Zhangzhi Cen

Boundary element methods for lower bound limit and shakedown analysis

Abstract Limit and shakedown theorems are exact theories of classical plasticity for the direct computation of the load-carrying capacity under constant and varying loads. Based on Melans theorem, a solution procedure for limit and shakedown analysis is established making use of symmetric Galerkin boundary element method (SGBEM) for two-dimensional (2D) structures and traditional boundary element method (BEM) for three-dimensional (3D) structures. 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 impose permanent strains obtained through elastic–plastic incremental analysis by SGBEM for 2D structures and by BEM for 3D structures, respectively. The Complex method is used to solve resulting non-linear programming directly and determine the maximal load amplifier. The numerical results show that it is efficient and accurate to solve limit and shakedown analysis problems by using the BEM and the Complex method. In this paper, the limit analysis is treated as a special case of shakedown analysis in which only proportional loading is considered.