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TECHNICAL PAPERS

Analysis of a Rocking and Walking Punch—Part II: General Numerical Solution Using Quadratic Programming

[+] Author and Article Information
D. Nowell

Department of Engineering Science, University of Oxford, Parks Road, Oxford OX1 3PJ, UK

J. Appl. Mech 71(2), 234-239 (May 05, 2004) (6 pages) doi:10.1115/1.1641062 History: Received November 18, 2002; Revised July 24, 2003; Online May 05, 2004
Copyright © 2004 by ASME
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References

Figures

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Geometry of the problem
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Auxiliary coordinates used for |s/a|>0.5
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Discretization of the shear tractions by overlapping triangular elements
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Alternative positions for the last collocation point (a) distance h from the contact edge, (b) coincident with the contact edge, and (c) between (a) and (b)
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Effect of the position of the last collocation point: difference between position of the stick/slip interface in numerical and analytical solutions plotted as a function of collocation point position, Q/fP=0.75
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Comparison of numerical predictions of the shear tractions and analytical values, 1, for the first quarter cycle of loading, Q/fP=0.75,−0.5<s/a<0
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Comparison of numerical predictions of slip and analytical values, 1, for the first quarter-cycle of loading Q/fP=0.75,−0.5<s/a<0
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Evolution of cumulative slip at the center of the punch with loading cycle for the first few cycles of loading as s/a varies between −0.5 and 0.5. Vertical lines show when the direction of travel of the normal load is reversed
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Comparison between numerical values for steady-state slip per cycle and those obtained by an integral equation approach, 1
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Normalized shear tractions as s/a is cycled between −0.5 and 0.5, Q/fP=0.75

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