Krüger, Jan ChristophJan ChristophKrügerKriegesmann, BenediktBenediktKriegesmann2024-10-152024-10-152024-07-10Structural and Multidisciplinary Optimization 67 (7): 124 (2024)https://hdl.handle.net/11420/49415This paper presents a new formulation of the second-order fourth-moment method (sometimes referred to as second-order perturbation method or second-order method of moments). The method allows to efficiently predict the stochastic moments of a response function and is therefore often used within robust design optimization. The new approach allows a non-intrusive implementation at the same cost as existing, highly intrusive formulations. Therefore, the new approach can be applied to any objective function without significant implementation effort. It is based on a few finite difference steps into special directions and hence is dependent on the corresponding step sizes. An automatic step size procedure is supplied beside a detailed convergence analysis. The advantages of the new formulation are demonstrated by robust design optimizations of a 2D and a 3D example using the geometrically nonlinear finite element method.en1615-148820247Springerhttps://creativecommons.org/licenses/by/4.0/Method of momentsRobust design optimization (RDO)Robust topology optimizationSecond-order perturbation approachNatural Sciences and Mathematics::519: Applied Mathematics, ProbabilitiesJournal Article10.15480/882.1339410.1007/s00158-024-03843-610.15480/882.13394Journal Article