REGULARIZED METHOD IN LIMIT ANALYSIS

The regularized problem proposed by Friaa is discussed in this paper. The Norton-Hoff viscoplastic law is first generalized and can be proved to be associated with the yield function of a plastic material. It can be demonstrated that, for any value of the coefficient of viscosity p, the viscoplastic-strain rates satisfy also the plastic-normality conditions. The creep-strain rates tend to plastic-strain rates when the coefficient p tends to one. Two dual variational formulations are then established for viscoplastic problems. These formulations have been proved well posed mathematically in view of the existence of solutions, and lead to efficient numerical computations. They are very useful for limit analysis, which is characterized by the minimization of a nonlinear functional in the space of kinematically admissible velocity fields. The optimized kinematically admissible velocity field is then used to justify the stability of structures under external loads. Different criterion functions of limit loads are discussed and the best one is proposed. An analytical example is presented and some numerical problems are presented to illustrate the performance of the regularized method.