Integral Equation Method for a Robin-Type Traction Problem in a Periodic Domain

Matteo Dalla Riva; Gennady Mishuris; Paolo Musolino

Integral Equation Method for a Robin-Type Traction Problem in a Periodic Domain

Matteo Dalla Riva, Gennady Mishuris, Paolo Musolino^*

^*Awdur cyfatebol y gwaith hwn

Mathemateg

Allbwn ymchwil: Cyfraniad at gyfnodolyn › Erthygl › adolygiad gan gymheiriaid

6 Wedi eu Llwytho i Lawr (Pure)

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In this note, we consider a Robin-type traction problem for a linearly elastic body occupying an infinite periodically perforated domain. After proving the uniqueness of the solution we use periodic elastic layer potentials to show that the solution can be written as the sum of a single layer potential, a constant function and a linear function of the space variable. The density of the periodic single layer potential and the constant are identified as the unique solutions of a certain integral equation.

Iaith wreiddiol	Saesneg
Tudalennau (o-i)	349-360
Nifer y tudalennau	12
Cyfnodolyn	Transactions of A. Razmadze Mathematical Institute
Cyfrol	176
Rhif cyhoeddi	3
Statws	Cyhoeddwyd - 31 Rhag 2022

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v176(3)-4Fersiwn derfynol wedi’i chyhoeddi, 198 KB

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1 Wrthi'n gweithredu
2 Wedi Gorffen

EffectFact: Effective Factorisation techniques for matrix-functions: Developing theory, numerical methods and impactful applications
Mishuris, G.
Horizon 2020 -European Commission
01 Medi 2021 → 31 Awst 2025
Prosiect: Ymchwil a ariannwyd yn allanol
Wolfson Visiting Fellowship
Mishuris, G.
The Royal Society
01 Gorff 2021 → 30 Meh 2023
Prosiect: Ymchwil a ariannwyd yn allanol
Ser Cymru IFA - Development of the tip element to account for singular physical fields near the crack tip and various propagation regimes.
Mishuris, G.
WEFO
01 Gorff 2020 → 30 Meh 2021
Prosiect: Ymchwil a ariannwyd yn allanol

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@article{b1889b9a8ce44e8b8ea272db6a02414a,

title = "Integral Equation Method for a Robin-Type Traction Problem in a Periodic Domain",

abstract = "In this note, we consider a Robin-type traction problem for a linearly elastic body occupying an infinite periodically perforated domain. After proving the uniqueness of the solution we use periodic elastic layer potentials to show that the solution can be written as the sum of a single layer potential, a constant function and a linear function of the space variable. The density of the periodic single layer potential and the constant are identified as the unique solutions of a certain integral equation.",

keywords = "Robin boundary value problem, Integral representations, Integral operators, Integral equations methods, Linearized elastostatics, Periodic domain, TRANSMISSION CONDITIONS, EFFECTIVE CONDUCTIVITY, HEAT-CONDUCTION, INTERFACE, INTERPHASE, COMPOSITE, EXPANSION, CRACKS, MODEL",

author = "Riva, {Matteo Dalla} and Gennady Mishuris and Paolo Musolino",

note = "Funding Information: P. M. and G. M. acknowledge the support from EU through the H2020-MSCA-RISE-2020 project EffectFact, Grant agreement ID: 101008140. M. D. R. and P. M. are members of the Gruppo Nazionale per l{\textquoteright}Analisi Matematica, la Probabilit{\`a} e le loro Applicazioni (GNAMPA) of the Istituto Nazionale di Alta Matematica (INdAM). P. M. also acknowledges the support of the grant “Challenges in Asymptotic and Shape Analysis - CASA” of the Ca{\textquoteright} Foscari University of Venice. Part of the work was done while P.M. was visiting Martin Dutko at Rockfield Software Limited. P. M. wishes to thank Martin Dutko for valuable discussions and Rockfield Software Limited for the kind hospitality. G. M. acknowledges also Ser Cymru Future Generation Industrial Fellowship number AU224 – 80761. G. M. thanks the Royal Society for the Wolfson Research Merit Award. Publisher Copyright: {\textcopyright} 2022 A. Razmadze Mathematical Institute of Iv. Javakhishvili Tbilisi State University. All rights reserved.",

