Computation of limit and shakedown using the NS-FEM and second-order cone programming

Abstract

This paper presents a novel numerical procedure for computation of limit and shakedown using node-based smoothed finite element method (NS-FEM) in combination with second-order cone programming (SOCP). The obtained discretization formulation is then cast in a form which involves second-order cone constraints, ensuring that the underlying optimization problem can be solved by highly efficient primal-dual interior point algorithm. Furthermore, in the NS-FEM, the system stiffness matrix is computed using the smoothed strains over the smoothing domains associated with nodes. This ensures that the size of the resulting optimization problem is kept to a minimum. The efficiency of the present approach is illustrated by examining several numerical examples.