Veröffentlichungen

Zusammenfassung

Within the framework of plane strain nonlinear elasticity, we present a discussion on the stability properties of various Enhanced Assumed Strain (EAS) finite element formulations with respect to physical and artificial (hourglassing) instabilities. By means of a linearized buckling analysis we analyze the influence of element formulations on the geometric stiffness and provide new mechanical insights into the hourglassing phenomenon. Based on these findings, a simple strategy to avoid hourglassing for compression problems is proposed. It is based on a modification of the discrete Green-Lagrange strain, simple to implement and generally applicable. The stabilization concept is tested for various popular element formulations (namely EAS elements and the assumed stress element by Pian and Sumihara). A further aspect of the present contribution is a discussion on proper benchmarking of finite elements in the context of hourglassing. We propose a simple bifurcation problem for which analytical solutions are readily available in the literature. It is tailored for an in-depth stability analysis of finite elements and allows a reliable assessment of its stability properties.

Zusammenfassung

In structural optimization processes, a common goal is to limit deflectionsor stresses through topological changes, shape adaption or cross-sectional adjust-ments. Beyond these well-established performance indicators, alternative measuresfor the assessment of structures based on the redundancy matrix can be used in thedesign and optimization process. This contribution shows the extension of the redun-dancy calculation to three-dimensional beam structures in detail. Using the conceptof redundancy for the design of structures, one goal is to homogeneously distributeredundancy within a structure in order to make an overall collapse due to failure ofindividual elements less likely. Furthermore, the sensitivity towards imperfections isquantified by the redundancy matrix, offering the opportunity to design connectionsof substructures, such that no constraint forces are introduced during the assemblyprocess. Those two concepts are showcased exemplarily within this contribution. Themethod is embedded into a computational co-design framework, which allows forquick, interactive feedback on design changes to strengthen the interplay between thedesign and engineering process.

Zusammenfassung

The linear design workflow for structural systems, involving a multitude of iterative loops and specialists, obstructs disruptive innovations. During design iterations, vast amounts of data in different reference systems, origins, and significance are generated. This data is often not directly comparable or is not collected at all, which implies a great unused potential for advancements in the process. In this paper, a novel workflow to process and analyze the data sets in a unified reference frame is proposed. From this, differently sophisticated iteration loops can be derived. The developed methods are presented within a case study using coreless filament winding as an exemplary fabrication process within an architectural context. This additive manufacturing process, using fiber-reinforced plastics, exhibits great potential for efficient structures when its intrinsic parameter variations can be minimized. The presented method aims to make data sets comparable by identifying the steps each data set needs to undergo (acquisition, pre-processing, mapping, post-processing, analysis, and evaluation). These processes are imperative to provide the means to find domain interrelations, which in the future can provide quantitative results that will help to inform the design process, making it more reliable, and allowing for the reduction of safety factors. The results of the case study demonstrate the data set processes, proving the necessity of these methods for the comprehensive inter-domain data comparison.

Zusammenfassung

In this thesis an implementation for Isogeometric Analysis (IGA) with trimmed NURBS- and B-spline surfaces is presented. IGA is characterised by the use of the same shape functions, that exactly describe the geometry, to approximate the searched-for variables and not the other way around, as it is common in Finite Element Analysis. Since IGA was first introduced to the public in 2005, there has been hope, that by not requiring a meshing process to obtain a finite element mesh, to realise a more direct integration of design and analysis processes. One of the main problems is that in many computer-aided engineering (CAE) processes, socalled trimming is used to obtain the geometries that are required. This can be, for example, the consideration of boreholes for the attachment of other components or the cutting away of corners in a steel sheet. One possibility to handle trimmed surfaces in IGA is to determine numerical integration schemes that integrate only over the remaining part of each element. In the presented implementation, this is realised by locally approximating the geometry by triangles. In this thesis, the theoretical basics are given to understand the difficulty, that trimmed surfaces pose to IGA, followed by an overview of the implementation details of the code. At last, the implementation is tested against two examples to show the quality of results, that can be expected. For both examples, a satisfactory convergence behaviour could be shown, with special attention also given to differences between element formulations, strategies for the geometry approximation and the continuity of the shape functions.

Zusammenfassung

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.

