On finite expansion of a hole in a thin infinite plate
Authors:
P. G. Hodge Jr. and R. Sankaranarayanan
Journal:
Quart. Appl. Math. 16 (1958), 73-80
MSC:
Primary 73.00
DOI:
https://doi.org/10.1090/qam/102974
MathSciNet review:
102974
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Abstract: A complete solution for all values of applied pressure is obtained for the expansion of a hole of zero radius in an initially uniform infinite sheet. The analysis is compared with those of previous investigators and found to be simpler and/or more complete. It is shown that the results are applicable to the expansion of a finite hole in a uniform sheet and to the expansion of a hole in a tapered sheet.
- William Prager, On the use of singular yield conditions and associated flow rules, J. Appl. Mech. 20 (1953), 317–320. MR 0059770
P. G. Hodge, Jr., Plastic bending of an annular plate, J. Math. & Phys. 36, 130–137 (1957)
- G. I. Taylor, The formation and enlargement of a circular hole in a thin plastic sheet, Quart. J. Mech. Appl. Math. 1 (1948), 103–124. MR 25923, DOI https://doi.org/10.1093/qjmam/1.1.103
- R. Hill, Plastic distortion of non-uniform sheets, Philos. Mag. (7) 40 (1949), 971–983. MR 32368
- J. M. Alexander and H. Ford, On expanding a hole from zero radius in a thin infinite plate, Proc. Roy. Soc. London Ser. A 226 (1954), 543–561. MR 70414, DOI https://doi.org/10.1098/rspa.1954.0274
R. v. Mises, Mechanik der plastischen Formaenderung von Kristallen, ZAMM 8, 161-185 (1928)
W. Prager, The theory of plasticity—a survey of recent achievements, James Clayton Lecture, Inst. Mech. Engrs., London, 1955
- P. G. Hodge Jr., Minimum principles of piecewise linear isotropic plasticity, J. Rational Mech. Anal. 5 (1956), 917–938. MR 82289, DOI https://doi.org/10.1512/iumj.1956.5.55034
W. Prager, On the use of singular yield conditions and associated flow rules, J. Appl. Mech. 20, 317-320 (1953)
P. G. Hodge, Jr., Plastic bending of an annular plate, J. Math. & Phys. 36, 130–137 (1957)
G. I. Taylor, The formation and enlargement of a circular hole in a thin plastic sheet, Quart. J. Mech. Appl. Math. 1, 103-124 (1948)
R. Hill, Plastic distortion of non-uniform sheets, Phil. Mag. Ser. 7, vol. xi, 971-983 (1949)
J. M. Alexander and H. Ford, On expanding a hole from zero radius in a thin infinite plate, Proc. Roy. Soc. A226, 543-561 (1954)
R. v. Mises, Mechanik der plastischen Formaenderung von Kristallen, ZAMM 8, 161-185 (1928)
W. Prager, The theory of plasticity—a survey of recent achievements, James Clayton Lecture, Inst. Mech. Engrs., London, 1955
P. G. Hodge, Jr., Minimum principles of piecewise linear isotropic plasticity, J. Ratl. Mech. and Anal. 5, 917-938 (1956)
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Article copyright:
© Copyright 1958
American Mathematical Society
