Manfred Bischoff

Zusammenfassung

This paper deals with a concept of lightweight construction that promises significant resource savings and extended service life by providing structures with the ability to actively adapt their load-bearing behaviour to adverse influences. In the case of truss structures, this concept requires the identification of structural topologies that facilitate adaptation, together with an appropriate actuator layout. Previous research addressed the exploration of adaptable and architecturally meaningful truss topologies through the development of an agent-based design method. This paper focuses on the future redesign, i.e., reconfiguration, of adaptive structures. Specifically, it investigates how sensor data from realised and operated structures can be (1) used to evaluate and resolve the performative consequences related to topological modifications, and (2) used by the agent model for design integration. A digital case study is presented whereby synthetic sensor data is generated, analysed, and translated to reconfiguration-specific design objectives and agent behaviours. Finally, the paper demonstrates the opportunities of combining adaptability feedback with sensor data based on two digital reconfiguration scenarios.

Zusammenfassung

Bridges are increasingly subjected to higher loads due to growing traffic volumes and the deployment of heavier transportation systems, such as new generations of trains. This case study investigates the extent to which a tied-arch bridge can be retrofitted with active hangers to counteract these increased loads. A detailed finite element model of the bridge is developed and used to formulate a multi- objective optimization problem. The two competing objectives are to minimize the actuation forces required by the active hangers and to limit the increase in stress within the arch. Additionally, constraints are imposed to ensure that displacement limits are not exceeded, maintaining structural integrity and serviceability.

Zusammenfassung

Adaptive structures are equipped with sensors and actuators to counteract deformations caused by external loads. For railway bridges, train-induced loads are the primary source of quasi-stationary deformations and oscillations. Active control of these can enhance the service life of bridges. This study examines the tied-arch railway bridge “EÜ Elbe-Lübeck Kanal” (Germany). A state and disturbance estimator is designed and applied to measurement data. Active static compensation and vibration damping are explored in simulations and assessed in terms of control performance and the resulting stresses within the bridge. As a result, the control goals are achieved with tolerable stresses, but further work is needed to reduce the required actuator forces.

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

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

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

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

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

Adaptive structures are equipped with hydraulic actuators for compensating external loads and damping vibrations, enabling lightweight construction and an extended operational lifetime. In the context of structural health monitoring, these actuators also provide the means for active diagnostic approaches, which can improve the diagnostic performance over conventional passive methods. This paper investigates a model-based active diagnosis method for structural faults resulting in a local loss of stiffness. Parametric uncertainties, which are often substantial in civil engineering and pose a major challenge in model-based structural health monitoring, are handled in a probabilistic framework. An upper bound on the probability of a diagnostic error is used as objective of the input optimization, with an alternative objective additionally taking the actuation energy into account. In a simulation study, the proposed method achieves notable improvements in the diagnosis performance and reduces either the required time by up to 75% or the actuation energy by up to 60%.

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

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

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

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

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

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

External post-tensioning offers significant potential to improve the load-bearing performance of bridges. However, typical external post-tensioning systems are effective for a specific load case. 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 acceleration constraints, which typically results in oversizing. The EAT system comprises under-deck cables deviated by linear actuators, which enable controlling the bending moment as the load changes. Simulations are carried out on simply supported beam bridges. Results show that active control through the EAT system allows satisfying vertical acceleration limits for mid-span HSR bridges, which cannot be met otherwise without incurring a weight penalty. In addition, the cyclic stress range is significantly reduced showing the potential for fatigue-life extension.

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.

Zusammenfassung

Taking advantage of adaptivity in the field of civil engineering is an ongoing research topic. Integration of adaptive elements in the load-bearing structure is already well established in many other engineering fields. First investigations promise large material saving potentials also in the field of civil engineering, especially when it comes to high-rise buildings or wide spanned structures like roofs or bridges. In times of emission problems and shortage of materials, the potentials of adaptive civil structures open various new possibilities. In the design and optimization process of adaptive civil structures, we address the differences between classical approaches for passive systems and new practices considering adaptivity. By using a suitable actuator placement, it is possible to manipulate the displacements of the structure as well as the force distribution within the structure. Both material and energy savings can be accomplished with an integrated design of the adaptive structure taking into account the actuation, suitable combination of structural design and actuator placement. For demonstration of the differences in the design process and in the resulting optimized structure, we use a small case study on a truss structure, which is inspired by a high-rise building, and consider static loads.

