A numerical method for lower bound limit analysis of 3-D structures with multi-loading systems

The determination of lower bound limit load of 3-D structures is by no mean s an easy task, especially for complex configurations and loading systems. In our previous work, a numerical method of upper bound limit analysis for 3-D structures with multi-loading systems was proposed. This method combine s FEM and mathematical programming technique in an iterative procedure. In the present article, on the basis of the nature of the iterative procedure for upper bound limit analysis, the statically admissible stress fields, wh ich satisfies the equilibrium equation and boundary conditions, are constru cted using some intermediate variables obtained by upper bound limit analys is procedure. Moreover, a mathematical programming formulation is set up fo r the static limit analysis of 3-D structures under multi-loading systems a nd a direct iterative algorithm used to determine the lower bound limit loa d multiplier is proposed, which depends on the static theorem of plasticity . The numerical examples are given to demonstrate the applicability of the procedure. (C) 1999 Elsevier Science Ltd. All rights reserved.