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Item type:Publication, Access status: with files , Scalable gradient-based approaches for topology and shape optimization under uncertaintyThis dissertation addresses the challenge of finding scalable frameworks for structural optimization under uncertainty. Therefore, efficient and non-intrusive formulations for the gradient computation of different Taylor series-based probabilistic methods are developed and a new probabilistic approach is presented. Additionally, challenges encountered by the multigrid finite element solver when dealing with (uncertain) anisotropic materials are discussed and a solution is presented.Publicationtype: Doctoral Thesis63 49 - Some of the metrics are blocked by yourconsent settings
Item type:Publication, Access status: with files , Robust design optimization of structures with multimodal responses using Taylor expansions(Springer, 2025-11-15); ; ; ; This paper shows how a combination of multiple linear approximations can efficiently capture nonlinear and non-smooth response functions in the framework of robust design optimization. The basic idea is to split the domain of random parameters into multiple subdomains along discontinuities of the response. For each subdomain, a linear approximation is used to determine the stochastic moments of the response function due to the scatter in that subdomain. The total stochastic distribution of the structural response is considered to be a multimodal distribution, and its moments are composed of the approximations in the subdomains. The application to use cases shows that indeed the structural response is multimodal in these cases, and the stochastic moments are shown to be sufficiently accurate using the proposed method.Publicationtype: Journal Article67 47 - Some of the metrics are blocked by yourconsent settings
Item type:Publication, Access status: with files , On the application of the multigrid method to topology optimization with orthotropic material with varying orientationMultigrid methods are known to show good performance for most topology optimization problems, but suffer from anisotropies. The main problems are caused by poor performance of the smoothing algorithms. This paper analyzes different standard and advanced smoothing algorithms using the local Fourier analysis with regard to orthotropic materials in the linear elasticity problem. The results are generalized to real problems and contrast-rich topology designs using numeric experiments. Based on the analyses, recommendations are given and a new spatial Jacobi smoothing algorithm is presented. The results are finally approved by a topology optimization example and a material orientation and topology optimization example.Publicationtype: Journal Article73 31 - Some of the metrics are blocked by yourconsent settings
Item type:Publication, Access status: with files , Robust design optimization using a non-intrusive second-order approximation of stochastic momentsThis 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.Publicationtype: Journal Article30 49 - Some of the metrics are blocked by yourconsent settings
Item type:Publication, Access status: without files , Efficient robust topology optimization of eigenfrequencies using the first-order second-moment methodDesign optimization has become an important field in engineering science since it allows a significant reduction in mass, cost and environmental impact.Publicationtype: Conference Paper72 - Some of the metrics are blocked by yourconsent settings
Item type:Publication, Access status: without files , An efficient and non-intrusive approach for robust design optimization with the first-order second-moment method(Elsevier, 2023-09-01); ; ; ; A modified robust design optimization approach is presented, which uses the first-order second-moment method to compute the mean value and the standard deviation for arbitrary objective functions. Existing approaches compute the gradient of the variance using the adjoint method, direct differentiation or finite differences, respectively. These approaches either access to the FE-code and/or have high computational cost. In this paper, a new approach for the computation of the gradient of the variance is provided. It can be easily implemented as a non-intrusive method, which behaves similar to finite differences with the cost of only one additional objective evaluation, independent of the number of variables. Here, a step-size has to be chosen carefully and therefore, a procedure to determine a problem-independent step-size is provided. As an alternative, the approach can be implemented as an analytic method with the same cost like the adjoint method, but providing wider applicability (e.g. eigenvalue problems). The provided approach is derived, analyzed and applied to several benchmark examples.Publicationtype: Journal Article163 - Some of the metrics are blocked by yourconsent settings
Item type:Publication, Access status: without files , Robust design optimization of structures with multimodal responses using Taylor expansions(2023-06-05); Publicationtype: Conference Presentation53