Automatic remeshing in limit analysis with deformable polygon discretization

Automatic remeshing holds promise for reducing mesh dependency in numerical simulations. However, its current application in limit analysis primarily relies on triangular meshes. Existing mesh refinement schemes are often not general enough to accommodate complex discretizations. To address this, the paper introduces a dissipation-based automatic remeshing strategy for finite element limit analysis, which supports meshes with arbitrary element shapes and enables interfacial velocity discontinuities and selective refinement. The element deformation is assumed to be homogeneous. The approach is applied to analyze the collapses of the weightless cohesive-frictional strip footing and of a masonry arch bridge interacting with the backfill. The results obtained both indicate the reliability and effectiveness of the proposed remeshing procedure, showing competitive efficiency when compared with a global uniform refinement. Applying remeshing to polygon discretizations is crucial since it can effectively release the locking effect induced by the constant-strain assumption inside the elements, and the converged load prediction can gain precision comparable to the triangular one. Polygon elements exhibit great efficiency in large-scale applications, requiring only 1/5 – 1/2 of processing time when compared with triangular meshes. Regular polygons are more recommended given the lower sensitivity to the initial mesh. The proposed procedure broadens the applicable scenarios of remeshing in limit analysis, providing also a paradigm for mesh refinement in other mesh-based simulations.