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Published in:
Contact Problems and Their Solution Read chapter Read first chapter

2016 | OriginalPaper | Chapter

11. Frictionless Contact Problems

Authors : Zdeněk Dostál, Tomáš Kozubek, Vít Vondrák

Published in: Scalable Algorithms for Contact Problems

Publisher: Springer New York

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Abstract

Now we shall extend the results introduced in the previous chapter to the solution of multibody contact problems of elasticity without friction. We shall restrict our attention to the problems of linear elasticity, i.e., we shall assume small deformations and linear stress–strain relations. Moreover, we shall be interested mainly in computationally challenging 3D problems.

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previous chapter TFETI for Scalar Problems
next chapter Contact Problems with Friction
Literature
1.
2.
Laursen, T.: Computational Contact and Impact Mechanics. Springer, Berlin (2002)MATH
3.
4.
Savenkov, E., Andrä, H., Iliev, O.: An analysis of one regularization approach for solution of pure Neumann problem. Berichte des Faruenhofer ITWM, Nr. 137, Kaiserslautern (2008)
5.
6.
Berman, A., Plemmons, R.J.: Nonnegative Matrices in the Mathematical Sciences. SIAM, Philadelphia (1994)CrossRefMATH
7.
Golub, G.H., Van Loan, C.F.: Matrix Computations, 2nd edn. Johns Hopkins University Press, Baltimore (1989)MATH
8.
Brzobohatý, T., Dostál, Z., Kozubek, T., Kovář, P., Markopoulos, A.: Cholesky decomposition with fixing nodes to stable computation of a generalized inverse of the stiffness matrix of a floating structure. Int. J. Numer. Methods Eng. 88(5), 493–509 (2011)MathSciNetCrossRefMATH
9.
Farhat, C., Mandel, J., Roux, F.-X.: Optimal convergence properties of the FETI domain decomposition method. Comput. Methods Appl. Mech. Eng. 115, 365–385 (1994)MathSciNetCrossRef
10.
11.
Hlaváček, I., Haslinger, J., Nečas, J., Lovíšek, J.: Solution of Variational Inequalities in Mechanics. Springer, Berlin (1988)CrossRefMATH
12.
13.
14.
Dureisseix, D., Farhat, C.: A numerically scalable domain decomposition method for solution of frictionless contact problems. Int. J. Numer. Methods Eng. 50(12), 2643–2666 (2001)CrossRefMATH
15.
Avery, P., Rebel, G., Lesoinne, M., Farhat, C.: A numerically scalable dual-primal substructuring method for the solution of contact problems - part I: the frictionless case. Comput. Methods Appl. Mech. Eng. 193, 2403–2426 (2004)CrossRefMATH
16.
Dostál, Z., Vondrák, V., Horák, D., Farhat, C., Avery, P.: Scalable FETI algorithms for frictionless contact problems. Lecture Notes in Computational Science and Engineering, vol. 60, pp. 263–270. Springer, Berlin (2008)
17.
Avery, P., Farhat, C.: The FETI family of domain decomposition methods for inequality-constrained quadratic programming: application to contact problems with conforming and nonconforming interfaces. Comput. Methods Appl. Mech. Eng. 198, 1673–1683 (2009)MathSciNetCrossRefMATH
18.
Felippa, C.A., Park, K.C.: The construction of free-free flexibility matrices for multilevel structural analysis. Comput. Methods Appl. Mech. Eng. 191, 2111–2140 (2002)CrossRefMATH
19.
Farhat, C., Géradin, M.: On the general solution by a direct method of a large scale singular system of linear equations: application to the analysis of floating structures. Int. J. Numer. Methods Eng. 41, 675–696 (1998)MathSciNetCrossRefMATH
20.
Kornhuber, R., Krause, R.: Adaptive multigrid methods for Signorini’s problem in linear elasticity. Comput. Vis. Sci. 4(1), 9–20 (2001)MathSciNetCrossRefMATH
21.
