A shape optimization problem on planar sets with prescribed topology

2021/01/08 by Luca Briani, Briani, L., Giuseppe Buttazzo +3 · 1 citation
Engineering · Computer Science · #Topology Optimization in Engineering #Advanced Mathematical Modeling in Engineering #Composite Material Mechanics

paper · pdf · doi:10.48550/arxiv.2101.02886

Abstract

We consider shape optimization problems involving functionals depending on perimeter, torsional rigidity and Lebesgue measure. The scaling free cost functionals are of the form P(Ω)T^q(Ω)|Ω|^-2q-1/2 and the class of admissible domains consists of two-dimensional open sets Ω satisfying the topological constraints of having a prescribed number k of bounded connected components of the complementary set. A relaxed procedure is needed to have a well-posed problem and we show that when q<1/2 an optimal relaxed domain exists. When q>1/2 the problem is ill-posed and for q=1/2 the explicit value of the infimum is provided in the cases k=0 and k=1.

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