Calculus of Variations and Geometric Measure Theory

G. Buttazzo - S. Nazarov

Optimal location of support points in the Kirchhoff plate

created by buttazzo on 30 Oct 2017


Published Paper

Inserted: 30 oct 2017

Journal: Journal of Mathematical Sciences
Volume: 176
Number: 6
Pages: 786-796
Year: 2011
Doi: 10.1007/s10958-011-0436-1
Links: paper at the journal web page


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 $P^1,\dots,P^J$, that is the deflexion $u(x)$ satisfies the Sobolev point conditions $u(P^1)=\dots=u(P^J)=0$. The optimal location of the support points is discussed such that either the compliance functional, or the minimal deflexion functional attains its minimum.

Keywords: compliance, optimization, Kirchhoff plate, minimal deflexion, Sobolev point conditions, potential energy