Zusammenfassung

Die Antwort einer Struktur auf Aktuierung wird maßgeblich vom Grad der statischen Unbestimmtheit und deren Verteilung in der Struktur beeinflusst. Die Redundanzmatrix enthält diese Informationen über das Tragwerk. Aus ihr können daher Rückschlüsse für die Aktorplatzierung und für die Bewertung der Aktuierbarkeit von Strukturen gezogen werden. Die Untersuchung eines Beispieltragwerks veranschaulicht einerseits die Einsatzmöglichkeiten der Redundanzmatrix und andererseits das Masseneinsparungspotential, das mithilfe des Einsatzes aktiver Elemente in passiven Strukturen erschlossen werden kann.

Zusammenfassung

Curved folding, a method to create curved 3D structures from a flat sheet, can be used to produce material and manufacturing efficient, static or dynamic structures. However, the complex assembly and folding sequence of curved crease patterns is the bottleneck in their fabrication process. This paper presents Self-shaping Curved Folding: a material programming approach to create curved crease origami structures that self-assemble from flat into 3D folded state upon exposure to external stimuli. We propose a digital fabrication process via the 3D-printing of shape-changing materials, accompanied by a computational design workflow in which the geometry of a crease pattern is correlated with the printing toolpaths and the layup of stimuli-responsive and passive materials to achieve a target shape-change. We demonstrate our method by producing multiple prototypes and documenting their shape-change upon actuation. Lastly, we explore the functional and performance benefits of self-shaping curved folding under three application scenarios relevant to the field of industrial design and architecture.

Zusammenfassung

In this contribution, a novel local, node-based time step estimate for reciprocal mass matrices with improved sharpness is proposed. Reciprocal mass matrices are sparse matrices used in explicit dynamics that allow computation of the nodal acceleration from the total force vector. They aim for higher critical time steps or/and accuracy than the lumped mass matrix approximation. Since the eigenvalue inequality by Fried does not hold for reciprocal mass matrices, element-based estimates may be not conservative and are consequently inadequate. Therefore, nodal time step estimates are preferred for reciprocal mass matrices. A nodal time step estimate requires an eigenvalue bound using row or/and column information associated with the nodal degrees of freedom. Recently, an efficient estimate was proposed that uses Gershgorin’s circle theorem and a corresponding bound. This estimate is always conservative but it usually leaves a 10-30% gap to the true eigenvalue. This raises the question whether a sharper estimate may be constructed by using a different eigenvalue bound. A recent paper by Cottereau and Sevilla compares five eigenvalue bounds for a diagonal mass matrix with spectral finite elements and indicates that the Ostrowski’s bound is the sharpest bound for most of the considered cases. In this contribution, the latter estimate is further developed for the case of reciprocal mass matrices and an extra improvement via similarity transformation for elements with rotary degrees of freedom is discussed. Finally, the estimate is tested for a set of common finite elements in explicit dynamics.

Zusammenfassung

Beyond the shell model of Reissner and Mindlin, which is available in LS-DYNA® for example in shell ELFORM=2/16, there have been many developments in the field of 3d-shell models in recent years. 3d-shell models can be beneficial in sheet metal forming simulations because they allow for three-dimensional stress states. 3d-shell elements are available in LS-DYNA®, e.g. ELFORM=25. In the doctoral dissertation of Fleischer it has been found that under certain conditions this element formulation suffers from an artificial stiffening effect. Although this finding dates back to 2009, this phenomenon has remained unexplained so far. In this contribution, the authors explain the reason for this stiffening effect and show a possibility to remove it. Moreover, an outlook on the development of higher order shell models for sheet metal forming simulation is given.

