Abstract

In this Note, we consider a layout optimization problem, where the dependence of the material coefficient with respect to the density is nonlinear. The particular case when the density only depends on one space variable is studied. We show that the original design problem can be relaxed into an optimization that only involves three shape variables. The structure of the optimal designs is characterized by expliciting optimality conditions of a relaxed functional. © Académie des Sciences/Elsevier, Paris.