Добірка наукової літератури з теми "Solid-beam element"

For rational seismic structural response analysis of a Reinforced Concrete (RC) structure, this paper presents a solid element in which a sophisticated concrete constitutive relation and cracking functionality are implemented. Hybrid finite element modeling that uses solid and beam elements for concrete and steel rebar is proposed, made tougher with a method of constructing the hybrid finite element. Well-balanced modeling is possible by first generating beam elements for the steel rebars and then generating solid elements for the concrete with nodes of the beam elements being shared by the solid element. A numerical experiment was carried out for a RC column subjected to unilateral loading, in order to examine the potential applicability of the hybrid finite element modeling. The computed results are compared with the experimental data, and the nonlinear relation between the displacement and reaction force is reproduced to some extent.

According to the standard Specification for Design of Hydraulic Tunnels (DL/T 5195-2004), the free-flow tunnel lining structure should be calculated with beam element of finite element method that based on structural mechanics. However, the practical calculation shows that when the lining structure reaches a certain thickness, the beam element calculation results are no longer accurate. Combining with the engineering example, stress and internal force of lining structure with different thickness were calculated by using beam3 beam element and the solid65 element respectively in frame beam analysis. Differences analysis shows that the solid element is better than beam element in calculation. The influence of solid elements grid size on the result accuracy was conducted, and used to amend the calculation result of the solid element, which provides a certain reference on choosing the right element in the similar projects or structure simulation.

Numerical study of the effect of spot weld pitch with respect to top-hat crash box crushing characteristics are presented in this paper. Belytschko-Lin-Tsay shell element was used for modeled columns wall with Piecewise Linear Plasticity material model. The impactor was modeled using hexahedral solid elements and assumed as a rigid body. Spot weld joints used to connect mild steel St37 plates of the columns were modeled using beam element and solid element. Impact characteristics related to the spot weld pitch and models were evaluated from simulation results in the form of crushing force vs axial deformation of the column. The results show that spot weld pitch does not significantly affect the crushing characteristics for top-hat crash box with beam element spot weld model, while solid element spot weld model show otherwise. The difference between beam element spot weld model and solid element spot weld model is larger at spot weld pitch 0.50H – H, and tend to close at higher spot weld pitch. Top-hat crash box model becomes stiffer with solid element applied as spot weld model.

A number of engineering applications involve contact with bodies modeled using specialized theories of solid mechanics like beams or shells. While computational models for contact in 2D and 3D solid mechanics have been extensively developed in the literature, problems involving contact with beams or shells have received less attention. When modeling contact between a solid body represented with beam or shell theory and a domain discretized with solid finite elements, the contact model faces the typical challenges of enforcing geometric compatibility and the transfer of a complete pressure field along the contact interface, with the added complications stemming from the different underlying mathematical formulations and finite element discretizations in the connecting domains. Resultant-based beam and shell theories do not provide direct estimates of surface tractions, therefore rendering the issue of pressure transfer on beam–solid and shell–solid interfaces more problematic. In the absence of specialized contact formulations for solid–beam and solid–shell interfaces, contact models have relied almost exclusively on the Node-To-Surface (NTS) geometric compatibility approach. This formulation suffers from well-known drawbacks, including instability, surface locking and incomplete pressure fields on the interface. The NTS approach, however, remains the method most readily applicable to contact with beam or shell elements among the vast variety of available methods for computational contact modeling using finite elements. The goal of this paper is to bridge the gap in the literature on coupling domains with beam and solid finite element discretizations. We propose an interface formulation for beam–solid interfaces that ensures the transfer of a complete pressure field while enforcing geometric compatibility using standard NTS constraints. The formulation uses a stabilization approach, based on a special form of the Discontinuous Galerkin method, to enforce weak continuity between the stress fields on the solid side of the interface, and the moment and shear resultants in the contacting beam. We show that the proposed formulation is a robust approach for satisfying compatibility constraints while ensuring the transfer of a complete pressure field on beam–solid finite element interfaces that can be used with bilinear and quadratic interpolations in the solid, and Euler or Timoshenko formulations for the beam.

In this paper, three kinds of FEM models, i.e., the truss element model, the beam element model and the mixed beam-solid element model are utilized to simulate the full-scale field test of transmission tower. Based on Abaqus software, the geometric and material nonlinearity of the structure is considered. Comparing the numerical results with test data, it is found that the truss element model is no longer suitable and the mixed beam-solid element model is more accurate than the beam element model. Thus, using solid element to discrete the key nodes of the tower can greatly enhance the accuracy and reliability of the numerical prediction.

This paper describes the effect of beam offsetting in finite element calculations. The effect is evaluated by considering two case studies involving beams, in which finite element analysis is performed with solid elements and with shell elements. It is seen that, under certain conditions, ignoring the beam offset can lead to erroneous results. Although the beam offsetting feature is available in most commercial codes, it is not always well documented.

