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Computing material collapse displacement fields on a cray X-MP/48 by the LP primal affine scaling algorithm

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Abstract

A pair of dual, highly degenerate linear programs modeling the static and kinematic principles of limit analysis are studied. They arise from mixed finite element discretizations of the continuous saddle point problem and piecewise linear approximations of the convex unbounded Mises set of admissible stresses. We use piecewise constant stresses and piecewise bilinear displacements, and present computational results with the Affine Scaling Algorithm a la Dikin (1967) and Karmarker (1984). Graphical displays are presented for material collapse fields of a rectangular solid with thin cuts under tension, in problem sizes up to 9000 variables and 7700 equations. To our knowledge, these stress fields have not been computed before.

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Authors and Affiliations

  1. Department of Mathematics, Odense University, DK-5230, Odense, Denmark

    E. Christiansen

  2. Department of Management Science, College of Business Administration, The University of Iowa, 52242, Iowa City, Iowa, USA

    K. O. Kortanek

Authors
  1. E. Christiansen
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  2. K. O. Kortanek
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Additional information

The research underlying this report was supported by NSF Grants ECS-8500940 at Carnegie-Mellon University and the University of Iowa and by ECS-8696087 at the University of Iowa. A preliminary version of this paper was presented at the Supercomputers and Large-Scale Optimization Workshop at the University of Minnesota, Minneapolis, May 16–18, 1988.

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Christiansen, E., Kortanek, K.O. Computing material collapse displacement fields on a cray X-MP/48 by the LP primal affine scaling algorithm. Ann Oper Res 22, 355–376 (1990). https://doi.org/10.1007/BF02023060

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