Inserted: 9 oct 2017
Journal: In "Variational Analysis and Aerospace Engineering: Mathematical Challenges for Aerospace Design'', Springer Optimization and Its Applications
Links: paper at the Springer web site
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, support points, Sobolev point conditions, potential energy