Zusammenfassung

In this contribution, coupled, parameterized second order systems are considered where the coupled, parameterized system is derived from the assembly of several parameterized component models. Two approaches for the Parametric Model Order Reduction of such coupled systems are presented and compared in a reduced order shape optimization example. In the first approach, the coupled, parameterized system is derived by coupling the parameterized, full order component models. Then, Parametric Model Order Reduction is executed for the coupled system. In the second approach, the parameterized, component models are first reduced independently of their actual mounting situation. Afterwards, the parameterized, reduced order component models are coupled to derive the parameterized, reduced order system model. It is shown that the first approach yields smaller parameterized, reduced order system models. However, the second approach allows to reuse and to recombine the parameterized, reduced order component models arbitrarily. It therefore introduces more flexibility in the modeling process, enabling for example a toolbox based optimization with parameterized, reduced order models.

Zusammenfassung

In this contribution a class of formulations for beams, plates and shells is presented, which intrinsically avoids locking, independent of the utilized discretization scheme. The key idea is the reparametrization of the kinematic equations to avoid locking on theory level – prior to discretization. Thus, the resulting formulations are locking‐free for any equal‐order interpolation. As demonstrator, we present both mixed and primal concepts for Timoshenko beams in both weak and strong form, as well as their theoretical relationships. Besides a weak form Galerkin‐type solution using B‐Splines, we show the generality of the presented concepts by employing isogeometric collocation based on the corresponding Euler‐Lagrange equations of the boundary value problem. The quality of both stress resultants and displacements is investigated. Although the underlying concept addresses beams, plates and shells, the present contribution illustrates the methodology for the Timoshenko beam.

Zusammenfassung

Within the collaborative research center Biological Design and Integrative Structures (CRC TRR 141), a research team of biologists, architects and engineers from Freiburg, Tübingen and Stuttgart is working on the development of biomimetic and bioinspired structures for implementation in architecture and building construction. One of the projects in this research center deals with the kinematics of planar, curved and corrugated plant surfaces as concept generators for deployable systems in architecture. It is an example for methods of engineering science at the interface between biology and architecture. The contribution will provide an insight into the process of analyzing the waterwheel plant Aldrovanda vesiculosa, a carnivorous plant that catches its prey by a quick closing movement of a snap trap consisting of two lobes attached to a midrib. At a first glance, the mechanism resembles the one of the famous Venus flytrap; however, it appears to be quite different from a mechanical point of view. In fact, a key aspect in the research presented here is the development of mechanical models and performing corresponding finite element analyses of the plant with the aim to obtain a better understanding of the compliant mechanism of Aldrovanda vesiculosa and its actuation. The latter is related to a change in turgor pressure in a so-called motor zone, adjacent to the midrib, possibly combined with prestressing effects. Apart from this scientific contribution to technical biology or reverse biomimetics, the abstraction of the trapping movement and its implementation in a façade element (Flectofold) as an example of biomimetic architectural design are briefly described.

Zusammenfassung

This paper presents results of the investigation of two biological role models, the shield bug (Graphosoma italicum) and the carnivorous Waterwheel plant (Aldrovanda vesiculosa). The aim was to identify biological construction and movement principles as inspiration for technical, deployable systems. The subsequent processes of abstraction and simulation of the movement and the design principles are summarized, followed by results on the mechanical investigations on various combinations of fibers and matrices with regard to taking advantage of the anisotropy of fiber-reinforced plastics (FRPs). With the results gained, it was possible to implement defined flexible bending zones in stiff composite components using one composite material, and thereby to mimic the biological role models. First small-scale demonstrators for adaptive façade shading systems – Flectofold and Flexagon – are proving the functionality.

