On kinematic method in shakedown theory - I. Duality of extremum problems. II - Modified kinematic method

In the present kinematic method for determining the safety factor in shakedown problems, convex analysis techniques are used to establish conditions under which the infimum of the kinematic upper bounds equals the safety factor. This is especially valuable in conditions under which it suffices to consider only smooth velocity fields for the safety factor calculation. In the second part of this work, attention is given to the shakedown problem with a polyhedral set of variable loads; the time variable is eliminated, and a simple explicit formula is derived for the kinematic functional's consideration on a set of regular fields. (AIAA)