Abstract
The contribution deals with contact problems for two elastic bodies with an orthotropic Coulomb friction law. To find a solution, the method of successive approximations is combined with the augmented Lagrangian algorithm. As the problem is discretized by the T-FETI domain decomposition method, the algorithm is scalable, i.e., the number of iterations needed to achieve a prescribed accuracy can be independent of the mesh norms. The scalability is experimentally demonstrated on a model example.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Bramble, J.H., Pasciak, J.E., Schatz, A.H.: The construction of preconditioners for elliptic problems by substructuring. I. Math. Comput. 47, 103–134 (1986)
Dostál, Z.: Optimal quadratic programming algorithms: with applications to variational inequalities. Springer, New York (2009)
Dostál, Z., Horák, D., Kučera, R.: Total FETI - an easier implementable variant of the FETI method for numerical solution of elliptic PDE. Communications in Numerical Methods in Engineering 22, 1155–1162 (2006)
Dostál, Z., Kučera, R.: An optimal algorithm for minimization of quadratic functions with bounded spectrum subject to separable convex inequality and linear equality constraints. SIAM J. Optimization 20, 2913–2938 (2010)
Dostál, Z., Schöberl, J.: Minimizing quadratic functions over non-negative cone with the rate of convergence and finite termination. Computational Optimization and Applications 30, 23–44 (2005)
Farhat, C., Lesoinne, M., LeTallec, P., Pierson, K., Rixen, D.: FETI-DP: a dual-primal unified FETI method. I. A faster alternative to the two-level FETI method. Internat. J. Numer. Methods Engrg. 50, 1523–1544 (2001)
Farhat, C., Mandel, J., Roux, F.: Optimal convergence properties of the FETI domain decomposition method. Comput. Methods Appl. Mech. Engrg. 115, 365–385 (1994)
Glowinski, R.: Numerical methods for nonlinear variational problems. Springer Series in Computational Physics. Springer, New York (1984)
Golub, G.H., Van Loan, C.F.: Matrix computation. The Johns Hopkins University Press, Baltimore (1996)
Hlaváček, I., Haslinger, J., Nečas, J., Lovíšek, J.: Numerical solution of variational inequalities. Springer Series in Applied Mathematical Sciences, vol. 66. Springer, New York (1988)
Haslinger, J.: Approximation of the Signorini problem with friction, obeying Coulomb law. Math. Meth. Appl. 5, 422–437 (1083)
Haslinger, J., Hlaváček, I., Nečas, J.: Numerical methods for for unilateral problems in solid mechanics. In: Ciarlet, P.G., Lions, J.L. (eds.) Handbook of Numerical Analysis, vol. IV, pp. 313–485. North-Holland, Amsterdam (1996)
Haslinger, J., Kučera, R., Kozubek, T.: Numerical solution of contact problems with orthotropic Coulomb friction based on quadratic programming approach with the elliptic friction cone (2011) (unpublished paper), http://homel.vsb.cz/~kuc14/ortho_fric.pdf
Kikuchi, N., Oden, J.T.: Contact problems in elasticity. SIAM, Philadelphia (1988)
Klawonn, A., Widlund, O.B., Dryja, M.: Dual-primal FETI methods for three-dimensional elliptic problems with heterogeneous coefficients. SIAM J. Numer. Anal. 40, 159–179 (2002)
Kozubek, T., Markopoulos, A., Brzobohatý, T., Kučera, R., Vondrák, V., Dostál, Z.: MatSol - MATLAB efficient solvers for problems in engineering, http://www.am.vsb.cz/matsol
Kučera, R.: Minimizing quadratic functions with separable quadratic constraints. Optim. Meth. Soft. 22, 453–467 (2007)
Kučera, R.: Convergence rate of an optimization algorithm for minimizing quadratic functions with separable convex constraints. SIAM J. Optim. 19, 846–862 (2008)
Kučera, R., Kozubek, T., Markopoulos, A., Machalová, J.: On the Moore-Penrose inverse in solving saddle-point systems with singular diagonal blocks. Num. Lin. Algebra Appl. 19, 677–699 (2012)
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2013 Springer-Verlag Berlin Heidelberg
About this chapter
Cite this chapter
Haslinger, J., Kučera, R. (2013). T-FETI Based Algorithm for 3D Contact Problems with Orthotropic Friction. In: Stavroulakis, G. (eds) Recent Advances in Contact Mechanics. Lecture Notes in Applied and Computational Mechanics, vol 56. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-33968-4_9
Download citation
DOI: https://doi.org/10.1007/978-3-642-33968-4_9
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-33967-7
Online ISBN: 978-3-642-33968-4
eBook Packages: EngineeringEngineering (R0)