Summary
Interaction of clamped orthotropic shallow spherical shells with nonlinear elastic foundations is studied under transient loads. The effect of softening and hardening foundation nonlinearities on the response behaviour of shallow shells has been investigated. Detailed analysis depicting the influence of hardening type foundation nonlinearity on the maximum response of orthotropic shallow spherical shells has been conducted. The numerical results suggest that for the shell-foundation interaction problems undergoing moderately large deformations, the nonlinear model for the foundation must be considered.
übersicht
Es wird die Wechselwirkung eingespannter orthotroper, leicht gekrümmter Schalen mit nichtnichtlinearer elastischer Bettung unter transienter Belastung behandelt. Dabei wird der Einfluß der erweichenden und der verfestigenden Nichtlinearität der Bettung auf das Antwortverhalten der schwach gekrümmten Schalen untersucht. Speziell wird der Einfluß der verfestigenden Bettungsnichtlinearität auf extreme Antwortverhalten von orthotropen, schwach sphärischen Schalen im einzelnen analysiert. Die numerischen Ergebnisse machen deutlich, daß bei Wechselwirkungsproblemen von Schale und Bettung mit mäßig großen Deformationen das nichtlineare Modell der Einbettung betrachtet werden muß.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Winkler, E.: Die Lehre von der Elastizität und Festigkeit. Prag: Dominicus 1867
Pasternak, P. L.: On a new method of analysis of an elastic foundation by means of two foundation constants (in Russian). Moscow: Gosudarstvennoe Izdatelstvo Literaturi Po Stroitelstou i Arkhitekture 1954
Hetényi, M.: Beams on elastic foundations. Ann Arbor: The Univ. of Michigan 1946
Kerr, A. D.: Elastic and viscoelastic foundation models. J. Appl. Mech. 31 (1964) 491–498
Levinson, M.; Bharatha, S.: Elastic foundation models — a new approach. Proc. 4th Symp. on Eng. Appl. Solid Mech., Canadian Society of Mechanical Engineering (R & D), Sheridan Park Research Community, Canada 1978, pp. 177–189
Fraser, W. B.; Budiansky, B.: The buckling of a column with random initial deflections. J. Appl. Mech. 36 (1969) 233–240
Amazigo, J. C.; Budiansky, B.; Carrier, G. F.: Asymptotic analyses of the buckling of imperfect columns on nonlinear elastic foundations. Int. J. Solids Struct. 6 (1970) 1341–1356
Elishakoff, I.: Buckling of a stochastically imperfect finite column on a non-linear elastic foundation. J. Appl. Mech. 46 (1979) 411–416
Massalas, C.: Fundamental frequency of vibration of a beam on a non-linear elastic foundation. J. Sound Vib. 54 (1977) 613–615
Massalas, C.; Soldatos, K.; Tzivanidis, G.: Vibration and stability of a thin elastic plate resting on a non-linear elastic foundation when the deformation is large. J. Sound Vib. 67 (1979) 284–288
Massalas, C.; Kafousias, N.: Non-linear vibrations of a shallow cylindrical panel on a non-linear elastic foundation. J. Sound Vib. 66 (1979) 507–512
Beaufait, F. W.; Hoadley, P. W.: Analysis of elastic beams on nonlinear foundations. Comput. Struct. 12 (1980) 669–676
Nath, Y.; Jain, R. K.: Non-linear dynamic analysis of orthotropic annular plates resting on elastic foundations. Earthquake Eng. Struct. Dyn. 11 (1983) 785–796
Nath, Y.; Jain, R. K.: Non-linear dynamic analysis of shallow spherical shells on elastic foundations. Int. J. Mech. Sci. 25 (1983) 409–419
Houbolt, J. C.: A recurrence matrix solution for the dynamic response of elastic aircraft. J. Aero. Sci. 17 (1950) 540–550
Fox, L.; Parker, I. B.: Chebyshev polynomials in numerical analysis. London: Oxford Univ. Press 1968
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Jain, R.K., Nath, Y. Effect of foundation nonlinearity on the nonlinear transient response of orthotropic shallow spherical shells. Ing. arch 56, 295–300 (1986). https://doi.org/10.1007/BF00542480
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF00542480