Non-linear programming applied to finite element lower bound limit analysis in soil mechanics

The non-linear programming theory along with active set algorithm is employed to solve the objective function of quadratic type problem in soil mechanics under plain strain and two dimensional loading conditions. Combination of lower bound limit analysis and finite element method leads to an appropriate procedure for determining the collapse load of the system. In this combined method, a linear approximation of yield surface is used and by applying the equilibrium, stress boundary and discontinuity condition and utilizing a suitable optimization technique, the statically admissible stress field is obtained from which a lower safe limit to collapse load is computed. In order to assess the usefulness of the proposed technique, a number of examples are given and the results obtained from this technique are compared with the published results on those examples. Based on the comparisons made, the accuracy and efficiency of the method are examined and discussed. Key-Words: Lower bound limit, Non-linear programming, Soil mechanics