Fictitious loading upper bound limit analysis approach based on elastic FEM

For the MSD method, the most crucial point is the construction of compatible and continuous plastic deformation fields. However, plastic deformation fields are difficult to be obtained, and there exists no universally applicable method for that task. A fictitious loading upper bound limit analysis approach is implemented by the elastic FEM, which practically overcomes the inconvenience of deformation field construction as a prior condition for the MSD method. The proposed method can simultaneously acquire the load and the corresponding velocity field under a prescribed displacement, and the time-consuming optimization process required in the traditional upper bound limit analysis is equivalently converted into iteration here. The proposed method is applied in analyzing the shaft of laterally loaded pile, strip foundation and deep anchor. Judged from the three classic cases in soil mechanics, the load-displacement curves obtained by the proposed method are generally consistent with those obtained by the elasto-plastic FEM, and the obtained ultimate bearing capacities are close to the acknowledged plastic solutions, validating the effectiveness of the proposed method in the entire loading process. Through analyzing the velocity fields in the loading process, the same initial velocity field is identified, which gradually transforms with iteration, and when the limit displacement is applied, it finally becomes to be similar to the plastic collapse mechanisms. The proposed method can be utilized to study complicated problems, whose plastic deformation mechanisms are not acquired yet.