Asymptotic Stability Analysis for Sheet Metal Forming—Part I: Theory

[+] Author and Article Information
W. Scherzinger

Sandia National Laboratories, P.O. Box 5800, MS 0847, Albuquerque, NM 87185  

N. Triantafyllidis

Department of Aerospace Engineering, The University of Michigan, Ann Arbor, MI 48109-2140

J. Appl. Mech 67(4), 685-690 (Jan 30, 2000) (6 pages) doi:10.1115/1.1325012 History: Received September 24, 1999; Revised January 30, 2000
Copyright © 2000 by ASME
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Grahic Jump Location
Three-dimensional kinematics for a shell-like structure. The midsurface is defined by the vector r while a point off the midsurface is defined by position vector p . The covariant midsurface basis is ai and the covariant three-dimensional basis is gi.
Grahic Jump Location
Contact between tooling surface and sheet. A point on the sheet’s lower surface with position vector p is at a distance D from the rigid surface. The penetration distance is positive when p−ps has the same orientation as ns, the outward unit normal to the rigid surface.




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