Optimal control for elasto-orthotropic plate

• Autorzy: Lovišek J. , Králik J.
• Języki publikacji: EN

Abstrakty

EN

The optimal control problems and a weight minimization problem are considered for elastic three-layered plate with inner obstacle and friction condition on a part of the boundary. The state problem is represented by a variational inequality and the design variables influence both the coefficients and the set of admissible state functions. We prove the existence of a solution to the above-mentioned problem on the basis of a general theorem on the control of variational inequalities. Next, the approximate optimization problem is proved on the basis of the general theorem for the continuous problem. When the mesh/size tends to zero, then any sequence of appropriate solutions converges uniformly to a solution of the continuous problem. Finally, the application to the optimal design of unilaterally supported of rotational symmetrical load elastic annular plate is presented.

Słowa kluczowe

EN

control of variational inequalities; elasto-orthotropic plate; optimal design; weight minimization; approximate optimization problem

• Wydawca: Systems Research Institute, Polish Academy of Sciences
• Czasopismo: Control and Cybernetics
• Rocznik: 2006
• Tom: Vol. 35, no 2
• Strony: 219--278
• Opis fizyczny: Bibliogr. 26 poz.

Twórcy

autor

Lovišek J.

autor

Králik J.

• Slovak University of Technology, Faculty of Civil Engineering, Starohorska 2, Bratislava, Slovak Republic

Bibliografia

• ADAMS, R.A. (1975) Sobolev Spaces. Academic Press, New York.
• BARBU, V. (1987) Optimal Control of Variational Inequalities. Pitman Advanced Publishing Program, Boston, London.
• BEGIS, D. and GLOWINSKI, R. (1975) Application de la mèthode des elements finis à l’approximation d’un problème de domaine optimal. Mèthodes de rèsolution des problèmes approches. Applied Mathematics. Optimsation 2, 130-169.
• BOCK, I. and LOVIŠEK, J. (1987) Optimal control problems for variational inequalities with controls in coefficients. Applications of Mathematics 32, 301-314.
• BREZZI, F. and FORTIN, M. (1991 Mixed and Hybrid Finite Element Methods. Springer-Verlag, New York.
• CEA, J. (1971) Optimisation. Théorie et algorithmes. Dunod. Paris.
• CIARLET, P.G. (1978) The Finite Element Method for Elliptic Problems. North Holland, Amsterdam.
• COMODI, M.I. (1985) Approximation of bending plate problem with a boundary unilateral constraint. Numer. Math. 47, 435-458.
• DUVAUT, J. and LIONS, L. (1972) Les inéquations en mécanique et en physique. Dunod. Paris.
• EKELAND, I. and TEMAN, R. (1974) Analyse convexe et problèmes variationnels. Dunod Paris.
• GLOWINSKI, R., LIONS, J.L. and TREMOLIERES, R. (1981) Numerical Analysis of Variational Inequalities. North-Holland, Amsterdam.
• HAUG, E., CHOI. K.K. and KOMKOV, V. (1986) Design Sensitivity Analysis of Structural Systems. Academic Press, New York.
• HLAVAČEK, I. and LOVIŠEK, J. (2001) Control in obstacle-pseudoplate problems with friction on the boundary. Optimal design and problems with uncertain data. Applicationes Mathematicae 28 (4), 407-426.
• KHLUDNEV, A.M. and SOKOLOWSKI, J. (1997) Modelling and Control in Solid Mechanics. Birkhäuser.
• KINDERLEHRER, D. and STAMPACCHIA, G. (1980) An Introduction to Variational Inequalities and Their Applications. Academic Press, New York.
• LIONS, J.L. (1969) Quelques mèthodes de résolution des problèmes aux limites nonlinéaires. Dunod.
• LITVINOV, W. (2000) Optimization in Elliptic Problems with Applications to Mechanics of Deformable Bodies and Fluid Mechanics. Birkhäuser.
• LOVIŠEK, J. and KRÁLIK, J. (2001) Optimal control of the elastic plate with inner obstacles. In: Budowa i Eksploatacja Maszyn, 61, Proceedings of Euroconference on Computational Mechanics and Engineering Practice, Szczyrk, Poland, Sept. 19-21, 217-224.
• MASSON, J. (1985) Methods of Functional Analysis for Application in Solid Mechanics. Elsevier.
• MOSCO, U. (1971) Convergence of convex sets and solutions of variational inequalities. In: G. Geymonant, ed.. Constructive Aspects of Functional Analysis, II. Centre Intern Matem., Estivo, 497-682.
• PANAGIOTOPOULOS, P.D. (1985) Inequality Problems in Mechanics and Applications. Birkhäuser, Basel.
• REDDY, J.N. (2003) Mechanics of Laminate Composite Plates and Shells. Theory and Analysis. CRC Press, Boca Raton, London.
• REISMANN, H. (1988) Elastic Plates - Theory and Applications. John Wiley and Sons, New York, Chichester.
• RODRIGUES, J.F.(1987) Obstacle Problem in Mathematical Physics. North-Holland.
• SALAC, P. (1995) Shape optimization of elastic axisymmetric plate of an elastic foundation. Applications of Mathematics 40 (4), 319-338.
• SCHWARTZ, L. (1966) Théorie des distributions. Herman.