Zusammenfassung

Part I deals with material modelling of woven fabric membranes. Due to their structure of crossed yarns embedded in coating, woven fabric membranes are characterised by a highly nonlinear stress-strain behaviour. In order to determine an accurate structural response of membrane structures, a suitable description of the material behaviour is required. A linear elastic orthotropic model approach, which is current practice, only allows a relative coarse approximation of the material behaviour. The present work focuses on two different material approaches: A first approach becomes evident by focusing on the meso-scale. The inhomogeneous, however periodic structure of woven fabrics motivates for microstructural modelling. An established microstructural model is considered and enhanced with regard to the coating stiffness. Secondly, an anisotropic hyperelastic material model for woven fabric membranes is considered. By performing inverse processes of parameter identification, fits of the two different material models w.r.t. measured data from a common biaxial test are shown. The results of the inversely parametrised material models are compared and discussed.

Zusammenfassung

The higher inter-element continuity of the Isogeometric Analysis (IGA) applying NURBS functions for geometry as well as mechanics opens up new possibilities in the analysis of thin-walled structures, i.e. beams, plates and shells. An important advantage is the straightforward implementation of classical theories, which require C1-continuity, e. g. Kirchhoff-Love shell formulations. Based on these "simplest" models shear deformable theories, introducing Timoshenko and Reissner-Mindlin kinematics, are formulated in a hierarchic manner. In contrast to using total rotations the present formulations introduce incremental transverse shear rotations as primary variables. This reparametrization of the kinematic equations can be established in several different fashions, which is addressed in this contribution. All parametrizations have in common, that they lead to shear deformable beam, plate and shell formulations being intrinsically free from transverse shear locking. This is a remarkable feature since the spectrum of different smooth discretization schemes in IGA and other fields of computational shell analysis is continuously growing and the proposed hierarchic shell formulations are locking-free, independent of the underlying discretization.

Zusammenfassung

The higher inter-element continuity of the Isogeometric Analysis (IGA) applying NURBS functions for geometry as well as mechanics opens up new possibilities in the analysis of thin-walled structures, i.e. beams, plates and shells. The contribution addresses the straightforward implementation of classical theories requiring C1-continuity, such as the Euler-Bernoulli beam and Kirchhoff-Love shell theory. Based on these “simplest” models shear deformable theories, introducing Timoshenko and Reissner-Mindlin kinematics, are formulated in a hierarchic manner. In contrast to the usual Finite Element concept using total rotations the present model picks up traditional formulations introducing incremental rotations as primary variables. Furthermore an alternative version is discussed with a split of the displacements into bending and transverse shear parts. Both hierarchic concepts can be easily extended to 3D–shell models. The key aspect of this alternative parameterization is the complete a-priori removal of the transverse shear locking and curvature thickness locking (in the case of 3D-shells).

Zusammenfassung

Um dynamische Finite-Elemente-Berechnungen mit expliziter Zeitintegration zu beschleunigen, ist es in der Praxis üblich, Massenskalierung anzuwenden. Damit soll die kritische Zeitschrittweite erhöht werden ohne maßgeblich an Genauigkeit in den entscheidenden niederfrequenten Moden zu verlieren. Bei der konventionellen Massenskalierung (CMS) wird künstliche Masse zu den Diagonaltermen der diagonalisierten Massenmatrix addiert und die Diagonalform der Massenmatrix bleibt erhalten. CMS wird gewöhnlich auf eine geringe Anzahl kleiner oder steifer Elemente angewandt, deren hohe Eigenfrequenzen die kritische Zeitschrittweite begrenzen. Dabei wird allerdings die Trägheit der Struktur erhöht, was zu unphysikalischen Effekten führen kann. Mit einer sogenannten selektiven Massenskalierung kann wenigstens die translatorische Trägheit (d.h. der Impuls bei gleichmäßiger Anfangsgeschwindigkeit) erhalten werden, allerdings auf Kosten von Nebendiagonaltermen in der Massenmatrix. Diese Methode lässt sich gleichmäßig auf die gesamte Struktur anwenden und hat geringere unphysikalische Nebeneffekte. Bislang werden skalierte Massenmatrizen rein algebraisch, z.B. steifigkeitsproportional konstruiert. Die Auswahl an Skalierungs-Templates ist beschränkt und ihnen liegt keine konsistente Formulierung zugrunde. In diesem Artikel werden variationelle Methoden zur selektiven Massenskalierung vorgestellt, die nicht nur mathematisch konsistent sind, sondern es auch erlauben, gezielt bestimmte Eigenschaften wie die Erhaltung der Trägheit, Reduktion der höchsten Frequenzen und Genauigkeit bei den niedrigen Frequenzen einzustellen. Die Leistungsfähigkeit der Methode wird an numerischen Beispielen mit Tetraeder- und Hexaeder-Elementen demonstriert.

