A DEGENERATING ROBIN-TYPE TRACTION PROBLEM IN A PERIODIC DOMAIN

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...

Full description

Saved in:
Bibliographic Details
Published inMathematical modelling and analysis Vol. 28; no. 3; pp. 509 - 521
Main Authors Dalla Riva, Matteo, Mishuris, Gennady, Musolino, Paolo
Format Journal Article
LanguageEnglish
Published Vilnius Vilnius Gediminas Technical University 01.09.2023
Subjects
Analysis
Asymptotes
Asymptotic properties
Boundary value problems
Composite materials
Dirichlet problem
Elasticity
integral equations methods
integral operators
integral representations
linearized elastostatics
Mathematical problems
periodic domain
Periodic functions
Porous materials
Power series
Robin boundary value problem
Traction
Italy
Online AccessGet full text

Cover

More Information
Summary: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.
ISSN:1392-6292
1648-3510
DOI:10.3846/mma.2023.17681