Zusammenfassung

We investigate the variational formulation and corresponding minimizing energies for the detection of energetically favorable magnetization states of thin cylindrical magnetic nanodots. Opposed to frequently used heuristic procedures found in the literature, we revisit the underlying governing equations and construct a rigorous variational approach that takes both exchange and demagnetization energy into account. Based on a combination of Ritz’s method and a Fourier series expansion of the solution field, we are able to pinpoint the precision of solutions, which are given by vortex modes or single-domain states, down to an arbitrary degree of precision. Furthermore, our model allows to derive an expression for the demagnetization energy in closed form for the in-plane single-domain state, which we compare to results from the literature. A key outcome of the present investigation is an accurate phase diagram, within the problem class of constant magnetization through the thickness and rotational symmetry, which we obtain by comparing the vortex mode’s energy minimizers with those of the single-domain states. This phase diagram is validated with data of two- and three-dimensional models from literature. By means of the phase diagram, we particularly find the critical radius at which the vortex mode becomes unfavorable with machine precision. All relevant data and codes related to the present contribution are available at Müller (2023).

Zusammenfassung

Structural failure in civil engineering can have catastrophic consequences such as property damage, economic losses and even loss of life. Therefore, early detection and identification are crucial. In addition to that, new technologies like adaptive structures demand for high safety as a prerequisite to gain acceptance. This contributio investigates the feasibility of using the redundancy matrix as a tool for detecting and identifying structural failure in adaptive structures via residual generation. Results provide prerequisites for detectability and suggest methodologies for the detection of structural failure by means of the redundancy matrix.

Zusammenfassung

Floor systems are typically designed to satisfy tight deflection limits under out-of-plane loading. Although the use of concrete flat slabs is common in the built environment due to the ease of construction, the load-bearing performance is inefficient because the material is not optimally distributed within the cross section to take the bending caused by external loads. This typically results in significant oversizing. Floor slabs account for more than 50% of the material mass and associated emissions embodied in typical low-rise reinforced concrete buildings. In addition, the volume of carbon-intensive cement production has tripled in the last three decades. Therefore, lightweight floor systems that use minimum material resources causing low emissions can have a significant impact on reducing adverse environmental impacts of new constructions. Recent work has shown that rib-stiffened slabs offer significant potential for material savings compared with flat slabs. This work investigates adaptive rib-stiffened slabs equipped with an adaptive tensioning system. The adaptive tensioning system comprises cables embedded within the concrete rib through a duct that enables varying the cable tension as required to counteract the effect of different loading conditions without applying permanent prestress that might cause unwanted long-term effects including tension loss and amplified deflection. The cables are positioned following a profile so that the tension force is applied eccentrically to the neutral axis of the slab-ribs assembly. The resulting system of forces causes a bending moment that counteracts the effect of the external load. The rib placement is optimized through a greedy algorithm with a heuristic based on the direction of the principal stresses. The deflection of the slab is reduced by adjusting the cable tensile forces computed by a quasi-static controller. Benchmark studies comparing different cable profiles and active rib layouts are carried out to determine an efficient control configuration. A case study of an 8x8 m adaptive rib-stiffened slab is implemented to evaluate material savings potential. Results show that the adaptive slab solution can achieve up to 67% of material savings compared with an equivalent passive flat slab.

Zusammenfassung

Large statically indeterminate truss and frame structures exhibit complex load-bearing behavior, and redundancy matrices are helpful for their analysis and design. Depending on the task, the full redundancy matrix or only its diagonal entries are required. The standard computation procedure has a high computational effort. Many structures fall in the category of moderately redundant, i.e., the ratio of the statical indeterminacy to the number of all load-carrying modes of all elements is less one half. This paper proposes a closed-form expression for redundancy contributions that is computationally efficient for moderately redundant systems. The expression is derived via a factorization of the redundancy matrix that is based on singular value decomposition. Several examples illustrate the behavior of the method for increasing size of systems and, where applicable, for increasing degree of statical indeterminacy.

Zusammenfassung

Floor and ceiling slabs are commonly used in construction and therefore provide a great potential to save material. In this paper, an adaptive ribbed ceiling is presented. The focus is on the design of the active prestressing. In addition, different design strategies of adaptive structures are compared with respect to their mass saving potential and the necessary actuation effort.

Zusammenfassung

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.

