Title

A Degenerating Robin-Type Traction Problem in a Periodic Domain.

Authors

Dalla Riva, Matteo; Mishuris, Gennady; Musolino, Paolo

Abstract

We consider a linearly elastic material with a periodic set of voids. On the boundaries of the voids we set a Robin-type traction condition. Then, we investigate the asymptotic behavior of the displacement solution as the Robin condition turns into a pure traction one. To wit, there will be a matrix function b[k](·) that depends analytically on a real parameter k and vanishes for k = 0 and we multiply the Dirichlet-like part of the Robin condition by b[k](·). We show that the displacement solution can be written in terms of power series of k that converge for k in a whole neighborhood of 0. For our analysis we use the Functional Analytic Approach.

Subjects

POWER series; MATRIX functions; BOUNDARY value problems; INTEGRAL operators; INTEGRAL representations; INTEGRAL equations; GENTRIFICATION

Publication

Mathematical Modelling & Analysis, 2023, Vol 28, Issue 3, p509

ISSN

1392-6292

Publication type

Academic Journal

DOI

10.3846/mma.2023.17681