| Abstrakt: |
We use the ideas of Adly, Attouch, and Cabot [in Nonsmooth Mechanics and Analysis, Adv. Mech. Math. 12, Springer, New York, 2006, pp. 289-304] on finite-time stabilization of dry friction oscillators to establish a theorem on finite-time stabilization of differential inclusions with a moving polyhedral constraint (known as polyhedral sweeping processes) of the form C + c(t). We then employ the ideas of Moreau [in New Variational Techniques in Mathematical Physics (Centro Internaz. Mat. Estivo (CIME), II Ciclo, Bressanone, 1973), Edizioni Cremonese, Rome, 1974, pp. 171-322] to apply our theorem to a system of elastoplastic springs with a displacement-controlled loading. We show that verifying the condition of the theorem ultimately leads to the following two problems: (i) identifying the active vertex "A"" or the active face "A"" of the polyhedron that the vector c\prime (t) points at; (ii) computing the distance from c\prime (t) to the normal cone to the polyhedron at "A."" We provide a computational guide for solving problems (i)--(ii) in the case of an arbitrary elastoplastic system and apply it to a particular example. Due to the simplicity of the particular example, we can solve (i)--(ii) by the methods of linear algebra and basic combinatorics. [ABSTRACT FROM AUTHOR] |
