Mesh-Free Lower Bound Limit Analysis

Abstract

A novel numerical approach is developed for computing lower bound limit load in soil mechanics problems under plane strain condition. In the presented technique, there is no need to mesh in the traditional sense, and a lower bound solution is obtained. To develop the lower bound optimization problem, a statically admissible stress field is constructed by Shepard's shape functions in conjunction with the stabilized nodal integration scheme. The linearized Mohr–Coulomb criterion is adopted to satisfy the plastic admissibility of the generated stress field. The obtained optimization problem with a considerable reduced number of constraints has been solved by the linear programming technique. Based on the derived formulations, a computer code has been developed and the accuracy and efficiency of proposed method is demonstrated by solving some examples at the end of the paper.