An adaptive remeshing procedure for discontinuous finite element limit analysis

An adaptive remeshing procedure is proposed for discontinuous finite element limit analysis. The procedure proceeds by iteratively adjusting the element sizes in the mesh to distribute local errors uniformly over the domain. To facilitate the redefinition of element sizes in the new mesh, the interelements discontinuous field of elemental bound gaps is converted into a continuous field, ie, the intensity of bound gap, using a patch‐based approximation technique. An analogous technique is subsequently used for the approximation of element sizes in the old mesh. With these information, an optimized distribution of element sizes in the new mesh is defined and then scaled to match the total number of elements specified for each iteration in the adaptive remeshing process. Finally, a new mesh is generated using the advancing front technique. This adaptive remeshing procedure is repeated several times until an optimal mesh is found. Additionally, for problems involving discontinuous boundary loads, a novel algorithm for the generation of fan‐type meshes around singular points is proposed explicitly and incorporated into the main adaptive remeshing procedure. To demonstrate the feasibility of our proposed method, some classical examples extracted from the existing literary works are studied in detail.