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Part of the book series: Lecture Notes in Engineering ((LNENG,volume 28))

Abstract

In this paper we are concerned with the nonlinear dynamic analysis of shells of revolution. Starting from a discretization procedure which is tailored to the particular geometry of these shells, we first discuss a direct time integration procedure. It employs the Newmark temporal operator, and a modified preconditioned conjugate-direction method is used to solve the resulting algebraic equations. Subsequently we present a closely related reduced basis technique which combines some of the features of the direct integration procedure with those of the standard reduction methods.

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References

  1. Wunderlich, W.: ‘Zur nichtlinearen Berechnung von Rotationsschalen (On the nonlinear analysis of shells of revolution)’, W.ss. Zeitschr. d. Hochschule f. Arch. u. Bauwesen, Weimar, Bd. 28 (1982) 221–225.

    Google Scholar 

  2. Rensch, H.J.: ‘Elastoplastisches Beulen und Imperfektionsempfindlichkeit torisphärischer Schalen (Elastic-plastic buckling and imperfection-sensitivity of torispherical shells)’, Techn. Wiss. Mitteilungen Nr. 82–13, Institut für Konstruktiven Ingenieurbau, Ruhr-Universität Bochum (1982).

    Google Scholar 

  3. Wunderlich, W., Rensch, H.J., Obrecht, H.: ‘Analysis of elastic-plastic buckling and imperfection-sensitivity of shells of revolution’, in ’Buckling of Shells’, Ramm, E. (ed.) Springer-Verlag, Berlin (1982) 137–174.

    Google Scholar 

  4. Wunderlich, W., Cramer, H., Obrecht, H.: ‘Application of ring elements in the nonlinear analysis of shells of revolution under nonaxisymmetriç;loading’, Comp. Meth.-Appl. Mech. Eng., vol. 51, (1985) 259–275.

    MATH  Google Scholar 

  5. Wunderlich, W., Cramer, H., Redanz, W.: ‘Nonlinear analysis of shells of revolution including contact conditions’, in ’Finite Element Methods for Nonlinear Problems’, Proc. Europe-US Symp., Trondheim, Aug. (1985), Bergan, P.G., Bathe, K.J., Wunderlich, W. (eds.), Springer-Verlag, Berlin (1986) 697–717.

    Google Scholar 

  6. Belytschko, T., Hughes, T.J.R. (eds.): ‘Computational Methods for Transient Analysis’, North-Holland, Amsterdam (1983).

    Google Scholar 

  7. Nickell, R.E.: ‘Nonlinear dynamics by mode superposition’, Comp. Meth. Appl. Mech. Eng., vol. 7 (1976) 107–129.

    Article  MATH  MathSciNet  Google Scholar 

  8. Morris, N.F.: ‘The use of modal superposition in nonlinear dynamics’, Comp. Struct., vol. 7 (1977) 65–72.

    Google Scholar 

  9. Nagy, D.A.: ‘Modal representation of geometrically nonlinear behavior by the finite element method’, Comp. Struct., vol. 10, Aug. (1979) 683–688.

    Article  MATH  Google Scholar 

  10. Almroth, B.O., Stern, P., Brogan, F.A.: ‘Automatic choice of global shape functions in structural analysis’, AIAA J., vol. 16, No. 5, May (1978) 525–528.

    Article  ADS  Google Scholar 

  11. Bathe, K.J., Gracewski, S.: ‘On nonlinear dynamic analysis using substructuring and mode superposition’, Comp. Struct., vol. 13 (1981) 699–707.

    MATH  Google Scholar 

  12. Noor, A.K., Peters, J.M.: ‘Reduced basis technique for nonlinear analysis of structures’, AIAA J., vol. 18, No. 4, April (1980) 455–462.

    Article  ADS  Google Scholar 

  13. Noor, A.K.: ‘Recent advances in reduction methods for nonlinear problems’, Comp. Struct., vol. 13 (1981) 31–44.

    Article  MATH  Google Scholar 

  14. Noor, A.K.: ‘On making large nonlinear problems small’ Comp. Meth. A.pl. Mech. Eng., vol. 34 (1982) 955–985.

    Article  MATH  Google Scholar 

  15. Utku, S., Clemente, J.L.M., Salama, M.: ‘Errors in reduction methods’, Comp. Struct., vol. 21, No. 6 (1985) 1153–1157.

    MATH  MathSciNet  Google Scholar 

  16. Wilson, E.L., Yuan, M.W., Dickens, J.M.: ‘Dynamic analysis by direct superposition of Ritz vectors’, Earthquake Eng. Struct. Dyn., vol. 10 (1982) 813–821.

    Article  Google Scholar 

  17. Bayo, E.P., Wilson, E.L.: ‘Use of Ritz vectors in wave propagation and foundation response’, Earthquake Eng. Struct. Dyn., vol. 12 (1984) 499–505.

    Article  Google Scholar 

  18. Wilson, E.L.: ‘A new method of dynamic analysis for linear and nonlinear systems’, Fin. E.em. Anal. Design, vol. 1 (1985) 21–23.

    Article  MATH  Google Scholar 

  19. Cardona, S., Idelsohn, S., Sander, G.: ‘Two stage finite element discretization in structural dynamics’, in ’Numerical Methods in Engineering’, Proc. 3 Int. Symp., Paris, March (1983) 437–445.

    Google Scholar 

  20. Idelsohn, S., Cardona, A.: ‘A reduction method for nonlinear structural dynamic analysis’, Comp. Meth. Appl. Mech. Eng., vol. 49 (1985) 253–279.

    Article  MATH  Google Scholar 

  21. Idelsohn, S., Cardona, A.: ‘A load-dependent basis for reduced nonlinear structural dynamics’, Comp. Struct., vol. 20 (1985) 203–210.

    MATH  Google Scholar 

  22. Arnold, R.R., Citerley, R.L., Chargin, M., Galant, D.: ‘Application of Ritz vectors for dynamic analysis of large structures’, Comp. Struct., vol. 21, No. 3 (1985) 461–467.

    MathSciNet  Google Scholar 

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© 1987 Springer-Verlag Berlin, Heidelberg

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Obrecht, H., Goebel, W., Wunderlich, W. (1987). Nonlinear Dynamic Analysis of Shells of Revolution. In: Elishakoff, I., Irretier, H. (eds) Refined Dynamical Theories of Beams, Plates and Shells and Their Applications. Lecture Notes in Engineering, vol 28. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-83040-2_35

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  • DOI: https://doi.org/10.1007/978-3-642-83040-2_35

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-17573-5

  • Online ISBN: 978-3-642-83040-2

  • eBook Packages: Springer Book Archive

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