.D. Russell, A collocation solver for mixed order systems of boundary value problems, Math. Comp., 33, 1979, 659–679.
U. Ascher, R.M.M. Mattheij and R.D. Russell, Numerical Solutions of Boundary Value Problems for Ordinary Differential Equations, (Classics in Applied Mathematics, vol. 13 ) SIAM Publications, Philadelphia, 1995.
M. Abramowitz and I.A. Stegun, Handbook of Mathematical Functions, AMS No. 55 of National Bureau of Standards, 1964, U.S. Government Printing Office, Washington D.C.
C.G. Lange and G.A. Kriegsmann, The axisymmetric branching behavior of complete spherical shells, Quart. Appl. Math., 39, 1981, 145–178.
Author information
Authors and Affiliations
Rights and permissions
Copyright information
© 2004 Springer Science+Business Media New York
About this paper
Cite this paper
Lange, C.G., Wan, F.Y.M. (2004). Bifurcation Analysis of Shallow Spherical Shells with Meridionally Nonuniform Loading. In: Complementarity, Duality and Symmetry in Nonlinear Mechanics. Advances in Mechanics and Mathematics, vol 6. Springer, Dordrecht. https://doi.org/10.1007/978-90-481-9577-0_8
Download citation
DOI: https://doi.org/10.1007/978-90-481-9577-0_8
Publisher Name: Springer, Dordrecht
Print ISBN: 978-94-015-7119-7
Online ISBN: 978-90-481-9577-0
eBook Packages: Springer Book Archive