UPPER-BOUND LIMIT ANALYSIS OF A RIGID-PLASTIC BODY WITH FRICTIONAL INTERFACES

A finite element formulation of the upper-bound theorem for rigid-plas tic solids, generalized to include interfaces with finite friction, is described. As proved by Collins [J. Mech. Phys, Solids 17, 323 (1969) ], the usual definition of a kinematically admissible velocity field i s unnecessarily restrictive when the upper-bound theorem is applied to many practical problems. This paper shows that a relaxed inequality c an be used successfully to derive upper bounds in the presence of Coul omb friction on interfaces, provided one considers a wide enough class of ''admissible'' velocity fields. One of the major advantages of usi ng a numerical formulation of the upper-bound theorem is that both com plex loading geometry and inhomogeneous material behaviour can be easi ly dealt with. Using a suitable linear approximation of the yield surf ace, the application of the necessary boundary conditions, the plastic flow rule and the yield criterion lead to a large linear programming problem. The numerical procedure uses constant-strain triangular eleme nts with the unknown velocities as the nodal variables. An additional set of unknowns, the plastic multiplier rates, is associated with each element. Kinematically admissible velocity discontinuities are permit ted along specified planes within the finite element mesh. During the solution phase, an active set algorithm is used to solve the linear pr ogramming problem.