Zusammenfassung

In this paper a two-dimensional discrete element method with rigid, polygonal particles is used to model material failure of granular as well as quasi-brittle materials. Different models for soft contact as well as cohesion between the particles are presented. The capabilities of the method are demonstrated simulating simplistic granular model materials as well as complex concrete specimens with an artificial microstructure.

Zusammenfassung

In many areas of mechanical engineering contact problems of thin-walled structures play a crucial role. Car crash tests and incremental sheet metal forming can be named as examples. But also in civil engineering, for instance when determining the moment-rotation characteristics of a bolted beam-column joint, contact occurs. Effective simulation of these and other contact problems, especially in three-dimensional non-linear implicit structural mechanic is still a challenging task. Modelling of those problems needs a robust method, which takes the thin-walled character and dynamic effects into account. We use a segment-to-segment approach for discretization of the contact and introduce Lagrange Multipliers, which physically represent the contact pressure. The geometric impenetrability condition is formulated in a weak, integral sense. Choosing dual shape functions for the interpolation of the Lagrange Multipliers, we obtain decoupled nodal constraint conditions. Combining this with an active set strategy, an elimination of the Lagrange multipliers is easily possible, so that the size of the resulting system of equations remains constant. Discretization in time is done with the implicit Generalized--$\alpha$ Method and the Generalized Energy-Momentum Method. Using the ”Velocity-Update” Method, the total energy is conserved for frictionless contact. Various examples show the performance of the presented strategies.

Zusammenfassung

Numerical simulation of large scale computational fluid dynamics (CFD) and fluid-structure interaction (FSI) problems is still today a very challenging task. The correct modeling of fluid flow, governed by the instationary incompressible Navier-Stokes equations, and the nonlinear structural behavior are challenges of their own. In addition coupling of both physical fields introduces further requirements on stability and efficiency of the involved algorithms. For this class of problems computing time is still a limiting factor for size and complexity of the problem. Especially for FSI simulations the necessary iterative coupling schemes dramatically increase the required computing time. Here, the use of advanced coupling strategies, reducing either the time needed for one iteration or the number of iterations, can considerably speed up the simulation. We will introduce a class of coupling schemes enhanced by a coarse grid solution to reduce calculation time and accelerate convergence. In addition, the single fields – especially the fluid – demand high efficiency of the solution algorithm. Here, assembly of the element matrices and in particular the iterative solver for the global system of linear equations are the most time consuming parts of the computational process. Very often these algorithms only use a small fraction of the available computer power in scientific codes. Therefore it is highly advisable to take a closer look at the efficiency of algorithms and improve them to make the best out of the available computer power. We will present approaches to significantly increase efficiency in the assembly and solution part of a finite element code. Here, the special features of vector super computers will be exploited.

Zusammenfassung

The present work deals with the comparison of three-dimensional (3d) finite element analysis of thin-walled structures to computations based on reduced, two-dimensional (2d) models which a priori satisfy the plane stress assumption. We apply a plasticity-based non-linear softening material model for concrete1 to simple four-node 2d plane stress elements and to a 7-parameter 3d shell formulation. Numerical results are compared to experimental data for an L-shaped panel.

