In this thesis, the idea of robust design optimization is adopted to improve the quality of a product or process by minimizing the deteriorating effects of variable or not exactly quantifiable parameters.Robustness can be achieved via different formulations, which are compiled and discussed in the present work. All of these formulations have in common that they require many function evaluations throughout the optimization process. Especially in the growing field of computational engineering, the governing equations are typically not explicit functions but rather a nonlinear system of equations - for instance, derived from a nonlinear finite element discretization. In this case, even pointwise solutions can be quite expensive to evaluate. To reduce the tremendous numerical effort related to the described robustness analyses, metamodeling techniques are used replacing the actual numerical analysis codes by a simpler formulation.In this thesis, a method is proposed to sequentially augment the significance of metamodels for robust design optimization through additional sampling at infill points. As a result, a robust design optimization can be applied efficiently to engineering tasks that involve complex computer simulations. Even though the suggested approach is applicable to many engineering disciplines, the present work is focused on problems in the field of structural mechanics.