Free material design deals with the question of finding the stiffest struct
ure with respect to one or more given loads which can be made when both the
distribution of material and the material itself can freely vary. The case
of one single load has been discussed in several recent papers, and an eff
icient numerical approach was presented in [M. Kocvara, M. Zibulevsky, and
J. Zow, RAIRO Model. Math. Anal. Numer. 32 (1998), pp. 255-281]. We attack
here the multiload situation (understood in the worst-case sense), which is
of much more interest for applications but also significantly more challen
ging from both the theoretical and the numerical points of view. After a se
ries of transformation steps we reach a problem formulation for which we ca
n prove existence of a solution; a suitable discretization leads to a semid
efinite programming problem for which modern polynomial time algorithms of
interior point type are available. A number of numerical examples demonstra
tes the efficiency of our approach.