Zusammenfassung

The contribution takes up the concept of preventing locking a priori in the theory of thin-walled structures instead of curing it during discretization. After briefly summarizing the successful concept for avoiding transverse shear locking through reparametrization of primary variables for beams, plates and shells we concentrate on the same approach for preventing also membrane locking. Here, we describe first steps referring to the plane curved Bernoulli beam as a conceptual proof for the new method. Inspired by the so-called Mixed Displacement variational method we discuss three variants of replacing primary displacement parameters by alternative variables.

Zusammenfassung

Fast snapping in the carnivorous Venus flytrap (Dionaea muscipula) involves trap lobe bending and abrupt curvature inversion (snap-buckling), but how do these traps reopen? Here, the trap reopening mechanics in two different D. muscipula clones, producing normal-sized (N traps, max. ≈3 cm in length) and large traps (L traps, max. ≈4.5 cm in length) are investigated. Time-lapse experiments reveal that both N and L traps can reopen by smooth and continuous outward lobe bending, but only L traps can undergo smooth bending followed by a much faster snap-through of the lobes. Additionally, L traps can reopen asynchronously, with one of the lobes moving before the other. This study challenges the current consensus on trap reopening, which describes it as a slow, smooth process driven by hydraulics and cell growth and/or expansion. Based on the results gained via three-dimensional digital image correlation (3D-DIC), morphological and mechanical investigations, the differences in trap reopening are proposed to stem from a combination of size and slenderness of individual traps. This study elucidates trap reopening processes in the (in)famous Dionaea snap traps – unique shape-shifting structures of great interest for plant biomechanics, functional morphology, and applications in biomimetics, i.e., soft robotics.

Zusammenfassung

The opening and closing of pine cones is based on the hygroscopic behavior of the individual seed scales around the cone axis, which bend passively in response to changes in environmental humidity. Although prior studies suggest a bilayer architecture consisting of lower actuating (swellable) sclereid and upper restrictive (non- or lesser swellable) sclerenchymatous fiber tissue layers to be the structural basis of this behavior, the exact mechanism of how humidity changes are translated into global movement are still unclear. Here, the mechanical and hydraulic properties of each structural component of the scale are investigated to get a holistic picture of their functional interplay. Measurements of the wetting behavior, water uptake, and mechanical measurements are used to analyze the influence of hydration on the different tissues of the cone scales. Furthermore, their dimensional changes during actuation are measured by comparative micro-computed tomography (µ-CT) investigations of dry and wet scales, which are corroborated and extended by 3D-digital image correlation-based displacement and strain analyses, biomechanical testing of actuation force, and finite element simulations. Altogether, a model allowing a detailed mechanistic understanding of pine cone actuation is developed, which is a prime concept generator for the development of biomimetic hygromorphic systems.

Zusammenfassung

Bei der Berechnung der Seilnetztragwerke für die Überdachungen der Sportstätten für die Olympischen Spiele 1972 in München spielte ein bislang unveröffentlichtes und auch in Fachkreisen bislang weithin unbekanntes Manuskript des französischen Bauingenieurs Marc Biguenet, damals Mitarbeiter von Jörg Schlaich im Ingenieurbüro Leonhardt und Andrä, eine wesentliche Rolle. Es wird in zwei Veröffentlichungen von Klaus Linkwitz und Hans-Jörg Schek aus 1971 zur Berechnung und Formfindung von Seilnetztragwerken erwähnt und liefert wichtige Vorarbeiten. Das Manuskript war in Archiven und Bibliotheken allerdings nicht aufzufinden und wurde dem ersten Autor nach intensiven Recherchen schließlich von Marc Biguenet persönlich zur Verfügung gestellt. Im Rahmen dieses Berichts wird der Inhalt des Manuskripts mit dem Ziel der Quellen- und Wissenssicherung erstmals veröffentlicht, vergleichend kommentiert und in den technikhistorischen Kontext eingebettet. Die logisch-historischen Wurzeln der Berechnung von Seilnetztragwerken stehen im Zusammenhang mit der Entwicklungsgeschichte nichtlinearer baustatischer Theorien, dem Bau weitgespannter Hängebrücken sowie der Herausbildung computergestützter Berechnungsmethoden.

Zusammenfassung

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.

