Analysis of a Contact Problem Problem Involving an Elastic Body with Dual-Phase-Lag

被引：6

作者：

Bazarra, Noelia ^{[1
]}

Bochicchio, Ivana ^{[2
]}

Fernandez, Jose R. ^{[1
]}

Naso, Maria Grazia ^{[3
]}

机构：

[1] Univ Vigo, Escola Enxeneria Telecomunicac, Dept Matemat Aplicada 1, Campus Lagoas Marcosende S-N, Vigo 36310, Spain

[2] Univ Salerno, Dipartimento Matemat, Via Giovanni Paolo II, I-84084 Fisciano, SA, Italy

[3] Univ Brescia, Dipartimento Ingn Civile Architettura Terr Ambien, Via Valotti 9, I-25133 Brescia, Italy

来源：

APPLIED MATHEMATICS AND OPTIMIZATION | 2021年 / 83卷 / 02期

关键词：

Thermoelasticity with dual-phase-lag; Normal compliance; Existence and uniqueness; Energy decay; Finite elements; A priori estimates; NUMERICAL-ANALYSIS; HEAT-CONDUCTION; EXPONENTIAL STABILITY; QUALITATIVE ASPECTS;

D O I：

10.1007/s00245-019-09574-1

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this work we study a contact problem between a thermoelastic body with dual-phase-lag and a deformable obstacle. The contact is modelled using a modification of the well-known normal compliance contact condition. An existence and uniqueness result is proved applying the Faedo-Galerkin method and Gronwall's inequality. The exponential stability is also shown. Then, we introduce a fully discrete approximation by using the implicit Euler scheme and the finite element method. A discrete stability property and a priori error estimates are obtained, from which the linear convergence of the algorithm is derived under suitable regularity conditions. Finally, some numerical examples are presented to demonstrate the accuracy of the approximation and the behaviour of the solution.

引用

页码：939 / 977

页数：39

共 20 条

[1] Numerical analysis of some dual-phase-lag models
Bazarra, N.
Copetti, M. I. M.
Fernandez, J. R.
Quintanilla, R.
[J]. COMPUTERS & MATHEMATICS WITH APPLICATIONS, 2019, 77 (02) : 407 - 426
[2] Phase-lag heat conduction: decay rates for limit problems and well-posedness
Borgmeyer, Karin
Quintanilla, Ramon
Racke, Reinhard
[J]. JOURNAL OF EVOLUTION EQUATIONS, 2014, 14 (4-5) : 863 - 884
[3] Numerical analysis and simulations of a dynamic frictionless contact problem with damage
Campo, M.
Fernandez, J. R.
Kuttler, K. L.
Shillor, M.
Viano, J. M.
[J]. COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING, 2006, 196 (1-3) : 476 - 488
[4] Chandrasekharaiah DS., 1998, Appl Mech Rev, V51, P705, DOI DOI 10.1115/1.3098984
[5] On the thermomechanical consistency of the time differential dual-phase-lag models of heat conduction
Chirita, Stan
Ciarletta, Michele
Tibullo, Vincenzo
[J]. INTERNATIONAL JOURNAL OF HEAT AND MASS TRANSFER, 2017, 114 : 277 - 285
[6] On the time differential dual-phase-lag thermoelastic model
Chirita, Stan
[J]. MECCANICA, 2017, 52 (1-2) : 349 - 361
[7] CIARLET P.G., 2002, The Finite Element Method for Elliptic Problems
[8] Stability and Second Law of Thermodynamics in dual-phase-lag heat conduction
Fabrizio, Mauro
Lazzari, Barbara
[J]. INTERNATIONAL JOURNAL OF HEAT AND MASS TRANSFER, 2014, 74 : 484 - 489
[9] Glowinski R., 1984, Numerical Methods for Nonlinear Variational Problems, DOI [10.1007/978-3-662-12613-4, DOI 10.1007/978-3-662-12613-4]
[10] A NUMERICAL-ANALYSIS OF A CLASS OF PROBLEMS IN ELASTODYNAMICS WITH FRICTION
MARTINS, JAC
ODEN, JT
[J]. COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING, 1983, 40 (03) : 327 - 360

← 1 2 →