Free Access
Volume 50, Number 4, July-August 2016
Page(s) 995 - 1009
Published online 16 June 2016
  1. G. Allaire, Numerical Analysis and Optimization: An Introduction to Mathematical Modelling and Numerical Simulation. Oxford University Press (2007). [Google Scholar]
  2. M. Bach, A.M. Khludnev and V.A. Kovtunenko, Derivatives of the energy functional for 2D-problems with a crack under Signorini and friction conditions. Math. Methods Appl. Sci. 23 (2000) 515–534. [CrossRef] [MathSciNet] [Google Scholar]
  3. G.P. Astrakhantsev, Domain decomposition method for the problem of bending heterogeneous plate. Comput. Math. Math. Phys. 38 (1998) 1686–1694. [MathSciNet] [Google Scholar]
  4. G. Bayada, J. Sabil and T. Sassi, A Neumann-Neumann domain decomposition algorithm for the Signorini problem. Appl. Math. Lett. 17 (2004) 1153–1159. [CrossRef] [MathSciNet] [Google Scholar]
  5. G. Bayada, J. Sabil and T. Sassi, Convergence of a Neumann-Dirichlet algorithm for two-body contact problems with non local Coulomb’s friction law. ESAIM: M2AN 42 (2008) 243–262. [CrossRef] [EDP Sciences] [Google Scholar]
  6. J. Céa, Optimisation, Théorie et algorithmes. Dunod, Gauthier - Villars Paris (1971). [Google Scholar]
  7. G.P. Cherepanov Mechanics of Brittle Fracture. New York, McGraw-Hill (1979). [Google Scholar]
  8. J. Daněk, I. Hlaváček and J. Nedomac, Domain decomposition for generalized unilateral semi-coercive contact problem with given friction in elasticity. Math. Comput. Simul. 68 (2005) 271–300. [CrossRef] [Google Scholar]
  9. G. Duvaut and J.-L. Lions, Inequalities in Mechanics and Physics. Springer-Verlag - Berlin, Heidelberg, New York (1976). [Google Scholar]
  10. I. Ekeland and R. Temam, Convex Analysis and Variational Problems. North-Holland Publishing Company, Amsterdam, Oxford (1976). [Google Scholar]
  11. L.C. Evans, Partial Differential Equations. AMS Press (1998). [Google Scholar]
  12. P. Grisvard,Singularities in Boundary Value Problems. Masson, Springer, Paris (1991). [Google Scholar]
  13. J. Haslinger, R. Kučera and T. Sassi, A domain decomposition algorithm for contact problems: analysis and implementation. Math. Model. Nat. Phenom. (2009) 4 123–146. [CrossRef] [EDP Sciences] [MathSciNet] [Google Scholar]
  14. F. Hecht, New development in FreeFem++. J. Numer. Math. 20 (2012) 251–265. [CrossRef] [MathSciNet] [Google Scholar]
  15. M. Hintermüller, K. Ito and K. Kunisch, The primal-dual active set strategy as a semismooth Newton method. SIAM J. Optim. (2003) 13 865–888. [CrossRef] [MathSciNet] [Google Scholar]
  16. M. Hintermüller, V. Kovtunenko and K. Kunisch, The primal-dual active set method for a crack problem with non-penetration. IMA J. Appl. Math. (2004) 69 1–26. [CrossRef] [MathSciNet] [Google Scholar]
  17. K. Ito and K. Kunisch, Lagrange multiplier approach to variational problems and applications. SIAM, Philadelphia (2008). [Google Scholar]
  18. M.S.D. Jacob, P.R. Arora and M. Saleem, M.A. Elsadig and S.M. Sapuan, Fretting fatigue crack initiation: An experimental and theoretical study. Int. J. Fatigue. 29 (2007) 1328–1338. [CrossRef] [Google Scholar]
  19. A.M. Khludnev and V.A. Kovtunenko, Analysis of cracks in solids. Southampton; WIT-Press, Boston (2000). [Google Scholar]
  20. A.M. Khludnev and V.A. Kozlov, Asymptotics of solutions near crack tips for Poisson equation with inequality type boundary conditions. Z. Angew. Math. Phys. 59 (2008) 264–280. [CrossRef] [MathSciNet] [Google Scholar]
  21. A.M. Khludnev and G. Leugering, On elastic bodies with thin rigid inclusions and cracks. Math. Methods Appl. Sci. 33 (2010) 1955–1967. [MathSciNet] [Google Scholar]
  22. A.M. Khludnev and A. Tani, Overlapping domain problems in the crack theory with possible contact between crack faces. Q. Appl. Math. 66 (2008) 423–435. [CrossRef] [Google Scholar]
  23. N. Kikuchi and J.T. Oden, Contact Problems in Elasticity. SIAM, Philadelphia (1988). [Google Scholar]
  24. J. Koko, Uzawa conjugate gradient domain decomposition methods for coupled Stokes flows. J. Sci. Comput. 26 (2006) 195–215. [CrossRef] [MathSciNet] [Google Scholar]
  25. J. Koko, Uzawa bloc relaxation domain decomposition method for a two-body frictionless contact problem. App. Math. Lett. (2009) 22 1534–1538. [CrossRef] [Google Scholar]
  26. V.A. Kovtunenko, Numerical simulation of the non-linear crack problem with nonpenetration. Math. Meth. Appl. Sci. (2004) 27 163–179. [CrossRef] [Google Scholar]
  27. V.A. Kozlov, V.G. Mazya and J. Rossmann, Spectral Problems Associated with Corner Singularities of Solutions to Elliptic Equations. Vol. 85 of Math. Surveys and Monographs, American Mathematical Society, Providence, RI (2001). [Google Scholar]
  28. Yu.M. Laevsky, A.M. Matsokin, Decomposition methods for the solution to elliptic and parabolic boundary value problems Sib. Zh. Vychisl. Mat. 2 (1999) 361–372. [Google Scholar]
  29. E. Laitinen, A.V. Lapin and J. Pieskä, Splitting iterative methods and parallel solution of variational inequalities. Lobachevskii J. Math. 8 (2001) 167–184. [MathSciNet] [Google Scholar]
  30. N.P. Lazarev and E.M. Rudoy, Shape sensitivity analysis of Timoshenko’s plate with a crack under the nonpenetration condition. Z. Angew. Math. Mech. 94 (2014) 730–739. [CrossRef] [MathSciNet] [Google Scholar]
  31. A. Quarteroni and A. Valli, Domain decomposition methods for partial differential equations. Clarendon Press (1999). [Google Scholar]
  32. E.M. Rudoy, Shape derivative of the energy functional in a problem for a thin rigid inclusion in an elastic body. Z. Angew. Math. Phys. 66 (2015) 1923–1937. [CrossRef] [MathSciNet] [Google Scholar]
  33. E.V. Vtorushin, Numerical investigation of a model problem for deforming an elastoplastic body with a crack under non-penetration condition Sib. Zh. Vychisl. Mat. (2006) 9 335–344. (in Russian) [Google Scholar]
  34. K. Yosida, Functional Analysis. Springer-Verlag, Berlin Heidelberg GmbH (1968). [Google Scholar]

Current usage metrics show cumulative count of Article Views (full-text article views including HTML views, PDF and ePub downloads, according to the available data) and Abstracts Views on Vision4Press platform.

Data correspond to usage on the plateform after 2015. The current usage metrics is available 48-96 hours after online publication and is updated daily on week days.

Initial download of the metrics may take a while.

Recommended for you