Veröffentlichungen

Zusammenfassung

This thesis deals with locking and hourglassing issues that arise in nonlinear finite element analyses of problems in mechanics. The major focus lies on the analysis of these numerical deficiencies, the design of suitable benchmarks and the development of novel remedies. A new nonlinear locking phenomenon is described. It is caused by parasitic nonlinear strain terms and it is particularly pronounced for large element deformations in combination with higher-order integration and a critical parameter, such as the element aspect ratio or the Poisson's ratio. To avoid this problem within the popular class of enhanced assumed strain formulations, novel strain enhancements are presented. An analytical solution of a tailored finite bending problem is used to benchmark the newly proposed element formulations. Further, the problem of hourglassing in both compression and tension of solid bodies is analysed. It is shown that the underlying causes of hourglassing can be explained by geometry-induced and material-induced trigger mechanisms of structural instabilities. Crucial for understanding as well as benchmarking is the analytical in-depth analysis of a large strain bifurcation problem. Based on these insights, an obvious remedy for the geometric hourglassing phenomenon is presented. The last part of this thesis is devoted to the efficient algorithmic treatment of the computation of instability points. The difficulties in choosing a suitable load-stepping approach with methods from the literature are discussed and a methodological idea of an adaptive load-stepping scheme is presented. Efficiency and practicability are demonstrated for several benchmarks.

Zusammenfassung

Seit ihrer Etablierung als theoretische Querschnittsdisziplin ist die Statik ein steter Treiber methodischer Innovation und digitaler Transformation. Ihr Gegenstand hat sich dabei vom Berechnen auf das Modellieren verschoben. Die Statik der Zukunft erschließt als kreative Disziplin bisher nicht gekannte Freiheiten und öffnet die engere Welt des Bauwesens für neue, interdisziplinäre Möglichkeiten. Anhand von vier Hypothesen zum Wesen der Statik wirft dieser Beitrag einen persönlichen Blick der Autoren auf Möglichkeiten und Herausforderungen in Forschung, Lehre und Praxis, die sich für deren Zukunft ergeben.

Zusammenfassung

Diese Arbeit beschäftigt sich mit optimierter Stützenplatzierung. Es wird ein Code entwickelt, der bei gegebenen Tragwerken automatisiert Stützen anordnen kann. Das Ziel ist es dabei, die mittlere Nachgiebigkeit des Systems zu minimieren. Ausgangspunkt der Optimierungsmethode ist ein FE-Modell, bei dem an jedem Knoten eine Feder mit einer vorgegebenen maximalen Steifigkeit angeordnet ist. Die relativen Federsteifigkeiten bezüglich dieses Maximums sollen solange verändert werden, bis sie für die meisten Federn Null sind und für die gewünschte Anzahl an Stützen Eins. Für dieses diskrete Problem wird der SIMP-Ansatz verwendet. Die Iterationen werden mittels eines mathematischen Optimalitätskriteriums durchgeführt. Die Iterationsvorschrift basiert dabei auf den Karush-Kuhn-Tucker-Bedingungen. Die Anzahl der Stützen wird als Nebenbedingung in die zugrundeliegende Lagrange-Funktion integriert und kann dadurch exakt erreicht werden. Das Ergebnis der Optimierungsmethode zur Stützenplatzierung ist stark parameterabhängig. Die Wahl der Parameterwerte ist deshalb wesentlich für die resultierende Stützenanordnung. Die Methode wird für Balken entwickelt. Eine analytisch ermittelte Stützenplatzierung für den statisch bestimmt gelagerten Balken mit zwei Lagern dient zur Kalibrierung der Parameterwerte. Für die Anwendung Methode zur optimierten Stützenplatzierung auf komplexe Grundrisse wird die Methode auf Plattentragwerke erweitert. Dafür müssen Modifikationen am FE-Modell vorgenommen und ein Filter eingeführt werden, der die Entwurfswerte glättet.

Zusammenfassung

Structural engineers often want to have a redundant structure where the loss of a member would not lead to structural collapse. For a truss, adding a bar beyond that required for static determinacy renders the structure redundant, but what is the spatial distribution of the static indeterminacy within the individual elements of a framework? Can an additional bar be redundant with several existing bars? Are there truss topologies and geometries that enhance redundancy? The assessment of structures based on such load-independent quantitative measures can be useful in early design stages to achieve an integrative planning process for designers and engineers. The degree of static indeterminacy and in particular its spatial distribution, quantified with the redundancy matrix can be used for assessing structural integrity of a framework. Focusing on structural properties independent of the individual member stiffness, such as geometry and topology, graph theory offers yet another tool to assess structural performance. This paper explores the integration of the Maxwell-Calladine count with the redundancy matrix from theoretical structural mechanics and with contributions of graph theory to explore a deeper understanding of structural redundancy.