Zusammenfassung

In coreless filament winding, resin-impregnated fibre filaments are wound around anchor points without an additional mould. The final geometry of the produced part results from the interaction of fibres in space and is initially undetermined. Therefore, the success of large-scale coreless wound fibre composite structures for architectural applications relies on the reciprocal collaboration of simulation, fabrication, quality evaluation, and data integration domains. The correlation of data from those domains enables the optimization of the design towards ideal performance and material efficiency. This paper elaborates on a computational co-design framework to enable new modes of collaboration for coreless wound fibre–polymer composite structures. It introduces the use of a shared object model acting as a central data repository that facilitates interdisciplinary data exchange and the investigation of correlations between domains. The application of the developed computational co-design framework is demonstrated in a case study in which the data are successfully mapped, linked, and analysed across the different fields of expertise. The results showcase the framework’s potential to gain a deeper understanding of large-scale coreless wound filament structures and their fabrication and geometrical implications for design optimization.

Zusammenfassung

Explizite Zeitintegrationsverfahren besitzen nur bedingte Stabilität. Diese hängt von der kritischen Zeitschrittweite ab, welche über die höchste Eigenkreisfrequenz des Systems bestimmt wird und nachweislich mit der kleinsten Elementabmessung in Verbindung steht. Speziell für dünnwandige Elemente wird ein neuer Ansatz zur selektiven Massenskalierung vorgestellt, der auf der Discrete-Shear-Gap-Methode nach Bletzinger u. a. (2000) basiert. Die eingeführte Massenskalierungsmethode beeinflusst in erster Linie die Dickenrichtung der Elemente, welche in dünnwandigen Strukturen eine deutlich geringere Abmessung als die in-ebenen-Dimensionen besitzt und reduziert damit lediglich die höchsten Frequenzen des Systems. Dadurch bleiben die niedrigen und strukturrelevanten Moden, die den hauptsächlichen Energieanteil besitzen, nahezu unbeeinflusst. Eine neue künstliche Massenmatrix mit anisotropem Aufbau und den gewünschten Eigenschaften kann erzeugt werden. Für nichtlineare Analysen, in denen sich die Steifigkeitsmatrix durch große Rotationen beständig ändert, wurde eine isotrope Version entwickelt. Diese beeinflusst auch einige niedrigere Eigenmoden des Systems, jedoch lassen sich damit die höchsten Eigenkreisfrequenzen des Systems weiter skalieren, was in expliziten Verfahren einen größeren Zeitschritt erlaubt. Für beide Versionen wurde eine Variante ermittelt, die das Frequenzspektrum noch besser abbildet, jedoch die maximal mögliche Reduktion der höchsten Frequenz partiell begrenzt. Die Methode und ihr Verhalten in Bezug auf Genauigkeit und Effektivität wird in numerischen Untersuchungen charakterisiert und anschließend diskutiert. Im Vergleich zu einigen bereits in der Literatur bekannten Methoden zur selektiven Massenskalierung liefert der hier vorgestellte Ansatz vergleichbare und unter großen Schlankheitswerten zum Teil bessere Ergebnisse. Zudem ist er auch für nahezu inkompressible Materialien in biegedominanten Problemen gut geeignet.

Zusammenfassung

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.

Zusammenfassung

Die Effizienz expliziter Zeitintegrationsverfahren hängt von der höchsten Eigenkreisfrequenz des diskretisierten Systems ab. Bei schubweichen Platten wird der kritische Zeitschritt durch die hochfrequenten, für die dynamische Systemantwort meist unbedeutenden, Querschubfrequenzen begrenzt. Durch die direkte Parametrisierung von Schubfreiheitsgraden können bei hierarchischen Plattenformulierungen die Querschubfrequenzen mit einer intrinsisch selektiven Massenskalierung gezielt skaliert werden, während die biegedominierten Frequenzen unbeeinflusst bleiben. In der vorliegenden Arbeit wird das Konzept der intrinsisch selektiven Massenskalierung von Balken- auf Plattenformulierungen erweitert und in MATLAB für verschiedene Diskretisierungsmethoden implementiert. Dabei werden B-Splines, Subdivision Surfaces und Maximum-Entropy Approximants verwendet. In Parameterstudien wird die Qualität und Effizienz der implementierten Verfahren anhand von Frequenzspektren und linearen, expliziten Simulationen aufgezeigt.

