• Previous Article
    Existence and estimate of the location of the free-boundary for a non local inverse elliptic-parabolic problem arising in nuclear fusion
  • PROC Home
  • This Issue
  • Next Article
    Energy-minimal transfers in the vicinity of the lagrangian point $L_1$
2011, 2011(Special): 1186-1195. doi: 10.3934/proc.2011.2011.1186

A proximal-like algorithm for vibro-impact problems with a non-smooth set of constraints

1. 

Université de Lyon, Université de Saint-Etienne, Jean Monnet, LaMUSE (Laboratoire de Mathématiques de l'Universitté de Saint-Etienne), 23 rue Michelon, 42023 Saint-Etienne Cedex 2, France

Received  July 2010 Revised  April 2011 Published  October 2011

We consider a discrete mechanical system subjected to perfect unilateral contraints characterized by some geometrical inequalities $f_\alpha(q) >=0$, $\alpha \in {1,...,v}$, with $v >=1$. We assume that the transmission of the velocities at impacts is governed by a Newton’s impact law with a restitution coefficient $e \in [0, 1]$, allowing for conservation of kinetic energy if $e=1$, or loss of kinetic energy if $e \in [0, 1)$, when the constraints are saturated. Starting from a formulation of the dynamics as a first order measure-differential inclusion for the unknown velocities, time-stepping schemes inspired by the proximal methods can be proposed. Convergence results in the single-constraint case $(v = 1)$ are recalled and extended to the multi-constraint case $(v > 1)$, leading to new existence results for this kind of problems.
Citation: Laetitia Paoli. A proximal-like algorithm for vibro-impact problems with a non-smooth set of constraints. Conference Publications, 2011, 2011 (Special) : 1186-1195. doi: 10.3934/proc.2011.2011.1186
[1]

Laetitia Paoli. A velocity-based time-stepping scheme for multibody dynamics with unilateral constraints. Discrete & Continuous Dynamical Systems - S, 2013, 6 (6) : 1609-1619. doi: 10.3934/dcdss.2013.6.1609

[2]

Chichia Chiu, Jui-Ling Yu. An optimal adaptive time-stepping scheme for solving reaction-diffusion-chemotaxis systems. Mathematical Biosciences & Engineering, 2007, 4 (2) : 187-203. doi: 10.3934/mbe.2007.4.187

[3]

Qingguang Guan, Max Gunzburger. Stability and convergence of time-stepping methods for a nonlocal model for diffusion. Discrete & Continuous Dynamical Systems - B, 2015, 20 (5) : 1315-1335. doi: 10.3934/dcdsb.2015.20.1315

[4]

Anatoli Babin, Alexander Figotin. Newton's law for a trajectory of concentration of solutions to nonlinear Schrodinger equation. Communications on Pure & Applied Analysis, 2014, 13 (5) : 1685-1718. doi: 10.3934/cpaa.2014.13.1685

[5]

Juhi Jang, Ian Tice. Passive scalars, moving boundaries, and Newton's law of cooling. Discrete & Continuous Dynamical Systems - A, 2016, 36 (3) : 1383-1413. doi: 10.3934/dcds.2016.36.1383

[6]

Jeongho Ahn, David E. Stewart. A viscoelastic Timoshenko beam with dynamic frictionless impact. Discrete & Continuous Dynamical Systems - B, 2009, 12 (1) : 1-22. doi: 10.3934/dcdsb.2009.12.1

[7]

Arno Berger. Multi-dimensional dynamical systems and Benford's Law. Discrete & Continuous Dynamical Systems - A, 2005, 13 (1) : 219-237. doi: 10.3934/dcds.2005.13.219

[8]

Yunan Wu, Guangya Chen, T. C. Edwin Cheng. A vector network equilibrium problem with a unilateral constraint. Journal of Industrial & Management Optimization, 2010, 6 (3) : 453-464. doi: 10.3934/jimo.2010.6.453

[9]

Andaluzia Matei, Mircea Sofonea. Dual formulation of a viscoplastic contact problem with unilateral constraint. Discrete & Continuous Dynamical Systems - S, 2013, 6 (6) : 1587-1598. doi: 10.3934/dcdss.2013.6.1587

[10]

Matthias Gerdts, Martin Kunkel. A nonsmooth Newton's method for discretized optimal control problems with state and control constraints. Journal of Industrial & Management Optimization, 2008, 4 (2) : 247-270. doi: 10.3934/jimo.2008.4.247

[11]

Chihurn Kim, Dong Han Kim. On the law of logarithm of the recurrence time. Discrete & Continuous Dynamical Systems - A, 2004, 10 (3) : 581-587. doi: 10.3934/dcds.2004.10.581

[12]

Zheng-Hai Huang, Jie Sun. A smoothing Newton algorithm for mathematical programs with complementarity constraints. Journal of Industrial & Management Optimization, 2005, 1 (2) : 153-170. doi: 10.3934/jimo.2005.1.153

[13]

Luju Liu, Jianhong Wu, Xiao-Qiang Zhao. The impact of migrant workers on the tuberculosis transmission: General models and a case study for China. Mathematical Biosciences & Engineering, 2012, 9 (4) : 785-807. doi: 10.3934/mbe.2012.9.785

[14]

Jérome Lohéac, Jean-François Scheid. Time optimal control for a nonholonomic system with state constraint. Mathematical Control & Related Fields, 2013, 3 (2) : 185-208. doi: 10.3934/mcrf.2013.3.185

[15]

Florent Berthelin, Thierry Goudon, Bastien Polizzi, Magali Ribot. Asymptotic problems and numerical schemes for traffic flows with unilateral constraints describing the formation of jams. Networks & Heterogeneous Media, 2017, 12 (4) : 591-617. doi: 10.3934/nhm.2017024

[16]

Andrea L. Bertozzi, Ning Ju, Hsiang-Wei Lu. A biharmonic-modified forward time stepping method for fourth order nonlinear diffusion equations. Discrete & Continuous Dynamical Systems - A, 2011, 29 (4) : 1367-1391. doi: 10.3934/dcds.2011.29.1367

[17]

Xiaojiao Tong, Shuzi Zhou. A smoothing projected Newton-type method for semismooth equations with bound constraints. Journal of Industrial & Management Optimization, 2005, 1 (2) : 235-250. doi: 10.3934/jimo.2005.1.235

[18]

Shuang Chen, Li-Ping Pang, Dan Li. An inexact semismooth Newton method for variational inequality with symmetric cone constraints. Journal of Industrial & Management Optimization, 2015, 11 (3) : 733-746. doi: 10.3934/jimo.2015.11.733

[19]

X. X. Huang, Xiaoqi Yang, K. L. Teo. A smoothing scheme for optimization problems with Max-Min constraints. Journal of Industrial & Management Optimization, 2007, 3 (2) : 209-222. doi: 10.3934/jimo.2007.3.209

[20]

Yongchao Liu, Hailin Sun, Huifu Xu. An approximation scheme for stochastic programs with second order dominance constraints. Numerical Algebra, Control & Optimization, 2016, 6 (4) : 473-490. doi: 10.3934/naco.2016021

 Impact Factor: 

Metrics

  • PDF downloads (1)
  • HTML views (0)
  • Cited by (0)

Other articles
by authors

[Back to Top]