Optimal control problem for deflection plate with crack
- 137 Downloads
We consider a control problem where the state variable is defined as the solution of a variational inequality. This system describes the vertical displacement of points of a thin plate with the presence of crack inside . As the control we define the force that originates the deection of the plate. In order to get the system of optimality for the control problem we use a penalized problem  and its reformation as a Lagrangian problem. We prove the existence of a Lagrange multiplier to obtain a system of optimality to the exact problem via Lagrangian. Applying the method of bounded increments  we get the final result that characterizes the optimal state and control.
Key words and phrasesOptimal control optimality system penalty problem method of bounded increments
2000 Mathematics Subject Classification53C17 22E30 49J15
Unable to display preview. Download preview PDF.
- 3.______, Optimal Control of Variational Inequalities. Research Notes in Mathematics 100, Pitman Advanced Publishing Program, Iasi (1983).Google Scholar
- 6.I. Ekeland and R. Teman, Analyse Convexe et Problèmes Variationelles. Paris, Dunod - Gauthier Villars (1973).Google Scholar
- 7.A. Khludnev and V. Kovtunenko, Analysis of Cracks in Solids. WIT Press, Southampton-Boston (2000).Google Scholar
- 9.R. Glowinski, R. Trémolieres and J. L. Lions, Analyse Numerique des Inéquations Variationelles 1 and 2, Dunod (1976).Google Scholar
- 10.A. Leontiev, Necessary Optimality Conditions for the Control Problem of the Kirhgoff Plates, Dinamika Splochnoy Sredy. Novosibirsk 103 (1991), 88–89.Google Scholar
- 13.______, Function Spaces and Optimal Control of Distributed Systems. IM-UFRJ, Rio de Janeiro, Brasil (1980).Google Scholar
- 14.______,Some aspects of the Optimal Control of Distributed Parameter Systems. SIAM, Philadelphia, Pennsylvania (1980).Google Scholar
- 16.J. L. Lions and G. Stampacchia, Variational Inequalities, Communications on Pure and Applied Mathematics XX (1967), 493–519.Google Scholar
- 20.Yu. N. Rabotnov, Mechanics of a defromed Solid Body. Nauka, Moscow (1979).Google Scholar