Quarterly of Applied Mathematics

Quarterly of Applied Mathematics

Online ISSN 1552-4485; Print ISSN 0033-569X



On shakedown of elastoplastic shells

Authors: Helmut Stumpf and Le Khanh Chau
Journal: Quart. Appl. Math. 49 (1991), 781-793
MSC: Primary 73K15; Secondary 73E99, 73V25
DOI: https://doi.org/10.1090/qam/1134753
MathSciNet review: MR1134753
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Abstract: An asymptotic theory of adaptation for elastoplastic shells under a variable loading is proposed. The hypothesis of membrane state of an elastic response is used to reduce the three-dimensional variational problems for shakedown factor to two-dimensional ones. The duality and the possibility of algebraization allow the membrane shell shakedown theory to be analytically solvable in many interesting cases. The asymptotic accuracy of the constructed membrane approximation is proved.

References [Enhancements On Off] (What's this?)

  • [1] E. Melan, Theorie statisch unbestimmter Tragwerke aus ideal-plastischem Baustoff, Sitzungsber. Akad. Wiss. Wien, Math. Naturwiss. Kl. Abt. 2A, 145, 195-218 (1938)
  • [2] W. T. Koiter, General theorems for elastic-plastic solids, Progress in solid mechanics, Vol. 1, North-Holland Publishing Co., Amsterdam, 1960, pp. 165–221. MR 0112405
  • [3] D. A. Gokhfeld, Some problems of shakedown of plates and shells, Trudy VI Vsesoyuznoj Konf. Plastin i Obolochek, Izdat. Nauka, Moscow, 1966, pp. 284-291 (Russian)
  • [4] A. Sawczuk, Evaluation of upper bounds to shakedown loads for shells, J. Mech. Phys. Solids 17, 291-301 (1969)
  • [5] J. J. Moreau, Sur les lois de frottement, de viscosité et plasticité, C. R. Acad. Sci. Paris Sér. I. Math. 271, 608-611 (1970)
  • [6] O. Debordes, Duality: some results in asymptotical elastoplasticity, Convex analysis and its applications (Proc. Conf., Muret-le-Quaire, 1976), Springer, Berlin, 1977, pp. 100–114. Lecture Notes in Econom. and Math. Systems, Vol. 144. MR 0502677
  • [7] A. L. Gol′denveĭzer, Theory of elastic thin shells, Translation from the Russian edited by G. Herrmann. International Series of Monographs on Aeronautics and Astronautics, Published for the American Society of Mechanical Engineers by Pergamon Press, Oxford-London-New York-Paris, 1961. MR 0135763
  • [8] P. P. Mosolov and V. P. Miasnikov, Asymptotic theory of rigid plastic shells, Prikl. Mat. Meh. 41 (1977), no. 3, 538–552 (Russian); English transl., J. Appl. Math. Mech. 41 (1977), no. 3, 550–566 (1978). MR 0478936, https://doi.org/10.1016/0021-8928(77)90047-8
  • [9] J. A. König, Shake-down of elastic-plastic structures, Elsevier, Amsterdam, 1987
  • [10] D. Weichert, Zum Problem geometrischer Nichtlinearitäten in der Plastizitätstheorie, Mitteilungen Institut für Mechanik, vol. 53, Ruhr-Universität Bochum, 1987
  • [11] J. Groβ-Weege, Zum Einspielverhalten von Flächentragwerken, Mitteilungen Institute für Mechanik, vol. 58, Ruhr-Universität Bochum, 1988
  • [12] W. Pietraszkiewicz, Introduction to the non-linear theory of shells, Mitteilungen Institut für Mechanik, vol. 10, Ruhr-Universität Bochum, 1977
  • [13] I. N. Vekua, Generalized analytic functions, Pergamon Press, London-Paris-Frankfurt; Addison-Wesley Publishing Co., Inc., Reading, Mass., 1962. MR 0150320

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DOI: https://doi.org/10.1090/qam/1134753
Article copyright: © Copyright 1991 American Mathematical Society

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