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Nonsmooth optimal design problems for the Kirchhoff plate with unilateral conditions. (English) Zbl 0789.73052
Summary: The form of directional derivative of the metric projection in the Sobolev space $$H^ 2_ 0(\Omega)$$ onto the convex set $$K=\{f\in H^ 2_ 0(\Omega)\mid f\geq \psi\}$$ is derived in [M. Rao and the author, Numer. Funct. Anal. Optimization 14, 125-143 (1993)]. In the present paper, this result is used to obtain the first order optimality conditions for a class of nonsmooth optimal design problems for the Kirchhoff plate with an obstacle.

##### MSC:
 74P99 Optimization problems in solid mechanics 74K20 Plates 49K20 Optimality conditions for problems involving partial differential equations 49J40 Variational inequalities
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##### References:
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