Finite-time stability of polyhedral sweeping processes with application to elastoplastic systems

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F67985840%3A_____%2F22%3A00558112" target="_blank" >RIV/67985840:_____/22:00558112 - isvavai.cz</a>

Výsledek na webu

<a href="https://doi.org/10.1137/20M1388796" target="_blank" >https://doi.org/10.1137/20M1388796</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1137/20M1388796" target="_blank" >10.1137/20M1388796</a>

Jazyk výsledku

angličtina

Název v původním jazyce

Finite-time stability of polyhedral sweeping processes with application to elastoplastic systems

Popis výsledku v původním jazyce

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(t) points at, (ii) computing the distance from c(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.

Název v anglickém jazyce

Finite-time stability of polyhedral sweeping processes with application to elastoplastic systems

Popis výsledku anglicky

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(t) points at, (ii) computing the distance from c(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.

Druh

J_imp - Článek v periodiku v databázi Web of Science

CEP obor

—

OECD FORD obor

10101 - Pure mathematics

Projekt

<a href="/cs/project/GA20-14736S" target="_blank" >GA20-14736S: Modelování hystereze v matematickém inženýrství</a><br>

Návaznosti

I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Rok uplatnění

2022

Kód důvěrnosti údajů

S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Název periodika

SIAM Journal on Control and Optimization

ISSN

0363-0129

e-ISSN

1095-7138

Svazek periodika

60

Číslo periodika v rámci svazku

3

Stát vydavatele periodika

US - Spojené státy americké

Počet stran výsledku

27

Strana od-do

1320-1346

Kód UT WoS článku

000809668500004

EID výsledku v databázi Scopus

2-s2.0-85130624676