A DEGENERATING ROBIN-TYPE TRACTION PROBLEM IN A PERIODIC DOMAIN-Reference-Cited by-同舟云学术

A DEGENERATING ROBIN-TYPE TRACTION PROBLEM IN A PERIODIC DOMAIN

Published:2023-09-04 Issue:3 Volume:28 Page:509-521
ISSN:1392-6292
Container-title:Mathematical Modelling and Analysis
language:
Short-container-title:

Author:

Dalla Riva Matteo¹,Mishuris Gennady²^ORCID,Musolino Paolo³^ORCID

Affiliation:

1. Dipartimento di Ingegneria, Università degli Studi di Palermo, Viale delle Scienze, Ed. 8, 90128 Palermo, Italy

2. Department of Mathematics, Aberystwyth University, Aberystwyth, SY23 3BZ Wales, UK

3. Dipartimento di Scienze Molecolari e Nanosistemi, Università Cá Foscari, Venezia via Torino 155, 30172 Venezia Mestre, Italy

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.

Publisher

Vilnius Gediminas Technical University

Subject

Modeling and Simulation,Analysis

Reference32 articles.

1. H. Ammari and H. Kang. Polarization and moment tensors, volume 162 of Applied Mathematical Sciences. Springer, New York, 2007. With applications to inverse problems and effective medium theory.

2. I. Andrianov, Gluzman S. and Mityushev V. Chapter 1 - L.A. Filshtinsky's contribution to applied mathematics and mechanics of solids. In Mechanics and Physics of Structured Media, pp. 1-40. Academic Press, 2022. https://doi.org/10.1016/B978-0-32-390543-5.00006-2

3. Y.A. Antipov, O. Avila-Pozos, S.T. Kolaczkowski and A.B. Movchan. Mathematical model of delamination cracks on imperfect interfaces. International Journal of Solids and Structures, 38(36):6665-6697, 2001. https://doi.org/10.1016/S0020-7683(01)00027-0

4. R. Bailey and R. Hicks. Behaviour of perforated plates under plane stress. Journal of Mechanical Engineering Science, 2(2):143-165, 1960.

5. M. Dalla Riva and M. Lanza de Cristoforis. Hypersingularly perturbed loads for a nonlinear traction boundary value problem. A functional analytic approach. Eurasian Math. J., 1(2):31-58, 2010.

Cited by 1 articles. 订阅此论文施引文献订阅此论文施引文献，注册后可以免费订阅5篇论文的施引文献，订阅后可以查看论文全部施引文献

1. A DEGENERATING ROBIN-TYPE TRACTION PROBLEM IN A PERIODIC DOMAIN;Mathematical Modelling and Analysis;2023-09-04