An adaptive selective ES-FEM for plastic collapse analysis

Abstract We present a selective edge-based smoothed finite element method (sES-FEM) of kinematic theorem for predicting the plastic limit loads in structures. The basic idea in this method is to use two levels of mesh repartitioning for the finite element limit analysis. The master level begins with an adaptive primal-mesh strategy guided by a dissipation-based indicator. The slave level consists of further subdividing each triangle into three sub-triangles and creating a dual mesh through a careful selection of a pair of two sub-triangles shared by the corresponding common element edge. By applying a strain smoothing projection operator to the strain rates on the dual mesh, the flow rule constraint is enforced over the edge-based strain smoothing domains, and likewise everywhere in the problem domain. This numerical procedure is performed for a cohesive-frictional material. This numerical procedure is also performed necessarily to avoid the volumetric locking problem for a purely cohesive material. The optimization formulation of limit analysis is next presented by the form of a second-order cone programming (SOCP) for the purpose of exploiting the efficiency of interior–point solvers. The present method uses linear triangular elements and handles a low number of optimization variables. This leads to a convenient way to design and solve the large-scale optimization problems effectively. Several numerical examples are given to demonstrate the simplicity and effectiveness of the proposed method.