Zusammenfassung

We present an objective, singularity-free, path independent, numerically robust and efficient geometrically non-linear Reissner-Mindlin shell finite element formulation. The formulation is especially suitable for higher order ansatz spaces. The formulation utilizes geometric finite elements presented by Sander 74 and Grohs 34 for the interpolation on non-linear manifolds. The proposed method is objective and free from artificial singularities and spurious path dependence. Due to the fact that the director field lives on the unit sphere, a special linearization procedure is required to obtain the stiffness matrix. Here, we use the simple constructions of as reported by Absil et al. 2, 3, which yields an easy way to obtain the correct tangent operator of the potential energy. Additionally, we compare three different interpolation schemes for the shell director that can be found in the literature, where one of them is applied for the first time for the Reissner-Mindlin shell model. Furthermore, we compare the exponential map to the radial return normalization as procedure to update the nodal directors and conclude the superiority of the latter, in terms of fewer load steps. We also investigate the construction of a consistent tangent base update scheme. Path independence, efficiency and objectivity of the formulation are verified via a set of numerical examples.

Zusammenfassung

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.

Zusammenfassung

Finite-Elemente-Modellierungsansätze nach dem aktuellen Stand der Technik stoßen bei der Simulation von bestimmten Blechumformprozessen an ihre Grenzen. Ein Lösungsansatz zur Verbesserung der Simulationsgenauigkeit dieser Blechumformprozesse wird zurzeit in einem IGF-Forschungsprojekt am Fraunhofer IWM und am Institut für Baustatik und Baudynamik der Universität Stuttgart gemeinsam entwickelt. Dieser basiert auf der Kombination von erweiterten Schalenformulierungen und 3D-Materialmodellen und soll zukünftig die Simulationsgenauigkeit dieser Blechumformprozesse verbessern.

Zusammenfassung

We show that most geometrically nonlinear three-dimensional shell elements and solid shell elements suffer from a previously unknown artificial stiffening effect that only appears in geometrically nonlinear problems, in particular in the presence of large bending deformations. It can be interpreted as a nonlinear variant of the well-known Poisson thickness locking effect. We explain why and under which circumstances this phenomenon appears and propose concepts to avoid it.

Zusammenfassung

In the present paper, theoretical foundations of redundancy in spatially continuous, elastostatic, and linear representations of structures are derived. Adopting an operator-theoretical perspective, the redundancy operator is introduced, inspired by the concept of redundancy matrices, previously described for spatially discrete representations of structures. Studying symmetry, trace, rank, and spectral properties of this operator as well as revealing the relation to the concept of statical indeterminacy, a continuum-mechanical theory of redundancy is proposed. Here, the notion “continuum-mechanical” refers to the representation being spatially continuous. Apart from the theory itself, the novel outcome is a clear concept providing information on the distribution of statical indeterminacy in space and with respect to different load carrying mechanisms. The theoretical findings are confirmed and illustrated within exemplary rod, plane beam, and plane frame structures. The additional insight into the load carrying behavior may be valuable in numerous applications, including robust design of structures, quantification of imperfection sensitivity, assessment of adaptability, as well as actuator placement and optimized control in adaptive structures.

Zusammenfassung

Nach dem Ende der Hochzeiten des Schalenbaus in den 1970er-Jahren gab es nur begrenzt Interesse die besonderen Trageigenschaften der gebauten Schalentragwerke weiter zu untersuchen. Die Ingenieure der damals geschaffenen Bauwerke verließen sich zur Beurteilung der Tragfähigkeit auf Intuition, Handrechenverfahren und physikalische Modelle. In neuer Zeit ist es mit computergestützten Methoden möglichst hinreichend genau das detaillierte Tragverhalten von Schalen zu untersuchen. In der hier vorliegenden Arbeit dies für einen Schalentypen vorgenommen. Anhand eines Modells einer Buckelschale des renommierten Schalenbauers Heinz Islers werden Verformungen und Spannungen mithilfe der Finiten-Elemente-Methode untersucht. Dafür wurde dem Autor eine Geometrie zur Verfügung gestellt, die ein Forscherteam um P. Eigenraam der TU Delft per 3D-Scan aus einem von Islers Modellen erstellen konnte. Die von ihnen darauf angestellte FE-Analyse der Schale war die erste, die an einer Buckelschale durchgeführt wurde. Im Zuge dieser Arbeit werden zunächst die notwendigen Grundlagen der Schalenkinematik und des Lastabtrags aufgearbeitet. Danach wird in Kürze auf die Person Heinz Islers und sein Wirken eingegangen. Der Hauptteil der Arbeit beginnt zunächst mit der Modellierung einer Kugelschale für die in der Literatur analytische Lösungen vorhanden sind, um die gewählte Software zu überprüfen. Für die 3D-Modellierung wird dabei das Programm Rhinoceros und für die FE-Analyse das Programm SOFiSTiK verwendet. Nachdem die Ergebnisse eine gute Vergleichbarkeit mit den Literaturlösungen aufwiesen, konnte die Buckelschale modelliert und untersucht werden. Dabei wurde die Schale mit den Lastfällen Eigengewicht und Schnee belastet. Es konnte gezeigt werden, dass die Schale sich weitestgehend in einem Membranspannungszustand ohne das Auftreten von größeren Biegeeffekten befindet. Nur in den Randbereichen und dem Randträger entstehen Zugkräfte und Biegung. Diese Effekte können mit günstig gewählter Vorspannung minimiert bzw. umgekehrt werden. Anschließend erfolgte ein Vergleich der Ergebnisse mit dem Modell von P. Eigenraam. Auch hier konnte eine gute qualitative Übereinstimmung erzielt werden, was die Sicherheit gibt mit dem Modell und der verwendeten Software weitere Untersuchungen zu dieser Schale oder andern Schalen durchführen zu können.

