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

Result code in 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>
Result on the web
<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>

Result language
angličtina
Original language name
Finite-time stability of polyhedral sweeping processes with application to elastoplastic systems
Original language description
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.
Czech name
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Czech description
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Type
J<sub>imp</sub> - Article in a specialist periodical, which is included in the Web of Science database
CEP classification
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OECD FORD branch
10101 - Pure mathematics

Project
<a href="/en/project/GA20-14736S" target="_blank" >GA20-14736S: Hysteresis modeling in mathematical engineering</a><br>
Continuities
I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Publication year
2022
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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