On kinematic method in shakedown theory. I: Duality of extremum problems. II: Modified kinematic method (Q1338395)

A kinematic method for determining the safety factor in shakedown problems is developed. An upper bound kinematic functional is defined on a set of kinematically admissible time-independent velocity fields. Every value of the functional is an upper bound for the safety factor. Using convex analysis methods, conditions are established under which the infimum of the kinematic upper bounds equals the safety factor, in particular, conditions under which it is sufficient to consider only smooth velocity fields for the safety factor calculation. A shakedown problem for a beam subjected to a concentrated load is considered as an example. A finite element discretization of the kinematic extremum problem is considered, and convergence of minimums of the discretized problems to the safety factor is proved.