Free material optimization via mathematical programming

This paper deals with a central question of structural optimization which is formulated as the problem of finding the stiffest structure which can be made when both the distribution of material as well as the material itself can be freely varied. We consider a general multi-load formulation and include the possibility of unilateral contact. The emphasis of the presentation is on numerical procedures for this type of problem, and we show that the problems after discretization can be rewritten as mathematical programming problems of special form. We propose iterative optimization algorithms based on penalty-barrier methods and interior-point methods and show a broad range of numerical examples that demonstrates the efficiency of our approach.