Abstract
This work is devoted to the study of simply supported and of clamped plates together with related variational inequalitiesand optimization problems. We introduce a new unitary approach based on distributed optimal control problems governed by second order elliptic boundary value problems and their penalization. This approach gives the possibility to approximate the solution via piecewise linear continuous finite elements and is simpler than other methods considered in the literature.The convergence with respect to the penalization parameter (ε) is proved under very general assumptions. In order to solve the obtained control problems, optimization procedures of steepest descent type are considered. Relevantnumerical examples illustrate the applicability of the proposed methods.
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