Upper bound limit analysis using smoothed finite element method considering discontinuous field

The finite element limit analysis based on strain smoothing provides an effective and highly accurate numerical approach for stability analysis in geotechnical engineering. A novel upper bound limit analysis using node-based smoothed finite element (NSFEM) is proposed to account for the discontinuous kinematic velocity field. By introducing a discontinuous velocity at the soil-structure interface, characterized by nodal velocity jumps between interface nodes, the strain-smoothed domains are reconstructed based on these interface nodes. The plastic dissipation rates of interfaces and strain-smoothed domains are separately calculated according to the Mohr-Coulomb yield criterion and associated flow rule. These criteria and rules are represented as a series of standard second-order cones. Consequently, the NSFEM-based upper bound limit analysis is formulated as a second-order cone programming (SOCP) problem, solvable effectively using the primal-dual interior point algorithm. The proposed method's reliability was initially confirmed through benchmark problem analysis in geotechnical engineering, revealing that the interface strength between soil and structure significantly influences the failure mechanism and ultimate bearing capacity of structures.