Large Problems in Numerical Limit Analysis: A Decomposition Approach

A decomposition approach of the kinematical method of limit analysis is first presented. It is based on a mixed variational approach and on a convex interior point solver, using linear or quadratic discontinuous velocity fields. Exposed in plane strain, this method appears rapidly convergent, as verified in the Tresca compressed bar problem. Then the method is applied to the classical problem of the stability factor of a Tresca vertical slope: the upper bound is lowered from 3.882 to 3.7778. This value is to be compared to the lower bound just increased from 3.772 to 3.7752 by using the same solver in the extension of the method to the statical decomposition problem with infinite elements.