Optimal Control of an Axisymmetric Conical Shell with a Unilateral Elastic Foundation and Rigid Supports
Igor Bock, Ján Lovíšek · PAMM · 2008
Abstract We study an optimal control problem for an elastic conical shell. The displacement vector u=(u,v) is then a function of one variable s∈(a,b), 0<a<b<∞. Here u is the meridional and v the normal displacement. The shell is assumed to be simply supported. Moreover, we consider several unilateral obstacles and an unilateral elastic foundation of Winkler type i.e. the reaction force is proportional of the positive part of the normal displacement. The state problem is formulated in a form of variational inequality for u. The design parameter e=(t,z,F) includes the variable thickness of the shell, the stiffness characteristics of the foundation and the friction coefficient. The existence of the optimal control will be explained. (© 2008 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)