Gade, J. (2024).
Distributed redundancy in elastostatics for the design of adaptive structures. Doktorarbeit, Bericht Nr. 78. Institut für Baustatik und Baudynamik der Universität Stuttgart.
https://doi.org/10.18419/opus-15141 Abstract
The present thesis is concerned with the concept of distributed redundancy in linear elastostatics of load-carrying structures. This concept addresses supernumerous self-equilibrating force states in a statically indeterminate structure activated by internal constraint due to geometric compatibility. The redundancy distribution in a truss or frame system can be considered for investigations on failure safety. A continuum-mechanical theory on distributed redundancy for statically determinate structural theories is presented. Here, the redundancy relation appears as an integral equation with a special influence function as integral kernel. From this influence function, the redundancy density function can be derived. Furthermore, the concept of distributed redundancy is introduced for finite element models. The redundancy matrix inherently appears in a hybrid-mixed displacement-stress formulation based on the Hellinger-Reissner variational principle. Moreover, the redundancy concept reflects the elastic response of a structural system due to prescribed inelastic strain quantities such as temperature loads or actuation. This reflection allows for the application of the concept for analysis and design of adaptive structures. A deeper understanding of the redundancy distribution and space of self-stress states based on the redundancy matrix can be employed for redistribution of forces and adaptation of displacements in adaptive trusses. As design aspects for adaptive trusses, two methods for load-case-independent actuator placement are described. Formulations for compensation of displacements or forces or a combination of both are presented. Finally, a novel formulation of displacement control minimizing the actuation work is developed. Its application in an exemplary adaptive truss bridge system shows significant potential for reducing actuation work compared to a conventional displacement control.BibTeX
Krauß, L.-M., Maierhofer, M., Prokosch, T., Trautwein, A., von Scheven, M., Menges, A., & Bischoff, M. (2024). Baustatische Methoden für Entwurf, Auslegung und Betrieb adaptiver Tragwerke. In B. Oesterle, A. Bögle, W. Weber, & L. Striefler (Eds.),
Berichte der Fachtagung Baustatik – Baupraxis 15, 04. und 05. März 2024, Hamburg (pp. 101--108).
https://doi.org/10.15480/882.9247 Abstract
Mit strukturmechanischer Einsicht und der Formulierung von Aktuierungszielen lassen sich Grundsätze für den Entwurf guter adaptiver Tragwerke sowie deren Auslegung ableiten. Dabei kann zwischen einer Adaption zur Reduktion der Verformungen und einer Adaption zur Manipulation der Kräfte im Tragwerk unterschieden werden. Durch den Einsatz von Aktoren zur Kraftmanipulation ist es möglich, die maximale Querschnittsausnutzung in der Struktur bei verschiedenen Belastungen zu reduzieren. Der jeweils optimale Aktuierungszustand ist derjenige, der die maximale Ausnutzung im Tragwerk minimiert. Mithilfe baustatischer Überlegungen kann diese Optimierungsaufgabe durch ein lineares Optimierungsproblem beschrieben und das globale Minimum mit dem Simplex-Algorithmus gefunden werden.BibTeX
Krauß, L.-M., von Scheven, M., & Bischoff, M. (2023). Combining the redundancy concept and vibration control for actuator placement in adaptive structures.
X ECCOMAS Thematic Conference on Smart Structures and Materials, SMART 2023, Patras, Greece.
https://doi.org/10.7712/150123.9826.444394 Abstract
Actuators can be used to control the dynamic behavior of vibrating structures. The placement of the actuators in the system has a significant impact on how well adaptive
structures perform. The actuator placement for damping particular modes can be assessed using the fraction of modal strain energy. Recent research in structural engineering has demonstrated that the redundancy concept is a useful tool for assessing actuator placement for quasi-static structural behavior because it provides information about the distribution of the degree of statical indeterminacy in the structure. In order to combine fundamental measures from control theory and structural engineering, the similarities between the frequency response function and the redundancy matrix are pointed out. It is shown that, by using the redundancy concept
and the fraction of modal strain energy as assessment criteria for actuator placement, adaptive structures can be optimally designed to withstand both static and dynamic loadings.BibTeX
Trautwein, A., Prokosch, T., Senatore, G., Blandini, L., & Bischoff, M. (2023). Analytical and numerical case studies on tailoring stiffness for the design of structures with displacement control.