Zusammenfassung

This paper presents the integration of a numerical structural model based on the redundancy matrix and experimental results of Multi-Layered Randomized Architected Materials (MLRAM). It presents a combination of the relatively new field of architected materials with a load-independent performance indicator from theoretical structural mechanics. The redundancy matrix by itself provides a measure for structural assessment that is independent of a specific load case. Various layouts of the MLRAM samples and recorded testing allow the analysis of the redundancy distribution within the structure as it undergoes failure. An in-depth analysis of the tested MLRAM samples is provided, as they show a high degree of static indeterminacy and thus, multiple different load paths. A special focus lies on the change of the redundancy distribution as global progressive failure happens. Another focus is set on the investigation of the failure initiation, meaning that the redundancy distribution can help to identify critical elements. A simple introductory example shows the interdependence between the variation of the geometric location of nodes and the redundancy distribution. The study shows, that the distribution of static indeterminacy can be used as a measure to quantify vulnerability to failure and rank the individual element's importance. Furthermore, progressive collapse is identified as a series of local effects in the highly statically indeterminate MLRAM samples, underlining the fact that the spatial distribution of static indeterminacy is of central importance for the assessment of structural safety.

Zusammenfassung

Zur Analyse von Tragwerken ist es in frühen Entwurfsphasen häufig ausreichend, Schnitt- und Verschiebungsgrößen, sowie Spannungen im Rahmen der linearen Elastizitätstheorie zu bestimmen. Eine weitere fundamentale Eigenschaft von Tragwerken ist der Grad der statischen Unbestimmtheit und deren Verteilung innerhalb des Tragwerks. Die Redundanzmatrix liefert diese Information und stellt damit ein lastfallunabhängiges Maß zur Beurteilung von Tragwerken hinsichtlich Robustheit, Assemblierbarkeit und Adaptierbarkeit zur Verfügung.

Zusammenfassung

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.

Zusammenfassung

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.

Zusammenfassung

Fiber-reinforced composites offer innovative solutions for architectural applications with high strength and low weight. Coreless filament winding extends industrial processes, reduces formwork, and allows for tailoring of fiber layups to specific requirements. A previously developed computational co-design framework for coreless filament winding is extended toward the integration of reciprocal design feedback to maximize design flexibility and inform design decisions throughout the process. A multi-scalar design representation is introduced, representing fiber structures at different levels of detail to generate feedback between computational design, engineering, and fabrication. Design methods for global, component, and material systems are outlined and feedback generation is explained. Structural and fabrication feedback are classified, and their integration is described in detail. This paper demonstrates how reciprocal feedback allows for co-evolution of domains of expertise and extends the existing co-design framework toward design problems. The developed methods are shown in two case studies at a global and component scale.

Zusammenfassung

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.

Zusammenfassung

The critical time step in explicit time integration methods depends on the highest natural angular frequency of the discretized problem. For shear deformable beam, plate and shell formulations, efficiency is therefore typically limited by the highest transverse shear frequencies, which are mostly of minor importance for the structural response. Direct parametrization using transverse shear variables within hierarchic structural element formulations allows a selective scaling of transverse shear frequencies in a simple manner, while bending frequencies remain practically unaffected. In particular, the novel concept of intrinsically selective mass scaling (ISMS) results in an efficient method that features high accuracy and preserves both linear and angular momentum for both consistent and lumped mass matrices. In addition, ISMS preserves the diagonal structure of lumped mass matrices. Similar to the underlying intrinsically locking-free, hierarchic concept for shear deformable structural element formulations, ISMS retains its beneficial properties for any smooth discretization scheme. In this contribution, we extend recent research on ISMS for beam formulations to the case of shear deformable plate formulations. We test our novel concept with respect to accuracy and efficiency by means of selected numerical experiments. We study both frequency spectra and the transient behavior in explicit time integration. To demonstrate the generality of ISMS, exemplarily both isogeometric discretizations based on B-splines and meshfree discretizations using local maximum-entropy approximants are investigated.

