MATHEMATICA BOHEMICA, Vol. 126, No. 2, pp. 281-292 (2001)

On the minimum of the work of interaction forces between a pseudoplate and a rigid obstacle

Igor Bock, Jan Lovisek

Igor Bock, Department of Mathematics, Faculty of Electr. Engineering and Inform. Tech., Slovak University of Technology, Ilkovicova 3, 812 19 Bratislava, Slovakia, e-mail:; Jan Lovisek, Department of Mechanics, Faculty of Civil Engineering, Slovak University of Technology, Radlinského 11, 813 68 Bratislava, Slovakia, e-mail:

Abstract: An optimization problem for the unilateral contact between a pseudoplate and a rigid obstacle is considered. The variable thickness of the pseudoplate plays the role of a control variable. The cost functional is a regular functional only in the smooth case. The existence of an optimal thickness is verified. The penalized optimal control problem is considered in the general case.

Keywords: elliptic variational inequality, pseudoplate, thickness, optimal control, penalization

Classification (MSC2000): 49J20, 35J85

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