The Dirichlet problem for the bi-harmonic equation is considered as the Kirchhoff model of an isotropic elastic plate clamped at its edge. The plate is supported at certain points P1,…,PJ, that is, the deflexion u(x) satisfies the Sobolev point conditions u(P1)=⋯=u(PJ)=0. The optimal location of the support points is discussed such that either the compliance functional or the minimal deflexion functional attains its minimum.


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