Zusammenfassung

Dedicated to simulating thin-walled structures using the finite element method, this thesis focuses on a consistent Reissner-Mindlin shell formulation through theoretical and numerical investigations. Emphasizing a robust mathematical foundation, particularly in differential geometry, the work explores aspects such as the derivation of stress resultants, consistent linearization, and properties of director interpolation. A pivotal outcome is a finite element formulation that outperforms existing ones, exhibiting key features like objectivity, adherence to unit length constraints, avoidance of path dependence, singularity prevention, and optimal convergence orders. Notably, the study of the consistent linearization process yields the correct tangent operator, identified as the symmetric Riemannian Hessian, serving as the stiffness matrix. This, combined with the study of the correct update of the nodal directors, contributes to the superior convergence behavior of a Newton-Raphson scheme compared to existing formulations. Addressing the assumption of zero transverse normal stress, the thesis proposes a novel numerical treatment, using optimization on manifolds, applicable to arbitrary material models. This method shows potential applicability to other models with stress constraints. The claim of a physically and algorithmically sound Reissner-Mindlin shell formulation is supported by results from numerical investigations. Beyond contributing to the algorithmic treatment of the Reissner-Mindlin shell model, the proposed procedures may have implications for improving the accuracy, efficiency, and reliability of numerical treatments of other structural models.

Zusammenfassung

Hierarchische Balken-, Platten- und Schalenformulierungen basieren auf einer geschickten Reparametrisierung der kinematischen Gleichungen, die sich für neuartige, glatte Diskretisierungsverfahren als vorteilhaft erweist. Im vorliegenden Beitrag werden die intrinsischen Eigenschaften des hierarchischen Konzepts anhand statischer und dynamischer Analysen von Flächentragwerken aufgezeigt und diskutiert.

Zusammenfassung

This work investigates the application of an external adaptive tensioning (EAT) system for high-speed railway (HSR) bridges. The design of HSR bridges involves strict displacement and acceleration limits, which typically results in oversizing. The EAT system comprises under-deck cables deviated by compressive struts that are equipped with linear actuators. Since the cable is eccentric to the bridge neutral axis, tensioning the under-deck cables by adjusting the length of the linear actuators generates a bending moment that counteracts the effect of the external loads. The response under variable loading is reduced by computing the actuator commands with a linear quadratic regulator (LQR). Numerical results show that active control through the EAT system allows satisfying displacement and acceleration limits, which otherwise cannot be met without increasing the stiffness and mass of the bridge. A significant reduction of the response is achieved when resonance conditions occur. In addition, peak stresses are significantly reduced, showing the potential for fatigue-life extension. Parametric analyses comparing different bridge depths and spans, EAT system dimensions, controller parameters and actuator placement are carried out to investigate system efficacy. Results show that the adaptive bridge solution can achieve up to 32% mass savings compared to an equivalent passive bridge.

Zusammenfassung

Consistent treatment of large rotations in common Reissner–Mindlin formula-tions is a complicated task. Reissner–Mindlin formulations that use a hierarchicparametrization provide an elegant way to facilitate large rotation shell anal-yses. This can be achieved by the assumption of linearized transverse shearstrains, resulting in an additive split of strain components, which technicallysimplifies implementation of corresponding shell finite elements. The presentstudy aims at validating this assumption by systematically comparing numeri-cal solutions with those of a newly implemented hierarchic and fully nonlinearReissner–Mindlin shell element.

Zusammenfassung

The mixed displacement (MD) method was initially developed to mitigate geometrical locking effects in beams, plates, and shells with the intention of having intrinsically locking-free characteristics while using equal-order interpolation for all degrees of freedom. In other words, it is an unlocking scheme that works independent of the element shape, polynomial order, and discretization scheme. It includes additional degrees of freedom that adhere to a carefully designed differential relation that can be interpreted as a kinematic law, incorporated in a mixed sense. Certain constraints are to be enforced on these additional degrees of freedom to obtain a well-posed system of equations. In this work, the MD method is extended for problems in solid mechanics. We present the underlying variational formulation, followed by its application to 2D solid elements. Additionally, we showcase an idea to enforce the additional constraints in a general sense. Various numerical examples, within the framework of the finite element method and isogeometric analysis, are outlined to demonstrate the performance of the MD method in the geometrically linear and geometrically nonlinear cases.

