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Abstract
In this note, we consider a Robintype 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.
Original language  English 

Pages (fromto)  349360 
Number of pages  12 
Journal  Transactions of A. Razmadze Mathematical Institute 
Volume  176 
Issue number  3 
Publication status  Published  31 Dec 2022 
Keywords
 Robin boundary value problem
 Integral representations
 Integral operators
 Integral equations methods
 Linearized elastostatics
 Periodic domain
 TRANSMISSION CONDITIONS
 EFFECTIVE CONDUCTIVITY
 HEATCONDUCTION
 INTERFACE
 INTERPHASE
 COMPOSITE
 EXPANSION
 CRACKS
 MODEL
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EffectFact: Effective Factorisation techniques for matrixfunctions: Developing theory, numerical methods and impactful applications
Mishuris, G. (PI)
01 Sept 2021 → 31 Aug 2025
Project: Externally funded research

Wolfson Visiting Fellowship  Professor Victor Eremeyev
Mishuris, G. (PI)
01 Jul 2021 → 30 Jun 2023
Project: Externally funded research

Ser Cymru IFA  Development of the tip element to account for singular physical fields near the crack tip and various propagation regimes.
Mishuris, G. (PI)
01 Jul 2020 → 30 Jun 2021
Project: Externally funded research