A new class of differential nonlinear system involving parabolic variational and history-dependent hemi-variational inequalities arising in contact mechanics

被引：21

作者：

Chen, Tao ^{[1
]}

Huang, Nan-jing ^{[1
]}

Li, Xue-song ^{[1
]}

Zou, Yun-zhi ^{[1
]}

机构：

[1] Sichuan Univ, Dept Math, Chengdu, Sichuan, Peoples R China

来源：

COMMUNICATIONS IN NONLINEAR SCIENCE AND NUMERICAL SIMULATION | 2021年 / 101卷

基金：

中国国家自然科学基金;

关键词：

History-dependent hemi-variational; inequality; parabolic variational inequality; frictional contact problem; wear; damage; long memory; error estimate; HEMIVARIATIONAL APPROACH; VISCOELASTIC MATERIALS; UNILATERAL CONSTRAINT; NUMERICAL-ANALYSIS; FRICTION; DAMAGE;

D O I：

10.1016/j.cnsns.2021.105886

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

This paper is devoted to study a new nonlinear system involving a parabolic variational inequality, a history-dependent hemi-variational inequality and a differential equation in Banach spaces. By employing the surjectivity argument and Banach's fixed point theorem, we derive a unique solvability theorem for such a problem under some mild conditions. Moreover, the main results are applied to obtain the unique solvability of a long memory elastic frictional contact problem with wear and damage. Finally, we use the fully discrete scheme to approximate the contact problem and provide the error estimates for numerical solutions. (C) 2021 Elsevier B.V. All rights reserved.

引用

页数：24

共 36 条

[1] A dynamic thermoviscoelastic contact problem with friction and wear [J].

Andrews, KT ;

Shillor, M ;

Wright, S ;

Klarbring, A .

INTERNATIONAL JOURNAL OF ENGINEERING SCIENCE, 1997, 35 (14) :1291-1309

[2]

[Anonymous], 2013, The Finite Element Method: Theory, Implementation, and Applications

[3]

Banks HT, 2011, LECT NOTES APPL COMP, V27

[4]

Barbu V., 1984, OPTIMAL CONTROL VARI

[5]

Capatina A, 2014, ADV MECH MATH, V31, P1, DOI 10.1007/978-3-319-10163-7

[6] Variational and numerical analysis of a dynamic viscoelastic contact problem with friction and wear [J].

Chen, Tao ;

Huang, Nan-jing ;

Xiao, Yi-bin .

OPTIMIZATION, 2020, 69 (09) :2003-2031

[7] Damage, gradient of damage and principle of virtual power [J].

Fremond, M ;

Nedjar, B .

INTERNATIONAL JOURNAL OF SOLIDS AND STRUCTURES, 1996, 33 (08) :1083-1103

[8] DAMAGE IN CONCRETE - THE UNILATERAL PHENOMENON [J].

FREMOND, M ;

NEDJAR, B .

NUCLEAR ENGINEERING AND DESIGN, 1995, 156 (1-2) :323-335

[9] Variational-Hemivariational Approach to a Quasistatic Viscoelastic Problem with Normal Compliance, Friction and Material Damage [J].

Gasinski, Leszek ;

Ochal, Anna ;

Shillor, Meir .

ZEITSCHRIFT FUR ANALYSIS UND IHRE ANWENDUNGEN, 2015, 34 (03) :251-275

[10] Numerical analysis of a contact problem with wear [J].

Han, Danfu ;

Han, Weimin ;

Jureczka, Michal ;

Ochal, Anna .

COMPUTERS & MATHEMATICS WITH APPLICATIONS, 2020, 79 (10) :2942-2951

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