Lower bound limit analysis using the Control Volume Finite Element Method

The paper presents a novel approach for lower bound limit analysis based on the Control Volume Finite Element Method. The central concept of the solution procedure is a force balance on control volumes corresponding to nodes, where tractions on control volume faces are evaluated using linear interpolation of the unknown stress components at nodal points. An optimization routine incorporating second-order cone programming is subsequently employed to find the stress field that maximizes applied load subject to constraints imposed by equilibrium, boundary conditions, and the yield condition, thereby finding a load that is closest to the true collapse load. The formulation is for plain strain (i.e. two dimensions) and material obeying the Mohr-Coulomb yield condition. The proposed approach is applied to the benchmark problem of a uniform strip load applied to a half space, and very good agreement between analytical and numerical results is found.