Free material design via semidefinite programming: The multiload case with contact conditions (Q2706420)

The paper explains how to find the stiffest structure with respect to one or more given loads when both the distribution of material and the material itself vary freely. The desired optimal structure is a continuum elastic body, and the design variables are material properties which vary from point to point. The aim is to optimize not only the distribution of material but also the material properties themselves. The main result: after a series of transformations, the authors reach a problem formulation for which they are able to prove the existence of solution; a suitable discretization of loads leads to a semidefinite programming problem for which modern polynomial-time algorithms of interior point type are available. Finally, numerical examples demonstrate the efficiency of the proposed approach.