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BRIEF NOTES

Upper and Lower Bounds for Incipient Failure in a Body Under Gravitational Loading

[+] Author and Article Information
J. A. Chamberlain, D. J. Horrobin, K. A. Landman, J. E. Sader

Department of Mathematics and Statistics, University of Melbourne, Victoria 3010, Australia e-mail: jsader@unimelb.edu.au

J. Appl. Mech 71(4), 586-589 (Sep 07, 2004) (4 pages) doi:10.1115/1.1767164 History: Received July 23, 2003; Revised January 27, 2004; Online September 07, 2004
Copyright © 2004 by ASME
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References

Figures

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Geometry and coordinate systems (a) plane-strain rectangular block (b) axisymmetric cylinder
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Diagram of the upper bound solutions for (a) perfect slip on the base (single velocity discontinuity) and (b) perfectly rough base (double velocity discontinuity)
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Height of incipient failure for the plane strain rectangular block: (a) perfect slip upper bound (UB) from Eq. (7), exact slip-line (EXACT) see Ref. 5, lower bound (LB) from Eq. (3); (b) perfectly rough base upper bound (UB) from Eq. (10), exact slip-line (EXACT) see Ref. 5, lower bound (LB) from Eq. (3)
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Height of incipient failure for the cylinder with perfect slip on the base: (a) Tresca yield condition upper bound (UB) from Eqs. (1213), slip-line lower bound (SLB) see Ref. 4, lower bound (LB) from Eq. (5); (b) von Mises yield condition upper bound (UB) from Eqs. (1415), slip-line lower bound (SLB) see Ref. 4, lower bound (LB) from Eq. (5)
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Height of incipient failure for the cylinder with a perfectly rough base: (a) Tresca yield condition upper bound (UB) from Eqs. (1718), slip-line lower bound (SLB) see Ref. 4, lower bound (LB) from Eq. (5); (b) von Mises yield condition upper bound (UB) from Eqs. (1920), slip-line lower bound (SLB) see Ref. 4, lower bound (LB) from Eq. (5).

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