Approximation and numerical realization of 3D contact problems with given friction and a coefficient of friction depending on the solution
Tóm tắt
Từ khóa
Tài liệu tham khảo
P.G. Ciarlet: The Finite Element Method for Elliptic Problems. Studies in Mathematics and its Applications, Vol. 4. North-Holland, Amsterdam-New York-Oxford, 1978.
P. Clement: Approximation by finite element functions using local regularization. Rev. Franc. Automat. Inform. Rech. Operat. 9, R-2 (1975), 77–84.
G. Duvaut, J.-L. Lions: Inequalities in Mechanics and Physics. Grundlehren der mathematischen Wissenschaften, Band 219. Springer, Berlin-Heidelberg-New York, 1976.
R. Glowinski: Numerical Methods for Nonlinear Variational Problems. Springer Series in Computational Physics. Springer, New York, 1984.
J. Haslinger, I. Hlaváček, J. Nečas: Numerical methods for unilateral problems in solid mechanics. Handbook of Numerical Analysis, Vol. IV (P.G. Ciarlet et al., eds.). North-Holland, Amsterdam, 1995, pp. 313–485.
J. Haslinger, O. Vlach: Signorini problem with a solution dependent coefficient of friction (model with given friction): Approximation and numerical realization. Appl. Math. 50, (2005), 153–171.
I. Hlaváěk: Finite element analysis of a static contact problem with Coulomb friction. Appl. Math. 45 (2000), 357–379.
I. Hlaváček, J. Haslinger, J. Nečas, J. Lovíšek: Solution of Variational Inequalities in Mechanics. Applied Mathematical Sciences, Vol. 66. Springer, New York, 1988.
N. Kikuchi, J.T. Oden: Contact Problems in Elasticity: A Study of Variational Inequalities and Finite Element Methods. SIAM Studies in Applied Mathematics, Vol. 8. SIAM, Philadelphia, 1988.
R. Kučera: Convergence rate of an optimization algorithm for minimizing quadratic functions with separable convex constraints. SIAM J. Optim. 19 (2008), 846–862.
T. Ligurský: Approximation and numerical realization of 3D contact problems with given friction and a coefficient of friction depending on the solution. Diploma thesis MFF UK, 2007 ( http://artax.karlin.mff.cuni.cz/~ligut2am/tl21.pdf ).