Florian Geiger

Abstract

Form-finding is an essential task in the design of efficient lightweight structures. It is based on the crucial assumption of one single shape-determining load case, usually represented by self-weight. Adaptive components integrated into the structure open a way to even more efficient lightweight designs, as such structures can adapt their shapes to varying external loads and redistribute internal forces. This article presents a method for form-finding of adaptive truss structures subject to multiple, independently acting load cases, also incorporating possible design constraints. To ensure the consistency of the manufacturing lengths of passive elements in all load cases, special constraints are considered. The method enables to reduce sensitivity of the structural shape with respect to various different loads by means of actuation to meet design and serviceability requirements with a lower structural mass compared to conventional design strategies. This is demonstrated within a replaced real-world-like setting of an adaptive suspension truss bridge.

Abstract

We present a comprehensive study on the approximation power of NURBS and the significance of exact geometry in stability analyses of shells. Pre-buckling analyses are carried out to estimate the critical load levels and the initial buckling patterns. Various finite element solutions obtained with the commercial code ANSYS are compared with solutions from the isogeometric version of the finite element method, using our in-house code NumPro. In some problem setups, the isogeometric shell elements provide superior accuracy compared to standard (as opposed to isogeometric) shell finite elements, requiring only a fractional amount of degrees of freedom for the same level of accuracy. The present study systematically investigates the sources of this superior accuracy of the isogeometric approach. In particular, hypotheses are tested concerning the influence of exact geometry and smoothness of splines.

Abstract

The design of adaptive structures is one method to improve sustainability of buildings. Adaptive structures are able to adapt to different loading and environmental conditions or to changing requirements by either small or large shape changes. In the latter case, also the mechanics and properties of the deformation process play a role for the structure’s energy efficiency. The method of variational motion design, previously developed in the group of the authors, allows to identify deformation paths between two given geometrical configurations that are optimal with respect to a defined quality function. In a preliminary, academic setting this method assumes that every single degree of freedom is accessible to arbitrary external actuation forces that realize the optimized motion. These (nodal) forces can be recovered a posteriori. The present contribution deals with an extension of the method of motion design by the constraint that the motion is to be realized by a predefined set of actuation forces. These can be either external forces or prescribed length chances of discrete, internal actuator elements. As an additional constraint, static stability of each intermediate configuration during the motion is taken into account. It can be accomplished by enforcing a positive determinant of the stiffness matrix.

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.

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.

Abstract

Adaptive structures in civil engineering are mechanical structures with the ability to modify their response to external loads. Actuators strongly affect a structure’s adaptivity and have to be placed thoughtfully in the design process to effectively compensate external loads. For constant loads, this property is introduced as steadystate disturbance compensability. This property can be linked to concepts from structural engineering such as redundancy or statical indeterminacy, thus representing an interdisciplinary approach. Based on the disturbance compensability matrix, a scalar performance metric is derived as quantitative measure of a structure’s ability to compensate the output error for arbitrary constant disturbances with a given set of actuators. By minimizing this metric, an actuator configuration is determined. The concept is applied to an example of a truss structure.

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.

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.

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.

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.

Abstract

Die Ermittlung von Gleichgewichtspfaden stabilitätsgefährdeter Strukturen im nachkritischen Bereich ist ein bis heute nicht vollständig gelöstes Problem. Es existieren verschiedene Möglichkeiten, die in dieser Arbeit ausführlich vorgestellt und verglichen werden. Mit kommerziellen Codes ermittelte Pfade werden mit den Pfaden aus dem am Institut für Baustatik und Baudynamik der Universität Stuttgart entwickelten Programm NumPro verglichen. Es werden dabei die in NumPro implementierten fortgeschrittenen Methoden vorgestellt und deren Funktionsweise erläutert. Zudem werden im Zuge der Arbeit implementierte Änderungen vorgestellt. Die erhaltenen Pfade werden durch dynamische Rechnungen verifiziert.

Abstract

Das Verständnis von statisch unbestimmte Tragwerke und Tragwerksteile ist bei der Erstellung von sicheren und effizienten Bauwerken unabdingbar. Die Lehre im Bachelorstudiengang Bauingenieurwesen beschäftigt sich hauptsächlich mit der numerischen Berechnung solcher Tragwerke, nicht aber mit dem Verständnis des Tragverhaltens. Diese Arbeit befasst sich mit der Erstellung eines Programms, das auf der Homepage des Instituts für Baustatik und Baudynamik zur Verfügung gestellt werden soll. Das Tool soll einen "spielerischen" Zugang zum Verständnis von statisch unbestimmtem Tragverhalten schaffen. Zuerst werden in der Arbeit die nötigen mechanischen und technischen Grundlagen von statisch unbestimmtem Tragverhalten, der direkten Steifigkeitsmethode und der verwendeten Software Matlab vorgestellt. Daraufhin werden Aufbau und Ablauf des Programms erläutert, Benutzunghinweise gegeben und anschließend werden die implementierten Beispiele vorgestellt. Im Rahmen der Beispiele sollen verschiedene Teilbereiche aufgezeigt werden, in denen statische Bestimmtheit eine große Rolle spielt: Tragverhalten in Abhängigkeit von Steifigkeitsverhältnissen und Zwangskräften aus erzwungenen Verformungen z.B. Temperaturbelastung und Stützensenkung.

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.