Direct computation of shakedown loads via incremental elastoplastic analysis

The problem of shakedown analysis is considered. The mathematical programming formulations of limit and incremental elastoplastic analysis are first briefly reviewed and a convenient standard form for shakedown analysis is then suggested. This standard form can formally be viewed as a problem of limit analysis. In this way, two different solution approaches are applicable: either the problem can be solved directly using general optimization methods or the problem can be converted into an equivalent fictitious incremental elastoplastic problem and solved as such. We further show that this result holds in general for arbitrary convex mathematical programs. Thus, all the methods and techniques developed for elastoplasticity are in principle applicable to general convex programming. For the solution of shakedown problems we employ a version of the well-known implicit solution procedure in combination with a number of equally well-known techniques from general optimization theory. The resulting algorithm enables an efficient and robust treatment of cone-shaped yield constraints of the Drucker-Prager type.