Numerical method for lower-bound solution of the rigid-plastic limit analysis problem

This paper describes a numerical method to determine the lower-bound soluti on of limit load of a rigid-perfectly plastic body obeying the von Mises yi eld criterion. The idea of this method is to construct a smoothed linear st ress field that satisfies the yield criterion everywhere in the body. Apply ing the similar stress recovery techniques as superconvergent patch recover y and recovery by equilibrium in patch in the elastic finite-element analys is, the nodal stresses are obtained from those stresses at the integration points from an iterative process of upper-bound limit analysis. Then, the i mproved stress fields and lower-bound solutions can be derived by ensuring all the nodal stresses within the yield surface. The convergence of this me thod is guaranteed. The validity of the proposed method is demonstrated wit h some numerical examples. The computational results show that more reliabl e lower-bound solutions can be obtained by using this method, especially fo r problems with strain singularity.