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
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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.
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- R. M. Haythornthwaite and R. T. Shield, A note on the deformable region in a rigid-plastic structure, J. Mech. Phys. Solids 6 (1958), 127–131. MR 92466, DOI https://doi.org/10.1016/0022-5096%2858%2990020-6
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R. Hill, A note on estimating yield-point loads in a plastic-rigid body, Phil. Mag. 43, 353–355 (1952)
D. C. Drucker and R. T. Shield, Design for minimum weight, Proc. 9th Intern. Congr. Appl. Mech., Brussel, 1956
W. Prager, Minimum weight design of plates, De Ingenieur 48 (1955)
J. Steiner, Einfache Beweise der isoperimetrischen Hauptsätze, Werke II, Berlin, 75–91, 1882
H. G. Hopkins and W. Prager, The load carrying capacities of circular plates, J. Mech. Phys. Solids 2, 1–13 (1953)
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)
D. C. Drucker, W. Prager and H. J. Greenberg, Extended limit design theorems of continuous media, Quart. Appl. Math. 9, 381–389 (1952)
G. Polya and G. Szegö, Isoperimetric inequalities in mathematical physics, Princeton (1951)
H. A. Schwarz, Gesammelte Math. Abhandlungen, vol. 2, Göttingen, 327–335, 1890
W. Prager, Probleme der Plastizitätstheorie, Basel, 1955
R. Hill, A note on estimating yield-point loads in a plastic-rigid body, Phil. Mag. 43, 353–355 (1952)
D. C. Drucker and R. T. Shield, Design for minimum weight, Proc. 9th Intern. Congr. Appl. Mech., Brussel, 1956
W. Prager, Minimum weight design of plates, De Ingenieur 48 (1955)
J. Steiner, Einfache Beweise der isoperimetrischen Hauptsätze, Werke II, Berlin, 75–91, 1882
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Article copyright:
© Copyright 1958
American Mathematical Society