Limit and shakedown analysis using the ns-fem and second-order cone programming

Tran Trung Dung, Nguyen Xuan Hung, Pham Duc Chinh, Le Van Canh

Abstract

This paper presents a novel numerical procedure for limit and shakedown analysis of plane stress problems using node-based smoothed finite element method (NS-FEM) in combination with second-order cone programming (SOCP). The discretization problem is transformed into the form of a second-order cone programming problem which can be solved using highly efficient interior-point solvers. 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 numerical examples are provided to show the efficiency and accuracy of the presented formulation.

Keywords Limit and shakedown analysis (LSA), node-based smoothed finite element method (NS-FEM), second-order cone programming (SOCP)