A Nonlinear Optimization Algorithm for Lower Bound Limit and Shakedown Analysis

Limit and shakedown analysis theorems are the theories of classical plasticity for the direct computation of the load-carrying capacity under proportional and varying loads. Based on Me lan's theorem, a solution procedure for lower bound limit and shakedown analysis of three-dimensional (3D) structures is established making use of the finite element method (FEM). The self-equilibrium stress fields are expressed by linear combination of several basic self-equilibrium stress fields with parameters to be determined. These basic self-equilibrium stress fields are elastic responses of the body to imposed permanent strains obtained through elastic-plastic incremental analysis by the three-dimensional finite element method (3D-FEM). The Complex method is used to solve the resulting nonlinear programming directly and determine the maximal load amplifier. The numerical results show that it is efficient and accurate to solve three-dimensional limit and shakedown analysis problems by using the 3D-FEM and the Complex method. The limit analysis is treated here as a special case of shakedown analysis in which only proportional loading is considered.