Mixed boundary value problems in soil mechanics
Author:
R. T. Shield
Journal:
Quart. Appl. Math. 11 (1953), 61-75
MSC:
Primary 73.2X
DOI:
https://doi.org/10.1090/qam/54512
MathSciNet review:
54512
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Abstract: The stress-strain law for an ideal soil formulated in a recent paper [1]$^{3}$ is applied here to obtain the velocity equations referred to the stress characteristic lines in plane strain problems. Simple velocity fields associated with families of straight characteristic lines are then examined, together with discontinuities in the velocity field. The results are applied to obtain the incipient velocity field for the indentation of a semi-infinite mass of material by a flat punch or footing, and to solve the problem of indentation by a lubricated wedge.
- D. C. Drucker and W. Prager, Soil mechanics and plastic analysis or limit design, Quart. Appl. Math. 10 (1952), 157–165. MR 48291, DOI https://doi.org/10.1090/S0033-569X-1952-48291-2
K. Terzaghi, Theoretical soil mechanics, John Wiley and Sons, p. 22, 1943. In this reference, ${\sigma _x}$ and and ${\sigma _y}$ denote compressive stresses, while in equation (1) ${\sigma _x}$ and ${\sigma _y}$ are positive when the stresses are tensile.
V. V. Sokolovsky, Statics of earthy media, Izdatelstvo Akademii Nauk S. S. R., Moscow, 1942.
F. Kötter, Berlin Akad. Berichte, p. 229, (1903).
R. v. Mises, Mechanik der plastischen Formaenderung von Kristallen, Z. angew. Math. Mech. 8, 161–185 (1928).
L. Prandtl, Ueber die Haerte plasticher Koerper, Goettinger Nachr., Math.-Phys. Kl. 1920, 74–85 (1920).
- R. Hill, The plastic yielding of notched bars under tension, Quart. J. Mech. Appl. Math. 2 (1949), 40–52. MR 29686, DOI https://doi.org/10.1093/qjmam/2.1.40
- R. Hill, E. H. Lee, and S. J. Tupper, The theory of wedge indentation of ductile materials, Proc. Roy. Soc. London Ser. A 188 (1947), 273–289 (1 plate). MR 19012, DOI https://doi.org/10.1098/rspa.1947.0009
D. C. Drucker and W. Prager, Soil mechanics and plastic analysis or limit design, Q. Appl. Math. 10, (1952).
K. Terzaghi, Theoretical soil mechanics, John Wiley and Sons, p. 22, 1943. In this reference, ${\sigma _x}$ and and ${\sigma _y}$ denote compressive stresses, while in equation (1) ${\sigma _x}$ and ${\sigma _y}$ are positive when the stresses are tensile.
V. V. Sokolovsky, Statics of earthy media, Izdatelstvo Akademii Nauk S. S. R., Moscow, 1942.
F. Kötter, Berlin Akad. Berichte, p. 229, (1903).
R. v. Mises, Mechanik der plastischen Formaenderung von Kristallen, Z. angew. Math. Mech. 8, 161–185 (1928).
L. Prandtl, Ueber die Haerte plasticher Koerper, Goettinger Nachr., Math.-Phys. Kl. 1920, 74–85 (1920).
R. Hill, The plastic yielding of notched bars under tension, Q. J. Mech. Appl. Math. 2, 40–52 (1949).
R. Hill, E. H. Lee, and S. J. Tupper, The theory of wedge indentation of ductile materials, Proc. Roy. Soc. London (A) 188, 273–289 (1947).
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© Copyright 1953
American Mathematical Society
