An algorithm for the numerical realization of 3D contact problems with Coulomb friction

Authors:
Jaroslav Haslinger;Radek Kučera;Zdeněk Dostál
Affiliations:
Department of Metal Physics, Charles University, Ke Karlovu 5, 121 16 Prague, Czech Republic;Department of Mathematics, VSB-Technical University of Ostrava, Tr. 17. listopadu 15, 708 33 Ostrava-Poruba, Czech Republic;Department of Applied Mathematics, VSB--Technical University of Ostrava, Tr. 17. listopadu 15, 708 33 Ostrava-Poruba, Czech Republic
Venue:
Journal of Computational and Applied Mathematics - Special Issue: Proceedings of the 10th international congress on computational and applied mathematics (ICCAM-2002)
Year:
2004

Citing 4
Cited 4

Box Constrained Quadratic Programming with Proportioning and Projections

SIAM Journal on Optimization
Implementation of the fixed point method in contact problems with Coulomb friction based on a dual splitting type technique

Journal of Computational and Applied Mathematics - Special issue: Proceedings of the 9th International Congress on computational and applied mathematics
Scalability and FETI based algorithm for large discretized variational inequalities

Mathematics and Computers in Simulation - MODELLING 2001 - Second IMACS conference on mathematical modelling and computational methods in mechanics, physics, biomechanics and geodynamics
Augmented Lagrangians with Adaptive Precision Control for Quadratic Programming with Simple Bounds and Equality Constraints

SIAM Journal on Optimization

Relaxation and block-relaxation procedures for the dual formulation of the Signorini-Coulomb frictional contact

ICCST '02 Proceedings of the sixth conference on Computational structures technology
Minimizing quadratic functions with separable quadratic constraints

Optimization Methods & Software
A scalable TFETI algorithm for two-dimensional multibody contact problems with friction

Journal of Computational and Applied Mathematics
An Optimal Algorithm for Minimization of Quadratic Functions with Bounded Spectrum Subject to Separable Convex Inequality and Linear Equality Constraints

SIAM Journal on Optimization

Quantified Score

Hi-index	0.00

Visualization

Abstract

This contribution deals with the numerical realization of static contact problems with Coulomb friction for three-dimensional elastic bodies. We first introduce auxiliary contact problems with given friction which define a mapping Φ associating with a given slip bound the normal contact stress in the equilibrium state. Solutions to contact problems with Coulomb friction are defined as fixed points of Φ and are computed by using the method of successive approximations. The mathematical model of contact problems with given friction leads to a variational inequality of the second kind. Its discretization is based on the so-called reciprocal variational formulation, i.e., the formulation in terms of the normal and tangential components of stresses on the contact boundary. Unlike the two-dimensional case, constraints imposed on the tangential components of contact stresses are quadratic. The main goal of this contribution is to show how to solve this problem by using existing fast algorithms for simple (box) constraints. Numerical experiments for several variants of our algorithm will be shown and compared.