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

Sheet metal forming simulations are crucial in various industries, such as automotive, aerospace, and construction. These simulations are commonly carried out using Reissner-Mindlin shell elements, which involve certain simplifying assumptions about zero normal stress in shell normal direction and cross-sectional fibers remaining straight during deformation 1. Because of this, the material model needs to be modified and no three-dimensional material model can be used. However, in critical forming situations such as bending with small radii relative to the sheet thickness, these assumptions do not hold, resulting in inaccurate simulation results. To address this issue, a higher-order 3D-shell element that incorporates a full three-dimensional constitutive model and that can account for cross-sectional warping and higher-order strain distributions has been developed 2. First findings on the benefits of using higher-order 3D-shell elements for accurately modeling sheet metal forming processes were presented in 3. The objective of this study is to expand upon this work by assessing the accuracy of simulations utilizing the higher-order 3D-shell element for critical sheet metal forming processes. Results of simulations with the higher-order 3D-shell elements are compared to experimental data and results obtained from simulations with solid elements and Reissner-Mindlin shell elements. It is demonstrated that simulations with higher-order 3D-shell elements provide more accurate predictions in sheet metal forming processes than the standard modeling approach, including but not limited to stress. Furthermore, we aim to support the efficient utilization of the higher-order 3D-shell element by identifying situations in which the additional deformation modes of this element are beneficial, and in which application of a standard shell element suffices. To achieve this, we analyze the influence of its higher-order deformation modes on the strain for parameter alterations in benchmark problems. To aid the modeling decision, mesh studies are conducted to quantify the influence of the element size on the results quality. Lastly, a comparison of numerical efficiency of different element formulations is given, showing the high efficiency of higher-order 3D-shell elements compared to solid elements. This contribution is part one of a two-part series that aims to present recent improvements of sheet metal forming simulations through a combination of higher-order 3D-shell elements and anisotropic 3D yield models. Part I focuses on the assessment of higher-order 3D-shell elements, while Part II investigates the effect of anisotropic 3D yield models with respect to the in-plane and out-of-plane behavior on sheet metal forming simulations. Together, these contributions aim to provide a comprehensive overview of the latest advances obtained in a joint research project at the Fraunhofer IWM in Freiburg and the Institute for Structural Mechanics at the University of Stuttgart.

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

Der Stand der Technik bei der Simulation von Blechumformprozessen ist die Verwendung von Schalenelementen, die auf dem Reissner-Mindlin-Modell beruhen und mit vereinfachten Materialmodellen verwendet werden. Dieser Modellierungsansatz basiert auf einigen vereinfachenden Annahmen. Für die Strukturmodellierung werden ein Ebenbleiben der Querschnittsfasern und vernachlässig-bare Normalspannungen in Blechdickenrichtung angenommen. Für die Materialmodellierung wird das richtungsabhängige Materialverhalten nur in der Blechebene abgebildet und damit werden anisotrope Effekte außerhalb der Blechebene vernachlässigt. Dieser Modellierungsansatz erreicht bei bestimmten Blechumformprozessen seine Grenzen, da einige der getroffenen Annahmen nicht mehr zutreffen. Dieses Forschungsvorhaben verfolgte die Weiterentwicklung eines alternativen Ansatzes zur Simulation von Blechumformprozessen und die Qualifizierung dieses Ansatzes für den industriellen Einsatz. Der Ansatz, der im Folgenden als „3D-Blechmodellierung" bezeichnet wird, nutzt 3D-Schalenelemente höherer Ordnung, die nicht den Einschränkungen des Reissner-Mindlin-Modells unterworfen sind, für die Simulation von Blechumformprozessen. Diese werden mit 3D-Materialmodellen verbunden, die einen vollständigen dreidimensionalen Dehnungs- und Spannungszustand berücksichtigen. Für diesen Ansatz wurden im Rahmen des Forschungsvorhabens die im Vorgängerprojekt entwickelten 3D-Schalenelemente höherer Ordnung bezüglich unterschiedlicher Aspekte verbessert. Außerdem wurde die Methode der »virtuellen Versuche« verbessert und für eine weitere Werkstoffklasse qualifiziert. Numerische Benchmarks, Vergleiche mit Versuchsergebnissen und Simulationen von Realbauteilen zeigen die erhöhte Ergebnisqualität der 3D-Blechmodellierung und die erfolgreiche Qualifizierung für den industriellen Einsatz.

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.