Zusammenfassung

Stabilized finite element methods have been developed mainly in the context of Computational Fluid Dynamics and have shown to be able to add stability to previously unstable formulations in a consistent way. In this contribution a deformation dependent stabilization technique, conceptually based on the above mentioned developments in the CFD area, is developed for Solid Mechanics to cure the well known Enhanced Assumed Strain (EAS) method from artificial instabilities (hourglass modes) that have been observed in the range of large compressive strains. In investigating the defect of the original formulation the dominating role of the kinematic equation as cause for the instabilities is revealed. This observation serves as key ingredient for the design of the stabilizing term, introduced on the level of the variational equation. A proper design for the stabilization parameter is given based on a mechanical interpretation of the underlying defect as well as of the stabilizing action. This stabilizing action can be thought of an additional constraint, introduced into the reparametrized Hu–Washizu functional in a least square form, together with a deformation dependent stabilization parameter. Numerical examples show the capability of this approach to effectively eliminate spurious hourglass modes, which otherwise may appear in the presence of large compressive strains, while preserving the advantageous features of the EAS method, namely the reduction of the stiffness for an ‘in–plane bending’ mode, i.e. when plane stress elements are used in a bending situation.

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

Concrete double-curved shell constructions have been used in architectural design and building constructions since the beginning of the twentieth century. Although monolithic shells show a high stiffness as their geometry transfers loads through membrane forces, they have been mostly replaced by the more cost-efficient lattice systems. As lattice systems are covered by planar glass or metal panes, they neither reach the structural efficiency of monolithic shells, nor is their architectural elegance reflected in a continuous curvature. The shells of sand dollars’ – highly adapted sea urchins – combine a modular and multi-plated shell with a flexible, curved as well as smooth design of a monolithic construction. The single elements of the sand dollars’ skeleton are connected by calcite protrusions and can be additionally supported by organic fibres. The structural efficiency of the sea urchin’s skeleton and the principles behind them can be used for innovations in engineering sciences and architectural design while, at the same time, they can be used to illustrate the biological adaptations of these ecologically important animals within their environments. The structure of the sand dollar’s shell is investigated using modern as well as established imaging techniques such as x-ray micro-computed tomography (µCT), scanning electron microscopy and various optical imaging techniques. 3D models generated by µCT scans are the basis for Finite Element Analysis of the sand dollar’s shell to identify possible structural principles and to analyse their structural behaviour. The gained insights of the sand dollar’s mechanical properties can then be used for improving the state-of-the-art techniques of engineering sciences and architectural design.

Zusammenfassung

We present ideas and concepts towards defining a common framework unifying abstract metrics in order to quantify key features of technical load-bearing structures and biological systems. Our aim is to transfer biological concepts to technical systems at this abstract level rather than on the basis of their outward appearance or actual functionality. This means that the biological concept generators for load-bearing structures do not have to be load-bearing structures themselves but may instead achieve rather different functionalities. We intend to carry out this transference by generalizing graph-based abstractions of both technical and biological worlds to allow comparisons to be made at an abstract level. We focus in particular on the intrinsically competing aims of optimality versus multi-functionality and robustness. In this review, we present initial attempts towards defining suitable quantitative measures for robustness to serve as a common ground for studying technical systems and biological systems simultaneously. We discuss generic properties of a ubiquitous signalling network motif and potential relationships to a minimal model for a robust truss structure. These case studies suggest that topological complexity can serve as a common source for a design that is insensitive to perturbations and thus robust in the measures of both worlds.

Zusammenfassung

We present ideas and concepts towards defining a common framework unifying abstract metrics in order to quantify key features of technical load-bearing structures and biological systems. Our aim is to transfer biological concepts to technical systems at this abstract level rather than on the basis of their outward appearance or actual functionality. This means that the biological concept generators for load-bearing structures do not have to be load-bearing structures themselves but may instead achieve rather different functionalities. We intend to carry out this transference by generalizing graph-based abstractions of both technical and biological worlds to allow comparisons to be made at an abstract level. We focus in particular on the intrinsically competing aims of optimality versus multi-functionality and robustness. In this review, we present initial attempts towards defining suitable quantitative measures for robustness to serve as a common ground for studying technical systems and biological systems simultaneously. We discuss generic properties of a ubiquitous signalling network motif and potential relationships to a minimal model for a robust truss structure. These case studies suggest that topological complexity can serve as a common source for a design that is insensitive to perturbations and thus robust in the measures of both worlds.

