2017/03/17 by Olbermann, Heiner
#49J20 #74B10 #Analysis of PDEs (math.AP) #FOS: Mathematics #Optimization and Control (math.OC)
paper · doi:10.48550/arxiv.1703.05989
We reconsider the minimization of the compliance of a two dimensional elastic body with traction boundary conditions for a given weight. It is well known how to rewrite this optimal design problem as a nonlinear variational problem. We take the limit of vanishing weight by sending a suitable Lagrange multiplier to infinity in the variational formulation. We show that the limit, in the sense of Γ-convergence, is a certain Michell truss problem. This proves a conjecture by Kohn and Allaire.