Robust optimal component design under consideration of local material defects

An important issue in additive manufacturing is the reliability and reproducibility of parts. One major problem in achieving this are uncontrolled local variations in the obtained material properties which arise in the complex manufacturing process and are usually not taken into account in the design of components. We consider the optimal layout of a part to withstand a given loading, under the assumption that the local material properties are not precisely known. The material uncertainties are treated by a worst case approach. This means that for each layout a given amount of defects in material properties is distributed in the design domain, such that the stiffness of the component is maximally weakened. As a consequence, an optimization result is obtained which is as insensitive as possible with respect to unknown variations in the material parameters. The general model is introduced and an algorithm for its solution using gradient based methods is suggested. Finally, numerical results are presented and discussed.