A Nonsmooth Optimization Approach for Hemivariational Inequalities with Applications to Contact Mechanics

被引：5

作者：

Jureczka, Michal ^{[1
]}

Ochal, Anna ^{[1
]}

机构：

[1] Jagiellonian Univ Krakow, Fac Math & Comp Sci, Lojasiewicza 6, PL-30348 Krakow, Poland

来源：

APPLIED MATHEMATICS AND OPTIMIZATION | 2021年 / 83卷 / 03期

基金：

欧盟地平线“2020”;

关键词：

Nonmonotone friction; Optimization problem; Error estimate; Finite element method; Numerical simulations; NUMERICAL-ANALYSIS; APPROXIMATION;

D O I：

10.1007/s00245-019-09593-y

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper we introduce an abstract nonsmooth optimization problem and prove existence and uniqueness of its solution. We present a numerical scheme to approximate this solution. The theory is later applied to a sample static contact problem describing an elastic body in frictional contact with a foundation. This contact is governed by a nonmonotone friction law with dependence on normal and tangential components of displacement. Finally, computational simulations are performed to illustrate obtained results.

引用

页码：1465 / 1485

页数：21

共 50 条

[1] A Nonsmooth Optimization Approach for Hemivariational Inequalities with Applications to Contact Mechanics
Michal Jureczka
Anna Ochal
[J]. Applied Mathematics & Optimization, 2021, 83 : 1465 - 1485
[2] Computational nonsmooth mechanics: Variational and hemivariational inequalities
Stavroulakis, GE
[J]. NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, 2001, 47 (08) : 5113 - 5124
[3] A nonsmooth optimization approach for time-dependent hemivariational inequalities
Jureczka, Michal
Ochal, Anna
Bartman, Piotr
[J]. NONLINEAR ANALYSIS-REAL WORLD APPLICATIONS, 2023, 73
[4] A survey of numerical methods for hemivariational inequalities with applications to contact mechanics
Ochal, Anna
Jureczka, Michal
Bartman, Piotr
[J]. COMMUNICATIONS IN NONLINEAR SCIENCE AND NUMERICAL SIMULATION, 2022, 114
[5] Dynamic hemivariational inequalities in contact mechanics
Migorski, S.
[J]. NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, 2005, 63 (5-7) : E77 - E86
[6] Applications of generalized fractional hemivariational inequalities in solid viscoelastic contact mechanics
Han, Jiangfeng
Li, Changpin
Zeng, Shengda
[J]. COMMUNICATIONS IN NONLINEAR SCIENCE AND NUMERICAL SIMULATION, 2022, 115
[7] THE ROTHE METHOD FOR VARIATIONAL-HEMIVARIATIONAL INEQUALITIES WITH APPLICATIONS TO CONTACT MECHANICS
Bartosz, Krzysztof
Sofonea, Mircea
[J]. SIAM JOURNAL ON MATHEMATICAL ANALYSIS, 2016, 48 (02) : 861 - 883
[8] Applications of generalized fractional hemivariational inequalities in solid viscoelastic contact mechanics
Han, Jiangfeng
Li, Changpin
Zeng, Shengda
[J]. Communications in Nonlinear Science and Numerical Simulation, 2022, 115
[9] Evolutionary variational–hemivariational inequalities with applications to dynamic viscoelastic contact mechanics
Jiangfeng Han
Liang Lu
Shengda Zeng
[J]. Zeitschrift für angewandte Mathematik und Physik, 2020, 71
[10] Numerical analysis of hemivariational inequalities in contact mechanics
Han, Weimin
Sofonea, Mircea
[J]. ACTA NUMERICA, 2019, 28 : 175 - 286

← 1 2 3 4 5 →