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Shakedown of Plates under Moving Patch Loads

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Physical Non-Linearities in Structural Analysis

Summary

Shakedown criteria for plates under moving patch loads are derived using a normal moment yield criterion. The formulation results in the determination of incremental collapse and alternating plasticity limits independent of each other. In developing a numerical method, the plate and the load program are discretised and shakedown criteria are linearised. The incremental collapse limit is computed using a linear programming procedure and knowing the active constraints the feasible collapse mechanism can be determined approximately. A simple inequality is used to obtain the alternating plasticity limit. The upper bound formulation is used to obtain the shakedown limit by trial yield line collapse mechanisms, providing a quicker method of calculation for simple cases.

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References

  1. NATO Advanced Study Institute, University of Waterloo, 1977, Engineering Plasticity by Mathematical Programming. Cohn, M.Z. and Maier, G., Pergamon, 1979.

    Google Scholar 

  2. Melan, E. Der Spannungszustand eines Hencky-Miseslschen Kontinuums bei verandlicher Belastung. Sber. Akad. Wiss, Wien, 147, 73, 1938.

    Google Scholar 

  3. Koiter, W.T., A new general theorem on shakedown of elastic-plastic structures. Proc. K. ned. Akad. Wet., B59, 24, 1956.

    MATH  MathSciNet  Google Scholar 

  4. Konig, J.A. Theory of shakedown of elastic-plastic structures. Archwm. Mech. Stosow, 18, pp. 227–236, 1966.

    Google Scholar 

  5. Grundy, P. and Spencer, W.J., Shakedown of Elastoplastic Grids. Proc. 5th Australasian Conf.Mechanics of Structures and Materials Melbourne, Aug. 1975, pp. 219–236.

    Google Scholar 

  6. Konig, J.A. Shakedown of Plates. Archwm. Mech. Stosow, 21, pp. 623–637, 1969.

    Google Scholar 

  7. Sawczuk, A. On incremental collapse of shells under cyclic loading. IUTAM Symposium, Copenhagen, 1967. Theory of Thin Shells, pp. 328–340, Springer-Verlag, 1969.

    Google Scholar 

  8. Save, M. A consistent limit analysis of reinforced concrete slabs. Mag. Cone. Res., V. 19, No. 58, pp. 3–12, 1967.

    Google Scholar 

  9. Lenschow, R. and Sozen, M. A yield criterion for reinforced concrete slabs. J.A.C.I., Proc., V64, No. 5, pp. 266–273, 1967.

    Google Scholar 

  10. Alwis, W.A.M. and Grundy, P., Shakedown of Plates under moving loads. Proc. 7th Austral. Conf. on Mechanics of Structures and Materials, Perth, May, 1980, pp. 191–196.

    Google Scholar 

  11. Munro, J. and Da Fonseca, A.M.A., Yield line methods by finite elements and linear programming. The Struct. Engineer, Vol. 56B, No. 2, pp. 37–44, June 1978.

    Google Scholar 

  12. Cookson, P.J., Generalized Yield Lines in Reinforced Concrete Slabs. J. Struct. Mech., 7 (1), pp 65–82, 1979.

    Article  Google Scholar 

  13. Grundy, P. and Alwis, W.A.M., Shakedown of Plates under Moving Patch Load. Monash Univ. Civ. Engg. Report No. 4/1980.

    Google Scholar 

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© 1981 Springer-Verlag, Berlin, Heidelberg

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Grundy, P., Alwis, W.A.M. (1981). Shakedown of Plates under Moving Patch Loads. In: Hult, J., Lemaitre, J. (eds) Physical Non-Linearities in Structural Analysis. International Union of Theoretical and Applied Mechanics. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-81582-9_14

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  • DOI: https://doi.org/10.1007/978-3-642-81582-9_14

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-81584-3

  • Online ISBN: 978-3-642-81582-9

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