2010/02/14 by Giuseppe Buttazzo, Buttazzo, Giuseppe, Faustino Maestre +1
Computer Science · Engineering · Mathematics · #Advanced Mathematical Modeling in Engineering #Nonlinear Partial Differential Equations #Topology Optimization in Engineering #math.AP #math.OC #msc:46E35 #msc:47A10 #msc:49J45 #msc:49Q10 #msc:74P05
paper · pdf · doi:10.48550/arxiv.1002.2770
17 pages, 6 figures
arxiv created 2010/02/14 · arxiv updated 2010/02/26
In this paper we analyze the relaxed form of a shape optimization problem with state equation \arrayll -div (a(x)Du)=f \hboxinD \hboxboundary conditions on∂ D. array. The new fact is that the term f is only known up to a random perturbation ξ(x,ω). The goal is to find an optimal coefficient a(x), fulfilling the usual constraints α≤ a≤β and ∫D a(x) dx≤ m, which minimizes a cost function of the form ∫Ω∫Dj(x,ω,ua(x,ω)) dx dP(ω). Some numerical examples are shown in the last section, to stress the difference with respect to the case with no perturbation.