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
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

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

Similar Articles

Retrieve articles in Quarterly of Applied Mathematics with MSC: 73K15, 73E99, 73V25

Retrieve articles in all journals with MSC: 73K15, 73E99, 73V25


Additional Information

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


Brown University The Quarterly of Applied Mathematics
is distributed by the American Mathematical Society
for Brown University
Online ISSN 1552-4485; Print ISSN 0033-569X
© 2017 Brown University
Comments: qam-query@ams.org
AMS Website