Geodesic
Solving of contact mechanics problem using h-adaptive finite element method
Sibirskie èlektronnye matematičeskie izvestiâ, Tome 11 (2014), pp. 220-228.

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We present an effective methodology of solving contact mechanics problems. The main feature is combining iterative domain decomposition method with h-adaptive finite element method, which were developed earlier by the authors. We demonstrate the usability of a new algorithm applying it to a test problem. The resulting mesh reveals a singularity near the contact zone.
Keywords: finite element method, boundary element method, mesh refinement, contact mechanics
Mots-clés : domain decomposition. 
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Yu. O. Yashchuk; I. I. Prokopyshyn. Solving of contact mechanics problem using h-adaptive finite element method. Sibirskie èlektronnye matematičeskie izvestiâ, Tome 11 (2014), pp. 220-228. http://geodesic.mathdoc.fr/item/SEMR_2014_11_a66/

[1] I. I. Vorovich, V. M. Aleksandrov, V. A. Babeshko, Neklassicheskie smeshannye zadachi teorii uprugosti, Nauka, M., 1974 | MR | Zbl

[2] V. G. Zubchaninov, Osnovy teorii uprugosti i plastichnosti, Vysshaya shkola, M., 1990

[3] A. S. Kravchuk, “Postanovka zadachi o kontakte neskolkikh deformiruemykh tel kak zadachi nelineinogo programmirovaniya”, Prikladnaya matematika i mekhanika, 42:3 (1978), 467–473 | MR

[4] I. I. Prokopishin, “Paralelni skhemi metodu dekompozitsiïoblasti dlya kontaktnikh zadach teoriïpruzhnosti bez tertya”, Visnik Lvivskogo universitetu. Seriya prikladna matematika ta informatika, 14 (2008), 123–133

[5] I. I. Prokopishin, Skhemi dekompozitsiïoblasti na osnovi metodu shtrafu dlya zadach kontaktu pruzhnikh til, avtoref. dis. ... kand. fiz.-mat. nauk: 01.05.02, Lviv, 2010

[6] Yu. O. Yaschuk, “Adaptivnii algoritm chiselnogo doslidzhennya zadachi teoriïpruzhnosti”, Visnik Lvivskogo universitetu. Seriya prikladna matematika ta informatika, 16 (2010), 96–105

[7] P. Avery, C. Farhat, “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. Engrg., 198 (2009), 1673–1683 | DOI | MR | Zbl

[8] W. Bangerth, R. Rannacher, Adaptive Finite Element Methods for Differential Equations, Birkhauser Verlag, Basel, 2003 | MR | Zbl

[9] C. Bernardi, Y. Maday, A. Patera, “A new non conforming approach to domain decomposition: The mortar element method”, Nonlinear partial differential equations and their applications, Paris, 1994, 13–51 | MR | Zbl

[10] Z. Dostál, T. Kozubek, V. Vondrák, T. Brzobohatý, A. Markopoulos, “Scalable TFETI algorithm for the solution of multibody contact problems of elasticity”, Int. J. Numer. Methods Engrg., 82:11 (2010), 1384–1405 | MR | Zbl

[11] I. I. Dyyak, I. I. Prokopyshyn, “Convergence of the Neumann parallel scheme of the domain decomposition method for problems of frictionless contact between several elastic bodies”, Journal of Mathematical Sciences, 171:4 (2010), 516–533 | DOI | MR

[12] I. I. Dyyak, I. I. Prokopyshyn, I. A. Prokopyshyn, Penalty Robin–Robin domain decomposition methods for unilateral multibody contact problems of elasticity: Convergence results, 2012, 32 pp., arXiv: http://arxiv.org/pdf/1208.6478.pdf

[13] A. Ya. Grigorenko, I. I. Dyyak, S. I. Matysyak, I. I. Prokopyshyn, “Domain decomposition methods applied to solve frictionless-contact problems for multilayer elastic bodies”, International Applied Mechanics, 46:4 (2010), 388–399 | DOI | MR | Zbl

[14] N. Kikuchi, J. T. Oden, Contact Problems in Elasticity: A study of Variational Inequalities and Finite Element Methods, SIAM, Philadelphia, 1988 | MR | Zbl

[15] J. Koko, “Uzawa block relaxation domain decomposition method for a two-body frictionless contact problem”, Applied Mathematics Letters, 22 (2009), 1534–1538 | DOI | MR | Zbl

[16] T. Sassi, M. Ipopa, F.-X. Roux, “Generalization of Lion's nonoverlapping domain decomposition method for contact problems”, Lect. Notes Comput. Sci. Engrg., 60, 2008, 623–630 | DOI | MR | Zbl

[17] B. Wohlmuth, “Variationally consistent discretization schemes and numerical algorithms for contact problems”, Acta Numerica, 2011, 569–-734 | DOI | MR | Zbl

[18] P. Wriggers, Computational Contact Mechanics, Second Edition, Springer, 2006 | Zbl