On strength design using free material subjected to multiple load cases

Multiple load cases and the consideration of strength is a reality that most structural designs are exposed to. Improved possibility to produce specific materials, say by fiber lay‐up, put focus on research on free material optimization. A formulation for such design problems together with a practical recursive design procedure is presented and illustrated with examples. The presented finite element analysis involve many elements as well as many load cases. Separating the local amount of material from a description with unit trace for the local anisotropy, gives the free materials formulation a more physical interpretation of the material constraint.