Nonlinear Buckling Simulations of Imperfect Shell Domes by Mixed Finite Elements
Publication: Journal of Engineering Mechanics
Volume 129, Issue 7
Abstract
A degenerated nine-node-shell element and interpolation formulation for stress resultant vectors are used. Fifty-two selected experiments previously performed by the second author on the elastic buckling of clamped thin-walled shallow spherical shells under external pressure are compared with the present finite element analytical results. The measured geometric initial imperfection distributions are incorporated in the finite element analytical procedure. The good agreements between the numerical simulations and the experimental measurements of not only maximum loads but also displacement distributions are obtained.
Get full access to this article
View all available purchase options and get full access to this article.
References
Ahmad, S., Irons, B. M., and Zienkiewicz, O. C.(1970). “Analysis of thick and thin shell structures by curved finite elements.” Int. J. Numer. Methods Eng., 2, 419–451.
Bathe, K. J., and Dvorkin, E. N.(1984). “A continuum mechanics based four-node shell element for general non-linear analysis.” Int. J. Computer-Aided Eng. Software, 1.
Budiansky, B. (1959). “Buckling of clamped shallow spherical shell.” Proc., Symp. on the Theory of Thin Elastic Shells, Delft, Holland, 64–94.
Gradshteyn, I. S., and Ryzhik, I. M. (1980). Tables of integrals, series, and products, Academic, New York.
Homewood, R. H., Brine, A. C., and Johnson, A. E.(1961). “Experimental investigation of the buckling instability of monocoque shells.” Proc. Soc. Exp. Stress Anal., 18, 88.
Huang, N. C.(1964). “Unsymmetric buckling of thin shallow spherical shells.” J. Appl. Mech., 31, 44–457.
Hughes, T. J. R., and Liu, W. K.(1981). “Nonlinear finite element analysis of shells: Part I: Three-dimensional shells.” Comput. Methods Appl. Mech. Eng., 26, 331–362.
Kaplan, A., and Fung, Y. C. (1954). “A nonlinear theory of bending and buckling of thin elastic shallow spherical shells.” NACA Note 3212.
Liu, W. K., Law, E. S., Lam, D., and Belyschko, T.(1986). “Resultant-stress degenerated-shell element.” Comput. Methods Appl. Mech. Eng., 55, 259–300.
Noguchi, H., and Hisada, T.(1992a). “An efficient formulation for a shell element considering finite rotation increments and its assessment.” Trans. Jpn. Soc. Mech. Eng., Ser. A, 58, 943–950 (in Japanese).
Noguchi, H., and Hisada, T.(1992b). “Development of a sensitivity analysis method in postbuckling problems.” Trans. Jpn. Soc. Mech. Eng., Ser. A, 58, 2415–2422 (in Japanese).
Ramm, E. (1977). “A plate/shell element for large deflections and rotations.” Formulations and algorithms in finite element analysis, MIT Press, Cambridge, Mass.
Sansour, C., and Bufler, H.(1992). “An exact finite rotation shell theory, its mixed variational formulation and finite element implementation.” Int. J. Numer. Methods Eng., 34, 73–115.
Simo, J. C., and Fox, D. D.(1989a). “On a stress resultant geometrically exact shell model. Part I: Formulation and optimal parametrization.” Comput. Methods Appl. Mech. Eng., 72, 267–304.
Simo, J. C., and Fox, D. D.(1989b). “On a stress resultant geometrically exact shell model. Part II: The linear theory; Computational aspects.” Comput. Methods Appl. Mech. Eng., 73, 53–92.
Simo, J. C., Fox, D. D., and Rifai, M. S.(1990). “On a stress resultant geometrically exact shell model. Part III: Computational aspects of the nonlinear theory.” Comput. Methods Appl. Mech. Eng., 79, 21–70.
Sunakawa, M., and Ichida, K.(1973). “Buckling of spherical shells subjected to external pressure, Parts 1 and 2.” J. Jpn. Soc. Aeronaut. Space Sci., 21, 263–270, 384–393 (in Japanese).
Tillman, S. C.(1970). “On the buckling behavior of shallow sphericalcaps under a uniform pressure load.” Int. J. Solids Struct., 6, 37–52.
von Karman, T., and Tsien, H. S.(1939). “The buckling of spherical shells by external pressure.” J. Aeronaut. Sci., 7, 43–50.
Yamada, S. (1980). “Experimental investigation of shallow spherical shells.” PhD dissertation, Tohoku University (in Japanese).
Yamada, S., Uchiyama, K., and Yamada, M.(1983). “Experimental investigation of the buckling of shallow spherical shells.” Int. J. Non-Linear Mech., 18, 37–54.
Yamada, M., and Yamada, S. (1983). “Agreement between theory and experiment on large-deflection behavior of clamped shallow spherical shells under external pressure.” Collapse, J. M. T. Thompson and G. W. Hunt, eds., Cambridge University Press, Cambridge, England, 431–441.
Information & Authors
Information
Published In
Copyright
Copyright © 2003 American Society of Civil Engineers.
History
Received: Nov 17, 2000
Accepted: Jul 9, 2002
Published online: Jun 13, 2003
Published in print: Jul 2003
Authors
Metrics & Citations
Metrics
Citations
Download citation
If you have the appropriate software installed, you can download article citation data to the citation manager of your choice. Simply select your manager software from the list below and click Download.