On limit analysis of plates
Author:
Walter Schumann
Journal:
Quart. Appl. Math. 16 (1958), 61-71
MSC:
Primary 73.00
DOI:
https://doi.org/10.1090/qam/102256
MathSciNet review:
102256
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Abstract: The bending of thin perfectly plastic plates of arbitrary shape under transverse load is studied. The collapse load for a concentrated force on such a plate is found to be $2\pi$ times the yield moment.
- H. G. Hopkins and W. Prager, The load carrying capacities of circular plates, J. Mech. Phys. Solids 2 (1953), 1–13. MR 57735, DOI https://doi.org/10.1016/0022-5096%2853%2990022-2
H. G. Hopkins, The theory of deformation of non-hardening rigid-plastic plates under transverse load, IUTAM Colloquium, Madrid, 176-183 (1955)
- D. C. Drucker, W. Prager, and H. J. Greenberg, Extended limit design theorems for continuous media, Quart. Appl. Math. 9 (1952), 381–389. MR 45573, DOI https://doi.org/10.1090/S0033-569X-1952-45573-2
- A. R. Rzhanitsyn, The shape at collapse of elastic-plastic plates simply supported along the edges, Tech. Rep. No. 19, Office of Naval Research, Contract Nonr-562 (10) NR-064-406, Division of Applied Mathematics, Brown University, Providence, R. I., 1957. MR 0097921
- William Prager, Probleme der Plastizitätstheorie, Birkhäuser Verlag, Basel und Stuttgart, 1955 (German). MR 0076573
W. Prager and P. G. Hodge, Jr., Theorie ideal plastischer Körper, Wien, 1954, p. 133
W. Blaschke, Differentialgeometrie, Bd. 1, Berlin, 1930, pp. 112, 179
C. E. Weatherburn, Differential geometry, vol. 1, Cambridge, 1927, p. 177
- William Prager, Discontinuous fields of plastic stress and flow, Proceedings of the Second U. S. National Congress of Applied Mechanics, Ann Arbor, 1954, American Society of Mechanical Engineers, New York, 1955, pp. 21–32. MR 0079413
R. Courant and D. Hilbert, Methoden der mathematischen Physik, Bd. 2, Berlin, 1932, p. 233
H. G. Hopkins and W. Prager, The load carrying capacities of circular plates, J. Mech. Phys. Solids 2 1-13 (1953)
H. G. Hopkins, The theory of deformation of non-hardening rigid-plastic plates under transverse load, IUTAM Colloquium, Madrid, 176-183 (1955)
D. C. Drucker, W. Prager and H. J. Greenberg, Extended limit design theorems of continuous media, Quart. Appl. Math. 9, 381-389 (1952)
A. R. Rzhanitsyn, The shape at collapse of elastic-plastic plates, simply supported along the edges (in Russian), Translated by R. M. Haythornthwaite, Tech. Rept. No. 19, Contract Nonr 562(10), Office of Naval Research
W. Prager, Probleme der Plastizitätstheorie, Birkhäuser, Basel 1955, p. 54
W. Prager and P. G. Hodge, Jr., Theorie ideal plastischer Körper, Wien, 1954, p. 133
W. Blaschke, Differentialgeometrie, Bd. 1, Berlin, 1930, pp. 112, 179
C. E. Weatherburn, Differential geometry, vol. 1, Cambridge, 1927, p. 177
W. Prager, Discontinuous fields of plastic stress and flow, Proc. Sec. Natl. Congr. Appl. Mech., June 1954
R. Courant and D. Hilbert, Methoden der mathematischen Physik, Bd. 2, Berlin, 1932, p. 233
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Article copyright:
© Copyright 1958
American Mathematical Society