Zusammenfassung

(1) Significance of geometry for bio-inspired hygroscopically actuated bilayer structures is well studied and can be used to fine-tune curvatures in many existent material systems. We developed a material design space to find new material combinations that takes into account unequal effective widths of the layers, as commonly used in fused filament fabrication, and deflections under self-weight. (2) For this purpose, we adapted Timoshenko’s model for the curvature of bilayer strips and used an established hygromorphic 4D-printed bilayer system to validate its ability to predict curvatures in various experiments. (3) The combination of curvature evaluation with simple, linear beam deflection calculations leads to an analytical solution space to study influences of Young’s moduli, swelling strains and densities on deflection under self-weight and curvature under hygroscopic swelling. It shows that the choice of the ratio of Young’s moduli can be crucial for achieving a solution that is stable against production errors. (4) Under the assumption of linear material behavior, the presented development of a material design space allows selection or design of a suited material combination for application-specific, bio-inspired bilayer systems with unequal layer widths.

Zusammenfassung

Hierarchic shear deformable structural element formulations possess the advantage of being intrinsically free from transverse shear locking, that is they avoid transverse shear locking a priori through reparametrization of the kinematic variables. This reparametrization results in shear deformable beam, plate and shell formulations with distinct transverse shear degrees of freedom. The basic idea of selective mass scaling within explicit dynamic analyses is to scale down the highest frequencies in order to increase the critical time step size, while keeping the low frequency modes mostly unaffected. In most concepts, this comes at the cost of non- diagonal mass matrices. In this contribution, we present first investigations on selective mass scaling for hierarchic formulations. Since hierarchic structural formulations possess distinct transverse shear degrees of freedom, they offer the intrinsic ability for selective scaling of the high frequency shear modes, while keeping the bending dominated low frequency modes mostly unaffected. The proposed instrinsically selective mass scaling concept achieves high accuracy, which is typical for selective mass scaling schemes, but in contrast to existing concepts it retains the simplicity of a conventianl mass scaling method and preserves the diagonal structure of a lumped mass matrix. As model problem, we study frequency spectra of different isogeometric Timoshenko beam formulations for a simply supported beam. We discuss the effects of transverse shear parametrization, locking and mass lumping on the accuracy of results.

Zusammenfassung

Adaptive structures are characterized by their ability to adjust their geometrical and other properties to changing loads or requirements during service. This contribution deals with a method for the design of quasi‐static motions of structures between two prescribed geometrical configurations that are optimal with regard to a specified quality function while taking large deformations into account. It is based on a variational formulation and the solution by two finite element discretizations, the spatial discretization (the standard finite element mesh) and an additional discretization of the deformation path or trajectory. For the investigations, an exemplary objective function, the minimization of the internal energy, integrated along the deformation path, is used. The method for motion design presented herein uses the Newton‐Raphson method as a second‐order optimization algorithm and allows for analytical sensitivity analysis. The proposed method is verified and its properties are investigated by benchmark examples including rigid body motions, instability phenomena and determination of inextensible deformations of shells.

Zusammenfassung

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.

