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

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. The authors use piecewise constant stresses and piecewise bilinear displacements, and present computational results with the Affine Scaling Algorithm a la Dikin and Karmarker. 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 the present knowledge, these stress fields have not been computed before.