Lower Bound Determination of Limit Load Using Shepard's Mesh-Free Method and Second Order Cone Programming

In this paper, a novel numerical limit analysis approach is presented for determination of lower bound of collapse load in the stability problems of soil mechanics by combining lower bound theory, Shepard's mesh-free technique and second order cone programming. Based on the proposed method, the domain of problem is simulated by nodes, and there is no need for traditional meshing process used in the conventional mesh-based numerical limit analysis approaches. To satisfy the conditions required for admissibility of stress field at the entire problem domain, a Voronoi cell is considered around each node and the stress gradient is smoothed in this Voronoi cell. As the Voronoi cells cover the entire domain, the obtained smoothed stress field leads to a rigorous lower bound solution. Based on the derived formulation, a computer code is developed and the accuracy and efficiency of proposed method is investigated at the end of the paper by solving some examples.