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Der vorliegende Beitrag zeigt die Ergebnisse einer experimentellen Studie, in der für 22 Kreiszylinderschalen die Traglast unter kombinierter Axialdruck- und Biegebelastung ermittelt wurde. Während die Beullast unter reinem Axialdruck bekanntermaßen stark streut, kann sich diese Streuung mit zunehmender Biegebeanspruchung verändern. Für den Vergleich werden die Ergebnisse aus Last und Moment zu einem normierten Lastfaktor zusammengefasst und als Zufallsfeld betrachtet., Deutsche Forschungsgemeinschaft (DFG)

In this paper, the general framework for contact-constrained topology optimization of Strömberg and Klarbring (2010) is extended to robust topology optimization. In doing so, a linear elastic design domain is considered and the augmented Lagrangian approach is used to model the unilateral contact. For topology optimization, the design space is parametrized with the SIMP-approach and the Sigmund’s filter is applied. Additionally, the robust framework considers uncertainties at the contact support such as deviations of the geometry of the contact surface and the friction coefficient. Both uncertainties are described by the first-order second-moment method which leads to minimal additional costs. In fact, only two additional linear equations must be solved to obtain the robust objective and its gradient with respect to the design variables. Having both the objective and the gradient, the design update is computed with the method of moving asymptotes. The robust framework is applied to 2D and 3D examples to prove its scalability for real-world applications.

This paper presents a method to consider uncertainties in the distortion prediction of additive manufacturing processes within robust topology optimization. The random variable of the stochastic additive manufacturing process is the inherent thermomechanical strain, typically determined by process characterization experiments. The value of the inherent strain per se encompasses uncertainty due to differences between characterization and production geometries, uncontrolled process variations, hatching pattern choices, and other effects not captured in layer-by-layer part-scale additive manufacturing simulation. These effects can be represented by different inherent strains for each realized layer, therefore, model the variability in part distortion. Instead of employing a more detailed simulation approach, requiring significantly more process data and computation time, our method aims at generating a robust design in this setting, to obtain parts exhibiting reduced distortion regardless of uncertainties in distortion prediction. The formulation benefits from the superposition potential within the employed process simulation. For robust optimization, the expected part distortion and its estimated variance are included in the standard density-based topology optimization algorithm's objective function. The effectiveness of the approach is demonstrated by simultaneously optimizing structural performance combined with a minimized additive manufacturing part distortion under uncertain process conditions., Computational Design and Mechanics

A semi-intrusive approach for robust design optimization is presented. The stochastic moments of the objective function and constraints are estimated using a Taylor series-based approach, which requires derivatives with respect to design variables, random variables as well as mixed derivatives. The required derivatives with respect to design variables are determined using the intrusive adjoint method available in commercial software. The partial derivatives with respect to random parameters as well as the mixed second derivatives are approximated non-intrusively using finite differences. The presented approach provides a semi-intrusive procedure for robust design optimization at reasonable computational cost while allowing an arbitrary choice of random parameters. The approach is implemented as an add-on for commercial software. The method and its limitations are demonstrated by academic test cases and industrial applications., Behörde für Wissenschaft, Forschung und Gleichstellung

Die Strukturoptimierung ist ein zunehmend wichtiger Bestandteil der Produktentwicklung geworden, vor allem in der Luft- und Raumfahrt, wo sich Gewichtseinsparungen durch Leichtbau besonders stark auf die Effizienz und damit auf die Wirtschaftlichkeit und Umweltverträglichkeit auswirken. Ein Gebiet der Strukturoptimierung ist die Topologieoptimierung, die maximale Gestaltungsfreiheit bietet und damit die größten Verbesserungen ermöglicht. Lastangepasste Entwürfe aus einer Topologieoptimierung sind allerdings in der Regel sehr empfindlich gegenüber einem unvorhersehbaren lokalen Steifigkeitsverlust, etwa durch zufällig auftretende Schäden an einzelnen Lastpfaden der Struktur. Diese Entwürfe gelten daher nicht als ausfallsicher. In dieser Arbeit wird ein zweistufiges Verfahren zur dichtebasierten Optimierung von ausfallsicheren Bauteilen vorgestellt. Bestehende Methoden sind entweder extrem rechenintensiv oder berücksichtigen die Anforderungen an die Ausfallsicherheit nicht explizit in der Optimierung. Der vorgestellte Ansatz stellt einen Kompromiss zwischen beiden Vorgehensweisen dar, indem er mit Hilfe einer zweistufigen Optimierung redundante Entwürfe liefert, die robust gegenüber dem Ausfall einzelner Lastpfade sind. In der ersten Stufe wird eine Topologieoptimierung mit lokalen Volumennebenbedingungen durchgeführt. Die zweite Stufe wird als "dichtebasierte Formoptimierung" bezeichnet, da sie nur die Umrisse der Struktur verändert, die weiterhin durch Pseudodichten in einem voxelartigen Finite-Elemente-Netz beschrieben ist. Die erzielbaren Verbesserungen und der damit verbundene Rechenaufwand durch Anwendung der vorgeschlagenen Methode werden anhand verschiedener 2D- und 3D-Beispiele demonstriert. Die Ergebnisse zeigen, dass die vorgestellte Methode im Gegensatz zu bestehenden Methoden mit expliziter Berücksichtigung von Ausfallsicherheit in der Topologieoptimierung mit vertretbarem Rechenaufwand durchgeführt werden kann. Für die gezeigten 2D-Beispiele verringert s, Structural optimization has become an increasingly important part of product development, especially in the aerospace industry, where weight savings due to lightweight design have a particularly strong impact on efficiency and thus economy and environmental compatibility. One area of structural optimization is topology optimization, which offers maximum design freedom and thus enables the greatest improvements. However, load-adapted designs obtained by topology optimization are usually highly sensitive to an unpredictable local loss of stiffness, like e.g. for the case of randomly inflicted damage to individual load paths of the structure. Therefore, these designs are not considered fail-safe. This thesis presents a two-stage procedure for density-based optimization towards a fail-safe design. Existing approaches are either computationally extremely expensive or do not explicitly consider fail-safe requirements in the optimization. The presented method trades off both aspects by employing a two-stage optimization approach to provide redundant designs that offer robustness to the failure of single load paths. In the first stage, a topology optimization with local volume constraints is performed. The second stage is referred to as "density-based shape optimization" since it only alters the outline of the structure while still acting on a fixed voxel-type finite element mesh with pseudo-densities assigned to each element. The performance gain and computational efficiency of the proposed method are demonstrated by application to various 2D and 3D examples. The results show, that the presented method can be carried out with reasonable computational effort, in contrast to existing approaches with explicit consideration of fail-safety in topology optimization. For the 2D examples considered, the number of analyses for a fail-safe optimization is reduced by three orders of magnitude compared to existing methods and is at most 5.6 times higher than for a standard topology op