year = "2022",

month = dec,

day = "31",

language = "English",

volume = "176",

pages = "349--360",

journal = "Transactions of A. Razmadze Mathematical Institute",

issn = "2346-8092",

publisher = "Razmadze Mathematical Institute",

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TY - JOUR

T1 - Integral Equation Method for a Robin-Type Traction Problem in a Periodic Domain

AU - Riva, Matteo Dalla

AU - Mishuris, Gennady

AU - Musolino, Paolo

N1 - Funding Information: P. M. and G. M. acknowledge the support from EU through the H2020-MSCA-RISE-2020 project EffectFact, Grant agreement ID: 101008140. M. D. R. and P. M. are members of the Gruppo Nazionale per l’Analisi Matematica, la Probabilità e le loro Applicazioni (GNAMPA) of the Istituto Nazionale di Alta Matematica (INdAM). P. M. also acknowledges the support of the grant “Challenges in Asymptotic and Shape Analysis - CASA” of the Ca’ Foscari University of Venice. Part of the work was done while P.M. was visiting Martin Dutko at Rockfield Software Limited. P. M. wishes to thank Martin Dutko for valuable discussions and Rockfield Software Limited for the kind hospitality. G. M. acknowledges also Ser Cymru Future Generation Industrial Fellowship number AU224 – 80761. G. M. thanks the Royal Society for the Wolfson Research Merit Award. Publisher Copyright: © 2022 A. Razmadze Mathematical Institute of Iv. Javakhishvili Tbilisi State University. All rights reserved.

PY - 2022/12/31

Y1 - 2022/12/31

N2 - In this note, we consider a Robin-type traction problem for a linearly elastic body occupying an infinite periodically perforated domain. After proving the uniqueness of the solution we use periodic elastic layer potentials to show that the solution can be written as the sum of a single layer potential, a constant function and a linear function of the space variable. The density of the periodic single layer potential and the constant are identified as the unique solutions of a certain integral equation.

AB - In this note, we consider a Robin-type traction problem for a linearly elastic body occupying an infinite periodically perforated domain. After proving the uniqueness of the solution we use periodic elastic layer potentials to show that the solution can be written as the sum of a single layer potential, a constant function and a linear function of the space variable. The density of the periodic single layer potential and the constant are identified as the unique solutions of a certain integral equation.

KW - Robin boundary value problem

KW - Integral representations

KW - Integral operators

KW - Integral equations methods

KW - Linearized elastostatics

KW - Periodic domain

KW - TRANSMISSION CONDITIONS

KW - EFFECTIVE CONDUCTIVITY

KW - HEAT-CONDUCTION

KW - INTERFACE

KW - INTERPHASE

KW - COMPOSITE

KW - EXPANSION

KW - CRACKS

KW - MODEL

UR - http://www.scopus.com/inward/record.url?scp=85149842582&partnerID=8YFLogxK

M3 - Article

SN - 2346-8092

VL - 176

SP - 349

EP - 360

JO - Transactions of A. Razmadze Mathematical Institute

JF - Transactions of A. Razmadze Mathematical Institute

IS - 3

ER -

Integral Equation Method for a Robin-Type Traction Problem in a Periodic Domain

Crynodeb

Mynediad at Ddogfen

Cysylltiad parhaol

Ffeiliau eraill a chysylltiadau

Ôl bys

Prosiectau

EffectFact: Effective Factorisation techniques for matrix-functions: Developing theory, numerical methods and impactful applications

Wolfson Visiting Fellowship

Ser Cymru IFA - Development of the tip element to account for singular physical fields near the crack tip and various propagation regimes.

Dyfynnu hyn