Abstract
We show that, under suitable conditions, the variational inequality that expresses the elastic-plastic torsion problem is equivalent to a variational inequality on a convex set which depends on δ(x)=d(x, ∂Ω). Such an equivalence allows us to find the related Lagrange multipliers and to exhibit a computational procedure based on the subgradient method.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Maugeri, A., Equilibrium Problems and Variational Inequalities, Equilibrium Problems: Nonsmooth Optimization and Variational Inequality Models, Edited by F. Giannessi, A. Maugeri and P. Pardalos, Kluwer Academic Publishers, Dordrecht, Holland, pp. 187–205, 2001.
Ting, T.W., Elastic-Plastic Torsion Problem, Archive for Rational Mechanics and Analysis, Vol. 34, pp. 228–244, 1969.
Brezis, H., and Stampacchia, G., Sur la Régularité de la Solution d'Inéquations Elliptiques, Bulletin de la Société Mathématique de France, Vol. 96, pp. 153–180, 1968.
Brezis, H., Multiplicateur de Lagrange en Torsion Elastic-Plastic, Archive for Rational Mechanics and Analysis, Vol. 49, pp. 32–40, 1972.
Brezis, H., and Sibony, M., Equivalence de Deux Inèquations Variationnelles et Applications, Archive for Rational Mechanics and Analysis, Vol. 41, pp. 254–265, 1971.
Lanchon, H., Solution du Probléme de Torsion é lastoplatique d'une Barre Cylindrique du Section Queldunque, Comptes Rendus de l'Académie des Sciences, Paris, Vol. 269, pp. 791–794, 1969.
Borwein, J. M., and Lewis, A.S., Practical Conditions for Fenchel Duality in Infinite Dimension, Pitman Research Notes in Mathematics Series, Pitman, London, England, Vol. 252, pp. 83–89, 1989.
Idone, G., Variational Inequalities and Applications to a Continuum Model of Transportation Network with Capacity Constraints, Journal of Global Optimization (to appear).
Daniele, P., Lagrangian Function for Dynamic Variational Inequalities, Rendiconti del Circolo Matematico di Palermo, Vol. 58, pp. 101–119, 1999.
ChiadÒ-Piat, V., and Percivale, D., Generalized Lagrange Multipliers in Elastoplastic Torsion, Journal of Differential Equations, Vol. 114, pp. 570–579, 1994.
Daniele, P., Maugeri, A., and Oettli, W., Time-Dependent Traffic Equilibria, Journal of Optimization Theory and Applications, Vol. 103, pp. 543–555, 1999.
Jahn, J., Introduction to the Theory of Nonlinear Optimization, Springer, Berlin, Germany, 1996.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Idone, G., Maugeri, A. & Vitanza, C. Variational Inequalities and the Elastic-Plastic Torsion Problem. Journal of Optimization Theory and Applications 117, 489–501 (2003). https://doi.org/10.1023/A:1023941520452
Issue Date:
DOI: https://doi.org/10.1023/A:1023941520452