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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.
Original language | English |
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Pages (from-to) | 349-360 |
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
- HEAT-CONDUCTION
- INTERFACE
- INTERPHASE
- COMPOSITE
- EXPANSION
- CRACKS
- MODEL
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EffectFact: Effective Factorisation techniques for matrix-functions: Developing theory, numerical methods and impactful applications
Mishuris, G. (PI)
01 Sept 2021 → 31 Aug 2025
Project: Externally funded research
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Wolfson Visiting Fellowship - Professor Victor Eremeyev
Mishuris, G. (PI)
01 Jul 2021 → 30 Jun 2023
Project: Externally funded research
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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