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Item type:Publication, Access status: with files , A generalized approach for robust topology optimization using the first-order second-moment method for arbitrary response functions(2023-04-13); ; The paper presents a rigorous formulation of adjoint systems to be solved for a robust design optimization using the first-order second-moment method. This formulation allows to apply the method for any objective function, which is demonstrated by considering deformation at certain point and maximum stress as objectives subjected to random material stiffness and geometry, respectively. The presented approach requires the solution of at most three additional adjoint systems per uncertain system response, when compared to the deterministic case. Hence, the number of adjoint systems to be solved is independent of the number of random variables. This comes at the expense of accuracy, since the objective functions are assumed to be linear with respect to random parameters. However, the application to two standard cases and the validation with Monte Carlo simulations show that the approach is still able to find robust designs.Publicationtype: Journal ArticleScopus© Citations 5 90 124 - Some of the metrics are blocked by yourconsent settings
Item type:Publication, Access status: with files , Probabilistic analysis of additively manufactured polymer lattice structuresFiligree lattice structures are sensible to geometrical imperfections and the scatter of material parameters which all depend on the stability of the manufacturing process. The aim of this study is to analyze these effects for polymer lattice structures and incorporate them in a finite element model for robust design. Micrographs of lattice structure slices show a smaller diameter for vertical struts. Basic mechanical tests on bulk material exhibit a tension–compression asymmetry which is captured with a Drucker-Prager material model in simulations. Digital image correlation measurements allow to determine true material properties. Plateau stress and failure strain are a result of the biggest flaw in the specimen. Hence, a new model to determine their probability distribution is proposed. This model outperforms standard approaches deriving the probability distribution from the central moments. A spatial correlation of geometric deviations and scatter of the material is investigated with variography subsequently allowing to model the varying properties with random fields. Simulations of dog-bone specimens show that the probability distributions of material properties are captured well. Also simulations of lattice structures are able to represent the probability distributions of their homogenized mechanical properties. The whole stress–strain response and the failure progression agree well with experimental results.Publicationtype: Journal ArticleScopus© Citations 9 221 910 - Some of the metrics are blocked by yourconsent settings
Item type:Publication, Access status: with files , An empirical study on stress-based fail-safe topology optimization and multiple load path designExplicitly considering fail-safety within design optimization is computationally very expensive, since every possible failure has to be considered. This requires solving one finite element model per failure and iteration. In topology optimization, one cannot identify potentially failing structural members at the beginning of the optimization. Hence, a generic failure shape is applied to every possible location inside the design domain. In the current paper, the maximum stress is considered as optimization objective to be minimized, since failure is typically driven by the occurring stresses and thus of more practical relevance than the compliance. Due to the local nature of stresses, it is presumed that the optimization is more sensitive to the choice of the failure shape than compliance-based optimization. Therefore, various failure shapes, sizes and different numbers of failure cases are investigated and compared on the basis of a general load-path-based evaluation scheme. Instead of explicitly considering fail-safety, redundant structures are obtained at much less computational cost by controlling the maximum length scale. A common and easy to implement maximum length scale approach is employed and fail-safe properties are determined and compared against the explicit fail-safe approach.Publicationtype: Journal ArticleScopus© Citations 17 167 335 - Some of the metrics are blocked by yourconsent settings
Item type:Publication, Access status: with files , Reciprocal first-order second-moment method(2021-05); This paper shows a simple parameter substitution, which makes use of the reciprocal relation of typical objective functions with typical random parameters. Thereby, the accuracy of first-order probabilistic analysis improves significantly at almost no additional computational cost. The parameter substitution requires a transformation of the stochastic distribution of the substituted parameter, which is explained for different cases.Publicationtype: Preprint83 12 - Some of the metrics are blocked by yourconsent settings
Item type:Publication, Access status: without files , Inverse homogenization using isogeometric shape optimization(2020-08-15); ; Finding periodic microstructures with optimal elastic properties is usually tackled by a highly resolved, regular finite element model and solid isotropic material penalization. This procedure not only has many advantages, but also requires a comparably high computational effort and challenges in representing stresses accurately. Therefore, an isogeometric shape optimization approach is applied to the inverse homogenization problem and combined with a reconstruction procedure for nearly optimal rank-3 laminates, which provides an efficient solution strategy with more accurate stress modelling. This allows to investigate the sensitivity of optimized microstructures in terms of stress concentrations.Publicationtype: Journal Article124 - Some of the metrics are blocked by yourconsent settings
