Finite-Time Stability of Polyhedral Sweeping Processes with Application to Elastoplastic Systems

We use the ideas of Adly, Attouch, and Cabot [in Nonsmooth Mechanics Analysis, Adv. Mech. Math. 12, Springer, New York, 2006, pp. 289--304] on finite-time stabilization dry friction oscillators to establish a theorem differential inclusions with moving polyhedral constraint (known as sweeping processes) form $C+c(t)$. then employ Moreau Variational Techniques in Mathematical Physics (Centro Internaz. Mat. Estivo (CIME), II Ciclo, Bressanone, 1973), Edizioni Cremonese, Rome, 1974, 171--322] apply our system elastoplastic springs displacement-controlled loading. show that verifying condition ultimately leads following two problems: (i) identifying active vertex “A” or face polyhedron vector $c'(t)$ points at; (ii) computing distance from normal cone at “A.” provide computational guide for solving problems (i)--(ii) case an arbitrary it particular example. Due simplicity example, we can solve by methods linear algebra basic combinatorics.