• Previous Article
    Amplitude equations close to a triple-(+1) bifurcation point of D4-symmetric periodic orbits in O(2)-equivariant systems
  • DCDS-B Home
  • This Issue
  • Next Article
    On the dynamics of a ratio dependent Predator-Prey system with diffusion and delay
November  2006, 6(6): 1339-1356. doi: 10.3934/dcdsb.2006.6.1339

Hemivariational inequality for a frictional contact problem in elasto-piezoelectricity

1. 

Jagiellonian University, Faculty of Mathematics and Computer Science, Institute of Computer Science, ul. Nawojki 11, 30-072 Krakow, Poland

Received  September 2005 Revised  April 2006 Published  August 2006

In this paper we study a class of inequality problems for static frictional contact between a piezoelastic body and a foundation. The constitutive law is assumed to be electrostatic and involves a nonlinear elasticity operator. The contact is described by Clarke subdifferential relations of nonmonotone and multivalued character in the normal and tangential directions on the boundary. We derive a variational formulation which is a coupled system of a hemivariational inequality and an elliptic equation. The existence of solutions to the model is a consequence of a more general result obtained from the theory of pseudomonotone mappings. Conditions under which a solution of the system is unique are also presented.
Citation: Stanislaw Migórski. Hemivariational inequality for a frictional contact problem in elasto-piezoelectricity. Discrete & Continuous Dynamical Systems - B, 2006, 6 (6) : 1339-1356. doi: 10.3934/dcdsb.2006.6.1339
[1]

Zijia Peng, Cuiming Ma, Zhonghui Liu. Existence for a quasistatic variational-hemivariational inequality. Evolution Equations & Control Theory, 2020  doi: 10.3934/eect.2020058

[2]

Oanh Chau, R. Oujja, Mohamed Rochdi. A mathematical analysis of a dynamical frictional contact model in thermoviscoelasticity. Discrete & Continuous Dynamical Systems - S, 2008, 1 (1) : 61-70. doi: 10.3934/dcdss.2008.1.61

[3]

Stanisław Migórski, Anna Ochal, Mircea Sofonea. Analysis of a frictional contact problem for viscoelastic materials with long memory. Discrete & Continuous Dynamical Systems - B, 2011, 15 (3) : 687-705. doi: 10.3934/dcdsb.2011.15.687

[4]

Stanislaw Migórski. A class of hemivariational inequalities for electroelastic contact problems with slip dependent friction. Discrete & Continuous Dynamical Systems - S, 2008, 1 (1) : 117-126. doi: 10.3934/dcdss.2008.1.117

[5]

Lijing Xi, Yuying Zhou, Yisheng Huang. A class of quasilinear elliptic hemivariational inequality problems on unbounded domains. Journal of Industrial & Management Optimization, 2014, 10 (3) : 827-837. doi: 10.3934/jimo.2014.10.827

[6]

Stanisław Migórski. A note on optimal control problem for a hemivariational inequality modeling fluid flow. Conference Publications, 2013, 2013 (special) : 545-554. doi: 10.3934/proc.2013.2013.545

[7]

Changjie Fang, Weimin Han. Stability analysis and optimal control of A stationary Stokes hemivariational inequality. Evolution Equations & Control Theory, 2020  doi: 10.3934/eect.2020046

[8]

Zhenhai Liu, Stanislaw Migórski. Noncoercive damping in dynamic hemivariational inequality with application to problem of piezoelectricity. Discrete & Continuous Dynamical Systems - B, 2008, 9 (1) : 129-143. doi: 10.3934/dcdsb.2008.9.129

[9]

Leszek Gasiński. Optimal control problem of Bolza-type for evolution hemivariational inequality. Conference Publications, 2003, 2003 (Special) : 320-326. doi: 10.3934/proc.2003.2003.320

[10]

Krzysztof Bartosz. Numerical analysis of a nonmonotone dynamic contact problem of a non-clamped piezoelectric viscoelastic body. Evolution Equations & Control Theory, 2020  doi: 10.3934/eect.2020059

[11]

Patrick Ballard. Can the 'stick-slip' phenomenon be explained by a bifurcation in the steady sliding frictional contact problem?. Discrete & Continuous Dynamical Systems - S, 2016, 9 (2) : 363-381. doi: 10.3934/dcdss.2016001

[12]

Khalid Addi, Oanh Chau, Daniel Goeleven. On some frictional contact problems with velocity condition for elastic and visco-elastic materials. Discrete & Continuous Dynamical Systems - A, 2011, 31 (4) : 1039-1051. doi: 10.3934/dcds.2011.31.1039

[13]

Yirong Jiang, Nanjing Huang, Zhouchao Wei. Existence of a global attractor for fractional differential hemivariational inequalities. Discrete & Continuous Dynamical Systems - B, 2020, 25 (4) : 1193-1212. doi: 10.3934/dcdsb.2019216

[14]

Leszek Gasiński. Existence results for quasilinear hemivariational inequalities at resonance. Conference Publications, 2007, 2007 (Special) : 409-418. doi: 10.3934/proc.2007.2007.409

[15]

David Yang Gao. Sufficient conditions and perfect duality in nonconvex minimization with inequality constraints. Journal of Industrial & Management Optimization, 2005, 1 (1) : 53-63. doi: 10.3934/jimo.2005.1.53

[16]

Alessandro Morando, Yuri Trakhinin, Paola Trebeschi. On local existence of MHD contact discontinuities. Discrete & Continuous Dynamical Systems - S, 2016, 9 (1) : 289-313. doi: 10.3934/dcdss.2016.9.289

[17]

Zhenhai Liu, Van Thien Nguyen, Jen-Chih Yao, Shengda Zeng. History-dependent differential variational-hemivariational inequalities with applications to contact mechanics. Evolution Equations & Control Theory, 2020  doi: 10.3934/eect.2020044

[18]

Changjie Fang, Weimin Han. Well-posedness and optimal control of a hemivariational inequality for nonstationary Stokes fluid flow. Discrete & Continuous Dynamical Systems - A, 2016, 36 (10) : 5369-5386. doi: 10.3934/dcds.2016036

[19]

Yongjian Liu, Zhenhai Liu, Ching-Feng Wen. Existence of solutions for space-fractional parabolic hemivariational inequalities. Discrete & Continuous Dynamical Systems - B, 2019, 24 (3) : 1297-1307. doi: 10.3934/dcdsb.2019017

[20]

Piotr Kowalski. The existence of a solution for Dirichlet boundary value problem for a Duffing type differential inclusion. Discrete & Continuous Dynamical Systems - B, 2014, 19 (8) : 2569-2580. doi: 10.3934/dcdsb.2014.19.2569

2019 Impact Factor: 1.27

Metrics

  • PDF downloads (42)
  • HTML views (0)
  • Cited by (38)

Other articles
by authors

[Back to Top]