Kornhuber, R., Krause, R., Sander, O., Deuflhard, P., Ertel, S.: A monotone multigrid solver for two body contact problems in biomechanics. Comput. Vis. Sci. 11, 3–15 (2008)MathSciNetCrossRef
22.
Iontcheva, A.H., Vassilevski, P.S.: Monotone multigrid methods based on element agglomeration coarsening away from the contact boundary for the Signorini’s problem. Numer. Linear Algebra Appl. 11(2–3), 189–204 (2004)MathSciNetCrossRefMATH
23.
Simo, J.C., Laursen, T.A.: An augmented Lagrangian treatment of contact problems involving friction. Comput. Struct. 42, 97–116 (1992)MathSciNetCrossRefMATH
24.
Glowinski, R., Le Tallec, P.: Augmented Lagrangian and Operator-Splitting Methods in Nonlinear Mechanics. SIAM, Philadelphia (1989)CrossRefMATH
25.
Conn, A.R., Gould, N.I.M., Toint, Ph.L.: LANCELOT: A FORTRAN Package for Large Scale Nonlinear Optimization (Release A). No. 17 in Springer Series in Computational Mathematics. Springer, New York (1992)
26.
Dostál, Z., Friedlander, A., Santos, S.A.: Solution of contact problems of elasticity by FETI domain decomposition. Domain Decomposition Methods 10. Contemporary Mathematics, vol. 218, 82–93. AMS, Providence (1998)
27.
Dostál, Z., Gomes, F.A.M., Santos, S.A.: Duality based domain decomposition with natural coarse space for variational inequalities. J. Comput. Appl. Math. 126(1–2), 397–415 (2000)MathSciNetCrossRefMATH
28.
Dostál, Z., Gomes, F.A.M., Santos, S.A.: Solution of contact problems by FETI domain decomposition with natural coarse space projection. Comput. Methods Appl. Mech. Eng. 190(13–14), 1611–1627 (2000)CrossRefMATH
29.
Dostál, Z., Horák, D., Kučera, R., Vondrák, V., Haslinger, J., Dobiáš, J., Pták, S.: FETI based algorithms for contact problems: scalability, large displacements and 3D Coulomb friction. Comput. Methods Appl. Mech. Eng. 194(2–5), 395–409 (2005)MathSciNetCrossRefMATH
30.
Dostál, Z., Kozubek, T., Vondrák, V., Brzobohatý, T., Markopoulos, A.: Scalable TFETI algorithm for the solution of multibody contact problems of elasticity. Int. J. Numer. Methods Eng. 82(11), 1384–1405 (2010)MathSciNetMATH
31.
Dostál, Z., Schöberl, J.: Minimizing quadratic functions over non-negative cone with the rate of convergence and finite termination. Comput. Optim. Appl. 30(1), 23–44 (2005)MathSciNetCrossRefMATH
32.
Dostál, Z.: Inexact semi-monotonic augmented Lagrangians with optimal feasibility convergence for quadratic programming with simple bounds and equality constraints. SIAM J. Numer. Anal. 43(1), 96–115 (2005)MathSciNetCrossRefMATH
33.
Dostál, Z.: Optimal Quadratic Programming Algorithms, with Applications to Variational Inequalities, 1st edn. Springer, New York (2009)MATH
34.
Dostál, Z., Horák, D., Kučera, R.: Total FETI - an easier implementable variant of the FETI method for numerical solution of elliptic PDE. Commun. Numer. Methods Eng. 22, 1155–1162 (2006)MathSciNetCrossRefMATH
35.
Toselli, A., Widlund, O.B.: Domain Decomposition Methods – Algorithms and Theory. Springer Series on Computational Mathematics, vol. 34. Springer, Berlin (2005)
36.
Jarošová, M., Klawonn, A., Rheinbach, O.: Projector preconditioning and transformation of basis in FETI-DP algorithms for contact problems. Math. Comput. Simul. 82(10), 1894–1907 (2012)MathSciNetCrossRefMATH
Metadata
Title
Frictionless Contact Problems
Authors
Zdeněk Dostál
Tomáš Kozubek
Vít Vondrák
Copyright Year
2016
Publisher
Springer New York
Book
Scalable Algorithms for Contact Problems

Print ISBN: 978-1-4939-6832-9

Electronic ISBN: 978-1-4939-6834-3

Copyright Year: 2016

DOI
https://doi.org/10.1007/978-1-4939-6834-3_11

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