Item type:Publication, Access status: without files , On the application of IGA to the inverse homogenization problem(2019-09); ; Publicationtype: Conference Presentation54 - Some of the metrics are blocked by yourconsent settings
Item type:Publication, Access status: with files , Robust compliance topology optimization using the first-order second-moment methodA robust topology optimization approach is presented which uses the probabilistic first-order second-moment method for the estimation of mean value and variance of the compliance. The considered sources of uncertainty are the applied load, the spatially varying Young’s modulus, and the geometry with focus on the latter two. In difference to similar existing approaches for robust topology optimization, the presented approach requires only one solution of an adjoint system to determine the derivatives of the variance, which keeps the computation time close to the deterministic optimization. For validation, also the second-order fourth-moment method and Monte Carlo simulations are embedded into the optimization. For all approaches, the applicability and impact on the resulting design are demonstrated by application to benchmark examples. For random load, the first-order second-moment approach provides unsatisfying results. For random, Young’s modulus and geometry, however, the robust topology optimization using first-order second-moment approach provides robust designs at very little computational cost.Publicationtype: Journal ArticleScopus© Citations 31 270 1035 - Some of the metrics are blocked by yourconsent settings
Item type:Publication, Access status: with files , Fail-safe optimization of beam structuresIn the current work, a fail-safe optimization of beam structures is carried out. This approach may provide an insight into the robustness of lattice structures. The use of beam elements allows a commonly used engineering approach for obtaining a fail-safe design to be applied. This consists of removing one beam element at a time and optimizing the remaining structure. At the end of the process, the maximum beam radii are used for the final design. This approach is computationally extremely expensive for lattice structures, as it requires one optimization per removed beam. In our contribution, we show that the design obtained from this approach does not actually achieve the desired fail-safe behaviour. We therefore apply a multi-model approach in which the fail-safe requirement is an optimization constraint. This is still computationally demanding and therefore, methods for reducing the number of failure cases to be considered within the optimization are discussed. Furthermore, the p-norm is applied to the stress constraints to reduce the computational effort for the gradient calculation. Reduction of failure cases and use of the p-norm have opposite effects on the conservatism of the result and therefore compensate each other to some extent.Publicationtype: Journal ArticleScopus© Citations 30 346 377 - Some of the metrics are blocked by yourconsent settings
Item type:Publication, Access status: without files , Optimization of fail-safe lattice structuresIn the current work, a fail-safe optimization of lattice structures is carried out. For the optimization, unit cells are not homogenized, but their members are modeled as beam elements. This allows applying a commonly used engineering approach for obtaining a fail-safe design. It consist of removing one beam element at a time and optimizing the remaining structure. At the end, the maximum beam radii are used for the final design. This approach is computationally extremely expensive for lattice structures, as it requires one optimization per removed beam. In our contribution, we show that the design obtained from this approach actually does not fulfill the desired fail-safe behavior. We therefore apply an alternative approach in which the fail-safe requirement is an optimization constraint. This is still computationally demanding and therefore, criteria are discussion for reducing the number of beam elements to be considered for the fail-safe requirement within the optimization.Publicationtype: Conference Paper48 - Some of the metrics are blocked by yourconsent settings
Item type:Publication, Access status: without files , Shape optimization of topologically optimized structures using NURBS(2016-10); Topology optimization using the solid isotropic material penalization method provides a density distribution, which contains elements with intermediate densities between void and solid. A discrete design is obtained by some geometric interpretation of this result, which is often determined manually. Afterwards, the design is sized with respect to stress, sometimes in the framework of a shape optimization. The current work provides a fully automated routine to obtain a geometric interpretation and parameterization of two dimensional topology optimized structures using non-uniform rational Bezier splines (NURBS), and a shape optimization of the parameterized structure afterwards. Automating both steps reduces development time and cost, and allows embedding them into a larger optimization framework (e.g., multidisciplinary or robustness optimization).Publicationtype: Conference Paper126