Zusammenfassung

Plant movements can inspire deployable systems for architectural purposes which can be regarded as ideal solutions combining resilient bio-inspired functionality with elegant natural motion. Here, we first give a concise overview of various compliant mechanisms existing in technics and in plants. Then we describe two case studies from our current joint research project among biologists, architects, construction engineers and materials scientists where the aesthetic movements of such role models from the plant kingdom are analysed, abstracted and implemented in bioinspired technical structures for sustainable architecture. Both examples are based on fast snapping movements of traps of carnivorous plants. The Waterwheel plant (Aldrovanda vesiculosa) captures prey underwater and the Venus flytrap (Dionaea muscipula) snaps in the air. We present results on the motion principles gained by quantitative biomechanical and functional-morphological analyses as well as their simulation and abstraction by using e.g. Finite Element Methods. The Aldrovanda mechanism was successfully translated into a similarly aesthetic and functional technical structure, named Flectofold, which exists in a prototype state. The Flectofold can be used as a façade shading element for complex curved surfaces as existing in modern architecture.

Zusammenfassung

The contribution describes a two-dimensional discrete element method with polygonal particles in a two-dimensional setting allowing the simulation of granular as well as quasi-brittle material. Different models for soft contact as well as cohesion between the particles are presented. Emphasis is put on the specific features of the polygonal particles. Simulations are compared to results of small scale experiments with regular particles of steel nuts. In addition the capabilities of the method are demonstrated simulating complex concrete specimens with a distinct heterogeneous microstructure.

Zusammenfassung

The 7-parameter shell model as proposed by Büchter and Ramm (1992) is an extension of conventional shear deformation theories with five degrees of freedom. Application of this model is especially sensible if complete three-dimensional constitutive laws ought to be applied allowing also to solve problems involving large deformations and large strains. Based on a mixed formulation the seventh degree of freedom can be eliminated on the element level. Thus, the numerical effort is only slightly larger compared to `usual' shell elements. The model can consequently also be utilized for analyses of such shell structures, where a conventional shell formulation would be sufficient. Büchter and Ramm (1992) describe the 7-parameter shell model along with a finite element formulation. Here, the seventh degree of freedom is introduced on the element level by means of a hybrid-mixed formulation. In the present work the 7-parameter model is derived independent from a finite element formulation. In this context it can be interpreted as semi-discretization of the shell continuum in thickness direction. The decisive difference to most of the conventional shell theories is that this discretization is based on a multifield variational formulation. By this procedure a system of partial differential equations can be obtained, describing the 7-parameter model as a two-dimensional, continuous theory with seven kinematical degrees of freedom per material point of the reference surface. It is also intended to give a physical interpretation of the kinematic and static variables appearing in the model. Here, the main emphasis is put on those quantities, which do not show up in a conventional 5-parameter formulation. The investigations provide some insight into the mechanical behavior of the model. For the linear part of the transverse shear strains a new shear correction factor is proposed, which can reduce the error with respect to the three-dimensional solution in membrane dominated situations. It is shown that the 7-parameter model is `optimal' concerning the number of kinematic and static variables involved. This means that exactly those components are involved which are necessary for a complete three-dimensional material description. Finally, a concept for the formulation of efficient finite elements for the 7-parameter model is presented. Here, established methods from the literature are combined with own developments. A special feature of the proposed concept is that a unified formulation for triangular and rectangular elements of arbitrary polynomial order is obtained. In addition, an improvement in the treatment of shells with kinks is proposed. In the course of the present study the concept is realized for linear and quadratic triangular and rectangular elements. The features of the proposed elements are investigated in numerical experiments, including both linear and geometrically and materially non-linear problems.