Frontiers in Built Environment,
9.
https://doi.org/10.3389/fbuil.2023.1135117 Abstract
This paper discusses the role that structural stiffness plays in the context of designing adaptive structures. The focus is on load-bearing structures with adaptive displacement control. A design methodology is implemented to minimize the control effort by making the structure as stiff as possible against external loads and as flexible as possible against the effect of actuation. This rationale is tested using simple analytical and numerical case studies.BibTeX
Geiger, F. (2022).
Strukturmechanische Charakterisierung von Stabtragwerken für den Entwurf adaptiver Tragwerke. Doktorarbeit, Bericht Nr. 74. Institut für Baustatik und Baudynamik der Universität Stuttgart.
https://doi.org/10.18419/opus-12299 Abstract
Diese Arbeit beschäftigt sich mit der strukturmechanischen Charakterisierung von Stabtragwerken mit dem Ziel, daraus Erkenntnisse und Empfehlungen für den Entwurf adaptiver Tragwerke zu gewinnen und abzuleiten. Hierfür werden wesentliche lastfall-abhängige und lastfallunabhängige Tragwerkseigenschaften betrachtet und deren Zusammenhang mit der Performanz und dem Potential adaptiver Tragwerke analysiert. Der im Rahmen dieser Arbeit betrachtete Entwurf von adaptiven Tragwerken beschreibt dabei sowohl den gesamten Entwurfsprozess, einschließlich beispielsweise des Aufbaus und der Dimensionierung von Tragwerken, als auch den Entwurf eines Aktuierungs-konzepts für bereits bestehende Tragwerke, die nachträglich verbessert bzw. ertüchtigt werden sollen. Neben einem ausführlichen Überblick über die in der Literatur beschriebenen Verfahren und Erkenntnisse werden verschiedene Varianten für die Modellierung der Aktuierung betrachtet, die Auswirkungen der Aktuierung auf den Tragwerkszustand detailliert analysiert und Verfahren zur automatisierten Platzierung von Aktoren im Tragwerk diskutiert. Anschließend werden in einer systematischen Studie die Auswirkungen der Aktuierung auf den Tragwerkszustand und die damit erreichbaren Ziele quantifiziert. Dazu werden die Einflüsse verschiedener Parameter, wie z. B. die Anzahl an Aktoren, der Grad der statischen Unbestimmtheit und das globale Tragverhalten, untersucht. Die dabei gewonnen Erkenntnisse werden abschließend zusammengefasst und können für den Entwurf adaptiver Tragwerke herangezogen werden.BibTeX
Krake, T., von Scheven, M., Gade, J., Abdelaal, M., Weiskopf, D., & Bischoff, M. (2022). Efficient Update of Redundancy Matrices for Truss and Frame Structures.
Journal of Theoretical, Computational and Applied Mechanics.
https://doi.org/10.46298/jtcam.9615 Abstract
Redundancy matrices provide insights into the load carrying behavior of statically indeterminate structures. This information can be employed for the design and analysis of structures with regard to certain objectives, for example reliability, robustness, or adaptability. In this context, the structure is often iteratively examined with the help of slight adjustments. However, this procedure generally requires a high computational effort for the recalculation of the redundancy matrix due to the necessity of costly matrix operations. This paper addresses this problem by providing generic algebraic formulations for efficiently updating the redundancy matrix (and related matrices). The formulations include various modifications like adding, removing, and exchanging elements and are applicable to truss and frame structures. With several examples, we demonstrate the interaction between the formulas and their mechanical interpretation. Finally, a performance test for a scaleable structure is presented.BibTeX
Böhm, M., Steffen, S., Gade, J., Geiger, F., Sobek, W., Bischoff, M., & Sawodny, O. (2020). Modellierung aktiver Strukturelemente als Erweiterung zum klassischen Workflow der FE-Analyse.
