Quarterly of Applied Mathematics

Quarterly of Applied Mathematics

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

   
 
 

 

On isoperimetric inequalities in plasticity


Author: Walter Schumann
Journal: Quart. Appl. Math. 16 (1958), 309-314
MSC: Primary 73.00
DOI: https://doi.org/10.1090/qam/103658
MathSciNet review: 103658
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: The purpose of this paper is the proof of the inequality $ P \ge 6\pi {M_0}$, where $ P$ is the total limit load, $ {M_0}$ the yield moment of a thin, perfectly plastic, simply supported, uniformly loaded plate of arbitrary shape and connection.


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

  • [1] H. G. Hopkins and W. Prager, The load carrying capacities of circular plates, J. Mech. Phys. Solids 2, 1-13 (1953) MR 0057735
  • [2] R. M. Haythornthwaite and R. T. Shield, A note on the deformable region in a rigid plastic structure, Brown University Tech. Rep. C11-26 (1957) MR 0092466
  • [3] D. C. Drucker, W. Prager and H. J. Greenberg, Extended limit design theorems of continuous media, Quart. Appl. Math. 9, 381-389 (1952) MR 0045573
  • [4] G. Polya and G. Szegö, Isoperimetric inequalities in mathematical physics, Princeton (1951) MR 0043486
  • [5] H. A. Schwarz, Gesammelte Math. Abhandlungen, vol. 2, Göttingen, 327-335, 1890
  • [6] W. Prager, Probleme der Plastizitätstheorie, Basel, 1955 MR 0076573
  • [7] R. Hill, A note on estimating yield-point loads in a plastic-rigid body, Phil. Mag. 43, 353-355 (1952)
  • [8] D. C. Drucker and R. T. Shield, Design for minimum weight, Proc. 9th Intern. Congr. Appl. Mech., Brussel, 1956
  • [9] W. Prager, Minimum weight design of plates, De Ingenieur 48 (1955)
  • [10] J. Steiner, Einfache Beweise der isoperimetrischen Hauptsätze, Werke II, Berlin, 75-91, 1882

Similar Articles

Retrieve articles in Quarterly of Applied Mathematics with MSC: 73.00

Retrieve articles in all journals with MSC: 73.00


Additional Information

DOI: https://doi.org/10.1090/qam/103658
Article copyright: © Copyright 1958 American Mathematical Society

American Mathematical Society