Zusammenfassung

Die „Große Beschleunigung“ bei Bevölkerungszahlen, klimaschädlichen Emissionen, Wasserverbrauch und vielem anderen stellt die gesamte Menschheit vor große Herausforderungen. Dies trifft besonders auf das Bauschaffen zu. Es gilt, zukünftig für mehr Menschen mit weniger Material emissionsfrei zu bauen. Hierfür muss unsere Art des Planens, Bauens und Nutzens von Bauwerken neu gedacht und neu konzipiert werden. Auf der bautechnischen Seite bedeutet dies die konsequente flächendeckende Umsetzung von Leichtbaustrategien. Zu diesen zählt neben dem klassischen Leichtbau und den Gradientenbauweisen auch das Bauen mit adaptiven Hüllen und Strukturen. Unter Adaptivität sind dabei unterschiedliche Veränderungen der Geometrie, der physikalischen Eigenschaften von einzelnen Bauteilen oder von ganzen Bauwerken zu verstehen. Durch Adaption können Spannungsfelder homogenisiert, Bauteilverformungen reduziert und bauphysikalische Verhalten von Bauteilen verändert werden. All dies verringert nicht nur den Materialbedarf, sondern liefert auch einen wesentlichen Beitrag zur Steigerung des Nutzerkomforts. Adaptivität im weiteren Sinne bezeichnet einen ganzheitlichen Ansatz, in dem die Anpassung sozialer, kultureller und räumlicher Erfahrungen sowie architektonischer und planerischer Handlungsweisen eng mit den technologischen Entwicklungen verknüpft wird. Die Zusammenführung dieser Perspektiven ist Anspruch des SFB, um ganzheitliche Lösungen für eine zukünftige gebaute Umwelt zu finden.

Zusammenfassung

Hammering tools uses damping elements of various geometries and hardness levels not only to reduce the reaction forces and vibrations, but also to protect the structural parts from failure. This makes damping elements a key component during the design phase of any tool. Since many design quantities initially rely on the results obtained via simulations for optimization and improvement purposes, it makes it essential to have an appropriate material model which could capture the behaviour of the damping elements accurately. Damping elements are made up of elastomeric compounds showcasing highly non-linear behaviour especially when subjected to very high strains and strain rates when mounted in a tool. This aim of this work is to study various phenomena regarding the rubber material behaviour and develop a user-defined material model in LS-DYNA which provides error-free stress updates at a given strain level for elastomers. The fundamental concepts of hyperelastic and viscoelastic constitutive theories are emphasized in the beginning as these theories are more suitable to model elastomeric behaviour. Material parameter identification procedure is also highlighted for both hyperelastic and linear viscoleastic material models. An Ogden-based linear viscoelastic model is programmed which is extended with strain-level based non-linearity included in the material model and later validated with the experimental results obtained with a gas-gun test fixture and O-ring specimens. Discussions regarding energy dissipation is focussed towards the end as it plays a crucial role in understanding the behaviour of the damping element.

Zusammenfassung

The degree of statical indeterminacy as a fundamental property in structural mechanics is today mainly known as a property of a complete system without any information about its spatial distribution. The redundancy matrix provides information about the distribution of statical indeterminacy in the system and by this gives an additional valuable insight into the load-bearing behaviour. The derivation and definition of the redundancy matrix are presented based on truss systems and its mathematical properties and their mechanical interpretations are provided. The definition of the redundancy matrix is extended to other discrete systems like beam structures and a definition of the redundancy density is given for the continuous 1D case. Potential applications of the concept include robust design of structures, quantification of imperfection sensitivity as well as assessment of optimal actuator placement in adaptive structures.

Zusammenfassung

For most sheet metal forming simulations, shell elements that consider a reduced stress state, in particular, assuming a zero transverse normal stress sigma_33 and neglecting the shear stress components sigma_13 and sigma_23 in the yield function, are used. Moreover, certain kinematic assumptions, like cross-sectional material fibers being assumed to remain straight during deformation, are typically applied. However, for some applications, like bending with small radii and thick sheets, this approach is not a workable solution to obtain accurate and reliable results, since the prerequisites that justify the aforementioned kinematic assumptions are not met anymore. In this contribution, a 3d-shell element is presented that allows for cross-sectional warping. For the evaluation, numerical results of a metal stripe drawn through a draw bead are compared against experimental data. The results demonstrate that the 3d-shell element is able to represent warping of cross-sectional material fibers during deformation. In addition, further numerical tests conducted with this element are shown.