Abstract
In Bielski and Telega (1998) the study of unilateral contact problems for elastic plates was started. Such a study was next extended to the linear Koiter shell model in Telega et al. (2001). The aim of the present contribution is to develop augmented Lagrangian methods applicable to nonconvex unilateral contact problems arising in structural mechanics. To this end we have extended the approach proposed by Ito and Kunisch (1990, 1995) for convex problems. An illustrative example pertains to a geometrically nonlinear elastic beam.
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References
Bielski W. R., and Telega, J. J. (1998) Existence of solutions to obstacle problems for linear and nonlinear elastic plates, Math. Comp. Modelling, 28, 55–66.
Telega, J.J., Galka, A., and Bielski, W. R. (2001) Augmented Lagrangian methods for a class of convex and nonconvex problems, J. Theor. Appl. Mech., 3, 741–768.
Ito, K., and Kunisch, K. (1990) An augmented Lagrangian technique for variational inequalities, Appl. Math. Optim., 21, 223–241.
Ito, K., and Kunisch, K. (1995) Augmented Lagrangian methods for nonsmooth, convex optimization in Hilbert spaces, in: Control of Partial Differential Equations and Applications, ed. Ito, K., and Kunisch, K, pp. 107–117, Marcel Dekker
Lewix ski, T and Telega, J. J. (2000) Plates, Laminates and Shells: Asymptotic Analysis and Homogenization, Series on Advances in Mathematics for Applied Sciences, vol. 52, World Scientific, Singapore.
He, Q.-C., Telega, J. J., and Curnier, A. (1996) Unilateral contact of two solids subject to large deformation and existence results, Proc. R. Soc., London, A452, 2691–2717.
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© 2002 Springer Science+Business Media Dordrecht
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Bielski, W.R., Gałka, A., Telega, J.J. (2002). Augmented Lagrangian Methods for a Class of Nonconvex Contact Problems in Structural Mechanics. In: Contact Mechanics. Solid Mechanics and Its Applications, vol 103. Springer, Dordrecht. https://doi.org/10.1007/978-94-017-1154-8_27
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DOI: https://doi.org/10.1007/978-94-017-1154-8_27
Publisher Name: Springer, Dordrecht
Print ISBN: 978-90-481-6099-0
Online ISBN: 978-94-017-1154-8
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