Manfred Bischoff, Malte von Scheven, Bastian Oesterle (Hrsg.) Berichte der Fachtagung Baustatik – Baupraxis 14, 23. und 24. März 2020, Universität Stuttgart.
https://doi.org/10.18419/opus-10762 BibTeX
Böhm, M., Wagner, J., Steffen, S., Gade, J., Geiger, F., Sobek, W., Bischoff, M., & Sawodny, O. (2020). Input modeling for active structural elements – extending the established FE-Workflow for modeling of adaptive structures.
IEEE/ASME International Conference on Advanced Intelligent Mechatronics (AIM), 1595--1600.
https://doi.org/10.1109/AIM43001.2020.9158996 BibTeX
Geiger, F., Gade, J., von Scheven, M., & Bischoff, M. (2020). A Case Study on Design and Optimization of Adaptive Civil Structures.
Frontiers in Built Environment,
6, 94.
https://doi.org/10.3389/fbuil.2020.00094 Abstract
Taking advantage of adaptivity in the field of civil engineering is a subject of ongoing research. Integration of adaptive elements in load-bearing structures is already well-established in many other engineering fields, albeit mostly for different purposes than withstanding predominantly static loads. Initial investigations have demonstrated potential for substantial material and energy savings also in the field of civil engineering, especially for high-rise buildings and wide-span structures, such as roofs or bridges. Adaptive civil structures show promise in tackling current challenges arising from emissions and shortages of materials. In this study, we compare the possible minimum-weight designs for different actuator placement approaches and for different structural topologies that satisfy various constraints for high-rise buildings. We use case studies as illustrative examples to show which advantages and disadvantages can be expected from a specific design. The overarching aim is to learn how truss and beam structures should be designed to perform well as adaptive structures.BibTeX
Geiger, F., Gade, J., von Scheven, M., & Bischoff, M. (2020). Optimal Design of Adaptive Structures vs. Optimal Adaption of Structural Design.
IFAC-PapersOnLine,
53(2), 8363--8369.
https://doi.org/10.1016/j.ifacol.2020.12.1604 Abstract
Taking advantage of adaptivity in the field of civil engineering is an ongoing research topic. Integration of adaptive elements in the load-bearing structure is already well established in many other engineering fields. First investigations promise large material saving potentials also in the field of civil engineering, especially when it comes to high-rise buildings or wide spanned structures like roofs or bridges. In times of emission problems and shortage of materials, the potentials of adaptive civil structures open various new possibilities.
In the design and optimization process of adaptive civil structures, we address the differences between classical approaches for passive systems and new practices considering adaptivity. By using a suitable actuator placement, it is possible to manipulate the displacements of the structure as well as the force distribution within the structure. Both material and energy savings can be accomplished with an integrated design of the adaptive structure taking into account the actuation, suitable combination of structural design and actuator placement. For demonstration of the differences in the design process and in the resulting optimized structure, we use a small case study on a truss structure, which is inspired by a high-rise building, and consider static loads.BibTeX
Geiger, F., Gade, J., von Scheven, M., & Bischoff, M. (2020). Anwendung der Redundanzmatrix bei der Bewertung adaptiver Strukturen.
