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.
Dalla Riva M., Mishuris G., Musolino P. (2022). INTEGRAL EQUATION METHOD FOR A ROBIN-TYPE TRACTION PROBLEM IN A PERIODIC DOMAIN. TRANSACTIONS OF A. RAZMADZE MATHEMATICAL INSTITUTE, 176(3), 349-360.
INTEGRAL EQUATION METHOD FOR A ROBIN-TYPE TRACTION PROBLEM IN A PERIODIC DOMAIN
Dalla Riva M.;
2022-01-01
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.
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