An efficient and synchronous mesh refining–coarsening strategy in kinematic upper-bound limit analysis

Abstract

This study presents an efficient and robust adaptive remeshing strategy in the kinematic upper-bound limit analysis in association with using six-node triangular elements and Second–Order Cone Programming (SOCP). In particular, a Synchronous Mesh Refining–Coarsening (SMRC) algorithm following a posterior plastic dissipation-based error indicator and the well-known Delaunay triangulation are implemented into the Upper Bound Finite Element Method (UBFEM). Detailed numerical implementation of the proposed method is presented, and its computational performance is demonstrated through several benchmark problems and comparisons with those solutions obtained using Pure Mesh Refinement (PMR) scheme. The proposed method, named UBFEM-SMRC, is proved to generate more rigorous solutions for all considered examples and significantly reduce the computational burdens of the UBFEM-PMR. Additionally, more clear adaptively refined mesh zones with intensive plastic dissipations, which can readily reproduce the potential failure mechanisms of geotechnical problems, are observed by successive performing of the proposed synchronous adaptive mesh refining–coarsening process.