Manfred Bischoff, Malte von Scheven, Bastian Oesterle (Hrsg.) Berichte der Fachtagung Baustatik – Baupraxis 14, 23. und 24. März 2020, Universität Stuttgart, 119–128.
https://doi.org/10.18419/opus-10762 Abstract
Die Antwort einer Struktur auf Aktuierung wird maßgeblich vom Grad der statischen Unbestimmtheit und deren Verteilung in der Struktur beeinflusst. Die Redundanzmatrix enthält diese Informationen über das Tragwerk. Aus ihr können daher Rückschlüsse für die Aktorplatzierung und für die Bewertung der Aktuierbarkeit von Strukturen gezogen werden. Die Untersuchung eines Beispieltragwerks veranschaulicht einerseits die Einsatzmöglichkeiten der Redundanzmatrix und andererseits das Masseneinsparungspotential, das mithilfe des Einsatzes aktiver Elemente in passiven Strukturen erschlossen werden kann.BibTeX
Fröhlich, B., Gade, J., Geiger, F., Bischoff, M., & Eberhard, P. (2019). Geometric element parameterization and parametric model order reduction in finite element based shape optimization.
Computational Mechanics,
63, 853–868.
https://doi.org/10.1007/s00466-018-1626-1 Abstract
This contribution proposes a new approach to derive geometrically parameterized, reduced order finite element models. An element formulation for geometrically parameterized finite elements is suggested. The parameterized elements are used to derive models with a parameterized geometry where the parameterized system matrices are expressed in an affine representa- tion. Parametric model order reduction can then be efficiently used to reduce the full order parameterized model to a reduced order parameterized model. The approach shows two beneficial features. First, design studies and shape optimizations can be conducted with parameterized reduced order model of much lower dimension compared to the parameterized, full order model. Second, it is possible to compute sensitivities analytically, and therefore, to avoid the computation of finite differences gradients. The approach is illustrated with two numerical examples. The first example includes a detailed error analysis. The second example is a shape optimization example of an adaptive structure.BibTeX
Fröhlich, B., Geiger, F., Gade, J., Bischoff, M., & Eberhard, P. (2018). Model order reduction of coupled, parameterized elastic bodies for shape optimization.
IUTAM Symposium on Model Order Reduction of Coupled Systems, May 22–25, 2018, Stuttgart, 151--163.
https://doi.org/10.1007/978-3-030-21013-7_11 Abstract
In this contribution, coupled, parameterized second order systems are considered where the coupled, parameterized system is derived from the assembly of several parameterized component models. Two approaches for the Parametric Model Order Reduction of such coupled systems are presented and compared in a reduced order shape optimization example. In the first approach, the coupled, parameterized system is derived by coupling the parameterized, full order component models. Then, Parametric Model Order Reduction is executed for the coupled system. In the second approach, the parameterized, component models are first reduced independently of their actual mounting situation. Afterwards, the parameterized, reduced order component models are coupled to derive the parameterized, reduced order system model. It is shown that the first approach yields smaller parameterized, reduced order system models. However, the second approach allows to reuse and to recombine the parameterized, reduced order component models arbitrarily. It therefore introduces more flexibility in the modeling process, enabling for example a toolbox based optimization with parameterized, reduced order models.BibTeX
Weidner, S., Kelleter, C., Sternberg, P., Haase, W., Geiger, F., Burghardt, T., Honold, C., Wagner, J., Böhm, M., Bischoff, M., Sawodny, O., & Binz, H. (2018). The implementation of adaptive elements into an experimental high-rise building.
Steel Construction,
11, 109–117.
https://doi.org/10.1002/stco.201810019 Abstract
In 2017, the University of Stuttgart started a Collaborative Research Centre with the title Adaptive Skins and Structures for the Built Environment of Tomorrow. The goal of this research project is to find an answer to today’s most urgent social and ecological questions as the global population continuously increases and the available resources remain limited. As the central approach to the solution of this problem, adaptive elements will be included in the structure, the interior and the façade of an experimental 37 m tall building. This paper introduces the topic of adaptivity in building structures and provides an overview of the research topics applied in this globally unique adaptive high-rise building. Due to the complexity of research topics of this Collaborative Research Centre, this paper only covers the research concerning the experimental high-rise building.BibTeX
