Large static problem in numerical limit analysis: A decomposition approach

doi:10.1002/nag.887

Large static problem in numerical limit analysis: A decomposition approach

2010-11-29

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DOI：10.1002/nag.887

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A general decomposition approach for the static method of limit analysis is proposed. It is based on piecewise linear stress fields, on a partition into finite element sub-problems and on a specific coordination of the subproblem stress fields through auxiliary interface problems. The final convex optimization problems are solved using nonlinear interior point programming methods. As validated for the compressed bar with Tresca/von Mises materials in plane strain, this method appears rapidly convergent, so that very large problems with millions of constraints and variables can be solved. Then the method is applied to the classical problem of the stability of a Tresca vertical cut: the static bound to the stability factor is improved to 3.7752, a value to be compared with the recent best upper bound 3.7776. Copyright (C) 2010 John Wiley & Sons, Ltd.

Keywords:

limit analysis

static method

finite elements

convex optimization

decomposition approach

vertical cut

Large static problem in numerical limit analysis: A decomposition approach

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