In this paper is presented a general methodology for predicting puckering instabilities in sheet metal forming applications. A novel approach is introduced which does not use shell theory approximations. The starting point is Hill’s stability functional for a three-dimensional rate-independent stressed solid which is modified for contact. By using a multiple scale asymptotic technique with respect to the small dimensionless thickness parameter ε, one can derive the two-dimensional version of the stability functional which is accurate up to thus taking into account bending effects. Loss of positive definiteness of this functional indicates possibility of a puckering instability in a sheet metal forming problem with a known stress and deformation state. An advantage of the proposed method is that the puckering investigation is independent of the algorithm used for calculating the deformed state of the sheet. [S0021-8936(00)00804-7]
Asymptotic Stability Analysis for Sheet Metal Forming—Part I: Theory
Contributed by the Applied Mechanics Division of THE AMERICAN SOCIETY OF MECHANICAL ENGINEERS for publication in the ASME JOURNAL OF APPLIED MECHANICS. Manuscript received by the ASME Applied Mechanics Division, Sept. 24, 1999; final revision, Jan. 30, 2000. Associate Technical Editor: S. Kyriakides. Discussion on the paper should be addressed to the Technical Editor, Professor Lewis T. Wheeler, Department of Mechanical Engineering, University of Houston, Houston, TX 77204-4792, and will be accepted until four months after final publication of the paper itself in the ASME JOURNAL OF APPLIED MECHANICS.
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Scherzinger, W., and Triantafyllidis, N. (January 30, 2000). "Asymptotic Stability Analysis for Sheet Metal Forming—Part I: Theory ." ASME. J. Appl. Mech. December 2000; 67(4): 685–690. https://doi.org/10.1115/1.1325012
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