On a minimum principle in dynamics of rigid-plastic bodies

Abstract

Uniqueness of the solution and variational principles are well known for the statics of rigid-plastic bodies [1]. The situation is completely different for the dynamics of rigid-plastic bodies. The first and only work on the variational methods in this area is a paper by Rzhanitsyn [2], where the author proposes to use Lagrange's principle for the determination of motion of beams and plates beyond the elastic range. A rigid condition however is imposed in that form of the motion remains unchanged in time. Moreover, the question whether the Lagrange's principle is applicable to rigid-plastic bodies remains open. Below an extermal property of the dynamics of rigid ideally plastic bodies is demonstrated. It is shown that a true instantaneous acceleration minimizes some functional, whereby the true instantaneous acceleration field is unique. This minimum principle can be used for approximate solutions of problems of dynamics of rigid-plastic bodies.