On the plastic bending of circular plates under uniform transverse loads
Author:
D. Trifan
Journal:
Quart. Appl. Math. 6 (1949), 417-427
MSC:
Primary 73.2X
DOI:
https://doi.org/10.1090/qam/30427
MathSciNet review:
30427
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Additional Information
- A. A. Ilyushin, Relation between the theory of St. Venant-Levy-Mises and the theory of small elastico-plastic deformations, Appl. Math. Mech. [Akad. Nauk SSSR. Prikl. Mat. Mech.] 9 (1945), 207–218 (Russian, with English summary). MR 0013377
W. Prager, On Isotropic Materials with Continuous Transition from Elastic to Plastic State, Proc. 5th Internat. Congr. Appl. Mech., Cambridge (Mass.) 1938, pp. 234-237.
- W. Prager, A new mathematical theory of plasticity, J. Appl. Math. Mech. [Akad. Nauk SSSR. Zhurnal Prikl. Mat. Mech.] 5 (1941), 419–430 (English, with Russian summary). MR 0007350
- G. H. Handelman, C. C. Lin, and W. Prager, On the mechanical behaviour of metals in the strain-hardening range, Quart. Appl. Math. 4 (1947), 397–407. MR 21844, DOI https://doi.org/10.1090/S0033-569X-1947-21844-8
L. Prandtl, Spannungsverteilung in plastischen Körpern, Proc. 1st Internat. Congr. Appl. Mech., Delft 1924, pp. 43-54.
E. Reuss, Berücksichtigung der elastischen Formaenderungen in der Plastizitaetstheorie, Z. angew. Math. Mech. 10, 266-274 (1930).
H. Hencky, Zur Theorie plastischer Deformationen und der hierdurch im Material hervorgerufenen Nachspannungen, Z. angew. Math. Mech. 4, 323-334 (1924).
A. Nadai, Plasticity, a Mechanics of the Plastic State of Matter, McGraw-Hill Book Co., Inc., New York, 1931.
- W. Prager, Strain hardening under combined stresses, J. Appl. Phys. 16 (1945), 837–840. MR 16016
- A. A. Ilyushin, Some problems on the theory of plastic deformations, Appl. Math. Mech. [Akad. Nauk SSSR. Prikl. Mat. Mech.] 7 (1943), 245–272 (Russian, with English summary). MR 0012040
- W. W. Sokolovsky, Elastico-plastic bending of circular plates and plane rings, Appl. Math. Mech. [Akad. Nauk SSSR. Prikl. Mat. Mech.] 8 (1944), 141–166 (Russian, with English summary). MR 0012588
I. S. Sokolnikoff, Mathematical Theory of Elasticity, mimeographed lecture notes, Brown Univ., Providence, 1941.
S. Timoshenko, Plates and Shells, McGraw-Hill Book Co., Inc., New York, 1940.
A. A. Ilyushin, Relation between the Theory of St. Venant–Lévy–Mises and the Theory of Small Elastic–Plastic Deformations, Prikl. Mat. Mekh. 9, 207-218 (1945).
W. Prager, On Isotropic Materials with Continuous Transition from Elastic to Plastic State, Proc. 5th Internat. Congr. Appl. Mech., Cambridge (Mass.) 1938, pp. 234-237.
W. Prager, A New Mathematical Theory of Plasticity, Prikl. Mat. Mekh. 5, 419-428 (1941).
G. H. Handelman, C. C. Lin, and W. Prager, On the Mechanical Behaviour of Metals in the Strain-Hardening Range, Q. Appl. Math. 4, 397-407 (1947).
L. Prandtl, Spannungsverteilung in plastischen Körpern, Proc. 1st Internat. Congr. Appl. Mech., Delft 1924, pp. 43-54.
E. Reuss, Berücksichtigung der elastischen Formaenderungen in der Plastizitaetstheorie, Z. angew. Math. Mech. 10, 266-274 (1930).
H. Hencky, Zur Theorie plastischer Deformationen und der hierdurch im Material hervorgerufenen Nachspannungen, Z. angew. Math. Mech. 4, 323-334 (1924).
A. Nadai, Plasticity, a Mechanics of the Plastic State of Matter, McGraw-Hill Book Co., Inc., New York, 1931.
W. Prager, Strain-Hardening under Combined Stresses, J. Appl. Phys. 16, 837-840 (1945).
A. A. Ilyushin, Some Problems in the Theory of Plastic Deformations, Prikl. Mat. Mekh. 7, 245-272 (1943).
V. V. Sokolovsky, Elastic-Plastic Bending of Circular and Annular Plates, Prikl. Mat. Mekh. 8, 141-166 (1944).
I. S. Sokolnikoff, Mathematical Theory of Elasticity, mimeographed lecture notes, Brown Univ., Providence, 1941.
S. Timoshenko, Plates and Shells, McGraw-Hill Book Co., Inc., New York, 1940.
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Article copyright:
© Copyright 1949
American Mathematical Society
