Shakedown in Elastic-Plastic Systems Under Dynamic Loadings

Following the derivations of Koiter, who gave a general proof of Melan’s shakedown theorem for elastic-plastic systems under quasi-static reversible parametric loadings, it is shown here that the inclusion of the inertia force due to dynamic loadings does not change the basic tendency for the system to shakedown, if it can. Because of the validity of this shakedown theorem, the problem of designing a system under dynamic loadings and with only a finite amount of allowable plastic work can be transformed into a quasi-static, elastic counterpart. For the case of proportional loadings, two methods for solving the “compounded” shakedown load are proposed. One is called the “Method of Zero Work;” the other, involving a systematic numerical procedure, is called the “Method of Direct Search.” The concept of “optimum preloading” is also introduced.