Obstacle control problem and the unilateral eigenvalue problem of an elastic pseudoplate

• Autorzy: Lovisek J.
• Języki publikacji: EN

Abstrakty

EN

This paper concerns an obstacle control problem of an elastic pseudoplate. The state problem is modelled by a semi-coercive variational inequality, where the control variable enters the coefficients of linear operator and a linear functional. Moreover, we consider the state eigenvalue problem for a minimal first eigenvalue associated with the vibration of pseudoplate. Existence of an optimal control is verified. Finally, approximate solutions with some convergence analysis are provided.

Słowa kluczowe

EN

elastic pseudoplate; obstacle control problem; control of variational inequalities; vibrations; state eigenvalue problem; uncertain input data

PL

pseudopłyta sprężysta; drgania; dane wejściowe niepewne

• Wydawca: Systems Research Institute, Polish Academy of Sciences
• Czasopismo: Control and Cybernetics
• Rocznik: 2003
• Tom: Vol. 32, no 2
• Strony: 259--300
• Opis fizyczny: Bibliogr. 23 poz.

Twórcy

autor

Lovisek J.

• Slovak University of Technology in Bratislava Radlinskeho 11, 813 68 Bratislava, Slovak Republic

Bibliografia

• ADLY, S. and GOELEVEN, D. (2000) A discretization theory for a class of semicoercive unilateral problems. Numer. Math. 87, 1-34.
• ARMAND, J. L. (1972) Application of the theory of optimal control of distributed parameter system to structural optimization. NASA, Washington D.C.
• BEN HAIM, Y. and ELISHAKOFF, I.E. (1990) Convex models of uncertainities in applied mechanics. In: Studies in Applied Mechanics 25, Elsevier, Amsterdam.
• BOCK, I. and LOVISEK, J. (2000) On optimal design problems for unilaterally supported structures subjected to buckling. VJifh International Conference on Numerical Methods in Continuum Mechanics, Liptovsky Jan, Slovak Republic.
• CEA, J. (1971) Optimisation theorie et algorithmes. Dunond, Paris.
• CIARLET, P.G. (1978) The Finite Element Method for Elliptic Problems. NorthHolland.
• DUVAUT, G. and LIONS, J. L. (1976) Inequalities in Mechanics and Physics. Springer-Verlag, Berlin, Heidelberg, New York.
• GLOWINSKI, R. (1980) Lectures on Numerical Methods for Non-linear Variational Problems. Tata Inst. Fund. Res., Springer-Verlag.
• HASLINGER, J. and NEITAANMAKI, P. (1996) Finite Element Approximation for Optimal Shape. Material and Topology Design. John Wiley and Sons, Chichester.
• HIRIART-URRUTY, J.B. and LAMARECHAL, C. (1996) Convex Analysis and Minimization. Springer-Verlag, Berlin.
• HLAVACEK, I. and LOVISEK J. (2001) Control in obstacle problems with friction on the boundary. Optimal design and reliable problems with uncertain data. Applicationes Mathematical 28, 4, 407- 426.
• HLAVACEK, 1., HASLINGER, J., NECAS, J. and LOVISEK, J. (1982) Solution of variational inequalities in mechanics. Applied Mathematical Sciences, 66, Springer-Verlag, New York.
• KHLUDNEV, A.M. and SOKOLOWSKI, J. (1997) Modelling and Control in Solid Mechanics. Birkhi:iuser Verlag, Basel-Boston-Berlin.
• KINDERLEHRER, D. and STAMPACCHIA, G. (1980) An Introduction to Variational Inequalities and Their Applications. Academic Press, New York.
• LIONS, J .L. (1960) Quelques methodes de resolution des problemes aux limites nonlineaires. Dunod, Paris.
• LITVINOV, G.W. (2000) Optimization of Elliptic Problems with Applications to Mechanics of Deformable Bodies and Fluid Mechanics. Birkhauser Verlag, Berlin.
• MIERSEMANN, E. (1981) Eigenwertaufgaben fiir variationsungleichungen. Math. Nachr. 100, 221-228.
• MYSLINSKI, A. and SOKOLOWSKI, J . (1985) Nondifferentiable optimization problems for elliptic systems. SIAM J. Control and Optization, 23, 632- 648.
• NAD', M. (2002) The effect of the pre-stressed areas on circular plate vibrations. V lith Int. Acoustic Conference - Noise and Vibration in Practice, 115- 120.
• PANAGIOTOPOULOS, P.D. (1985) Inequality Problems in Mechanics and Applications. Birkhauser Verlag, Boston.
• RODRIGUEZ, J. F. (1987) Obstacle Problems in Mathematical Physics. NorthHolland Mathematical Studies 134, Amsterdam.
• ROUSSELET, B. and CHENAIS, D. (1990) Continuite et differentiabilite d 'elements propres: Application a l'optimization de structures, Appl. Math. Optim. 22, 27-59.
• SCHWARTZ L. (1966) Theorie des distributions. Herman, Paris.