Vibration-based diagnostic methods are used for the detection of the presence of cracks in beams and other structures. To simulate such a beam with an edge crack, it is necessary to model the beam using finite elements. Cracked beam finite elements, being one-dimensional, cannot model the stress field near the crack tip, which is not one-dimensional. The change in neutral axis is also not modeled properly by cracked beam elements. Modeling of such beams using two-dimensional plane elements is a better approximation. The best alternative would be to use three-dimensional solid finite elements. At a sufficient distance away from the crack, the stress field again becomes more or less one-dimensional. Therefore, two-dimensional plane elements or three-dimensional solid elements can be used near the crack and one-dimensional beam elements can be used away from the crack. This considerably reduces the required computational effort. In the present work, such a coupling of dissimilar elements is proposed and the required transition element is formulated. A guideline is proposed for selecting the proper dimensions of the transition element so that accurate results are obtained. Elastic deformation, natural frequency and dynamic response of beams are computed using dissimilar elements. The finite element analysis of cracked rotating shafts is complicated because of the fact that elastic deformations are superposed on the rigid-body motion (rotation about an axis). A combination of three-dimensional solid elements and beam elements in a rotating reference is proposed here to model such rotors.

The critical speeds of all kinds of high-speed rotors must be calculated in project so that all rotors can work in the safe range of speeds and avoid resonance. A single-span-two-disc rotor system is investigated by using finite element method based on ANSYS. Natural frequencies are calculated by using beam, solid, mass, shell, beam-solid, beam-shell elements and critical speeds are obtained from Campbell diagram. Finally, the first and second critical speeds are measured by a test rig. Comparison of theoretical and experimental results is performed to assess the accuracy of different element combining forms.

This paper focuses on the latest development of a solid hexahedron element for composite delamination analysis. The 8-node solid is derived from a 20-node hexahedron. It is transformed into two physical independent 4-node shell elements according to the propagation of delamination process within the element. This transformation is driven by a transfer and damage laws that are defined by calibrating the element with a FE modeling for a double cantilever beam (DCB) test. According to the position of the crack in the element, one parameter defines the degradation of the transverse properties at the Gauss point as well as the transfer of the volume element towards the bi-plate formulation. A sensitivity study of the element is presented. A global-local finite element approach coupled with the traditional virtual crack closure technique (VCCT) method allows to calculate the energy release rates and to control the propagation of cracking in the element. This method is validated by comparison between conventional FE models and experimental tests [DCB, and end load split (ELS)]. Experimental asymmetric double cantilever beam (ADCB) test is carried out and modelled using the developed element. The numerical simulation properly correlates with the experimental results.

La méthode des éléments finis est couramment utilisée depuis les années 1970 pour prédire le comportement de structures telles que des automobiles, des avions, des machines, des ponts ou des bâtiments. Les choix de modélisation sont essentiels afin de construire un modèle représentatif, tout en maîtrisant le nombre de degrés de liberté. De nombreux travaux ont cherché à optimiser le modèle d’un point de vue du maillage en proposant notamment des techniques de maillage adaptatif. En revanche, concernant le choix de théorie, peu de travaux ont été menés pour obtenir un modèle éléments finis optimal. Dans le contexte de l’analyse linéaire statique et vibratoire, cette thèse a pour objectif de proposer une méthodologie de modélisation adaptative afin d’obtenir un modèle éléments finis optimal d’un point de vue du choix de théorie. Le maillage, composé uniquement d’éléments volumiques, est raffiné à chaque itération de la méthodologie. Un choix approprié entre les théories de poutre, de coque et d’élasticité 3D est effectué sur chaque élément fini à l’issue de chaque analyse. Dans les zones où les théories de poutre ou de coque sont pertinentes, des champs de déplacements spécifiques sont appliqués. De nouvelles approches volume-coque et volume-poutre, basées respectivement sur la théorie des coques et la théorie des poutres, sont développées à cet effet. Pour chacune de ces approches, des théories de premier ordre et d’ordre supérieur sont proposées. Dans ces zones l’application de relations cinématiques aux noeuds du maillage volumique, se traduisant par des équations linéaires, mène à une réduction du nombre de degrés de liberté. Dans le cadre de l’analyse statique et vibratoire, plusieurs exemples sont traités pour évaluer la méthodologie de modélisation adaptative. Les résultats numériques obtenus sont toujours très proches de ceux d’un modèle volumique de référence et la modélisation adaptative mène à une réduction significative de la taille du modèle
The finite element method has been widely used since the 1970s to predict the behavior of structures such as automobiles, airplanes, machines, bridges or buildings. The modeling choices are essential to build a representative model and control the number of degrees of freedom. Many works have sought to optimize the model from a mesh point of view, namely by proposing adaptive meshing techniques. On the other hand, concerning the theory choice, seldom work has been carried out to obtain an optimal finite element model. In the context of static and vibratory linear analysis, this thesis aims to propose an adaptive modeling methodology in order to obtain an optimal finite element model from the theory choice point of view. The mesh, composed only of solid elements, is refined at each iteration of the methodology. An appropriate choice between beam, shell and 3D elasticity theories is made on each finite element of the model at each analysis. In areas where beam or shell theories are relevant, specific displacement fields are applied. New solid-shell and solid-beam approaches, based respectively on shell theory and beam theory, have been developed for this purpose. For each of these two approaches, first-order and higher-order theories are proposed. In these areas, the application of kinematic relations at nodes of the solid mesh, by using linear equations, leads to a reduction of the number of degrees of freedom. In the context of static and vibratory analysis, several examples are treated to evaluate the methodology of adaptive modeling. The numerical results obtained are always very close to those of a reference solid model and the adaptive modeling method leads to a significant reduction in the model size

"Mammalian skeletal muscle is a very complicated biological structure to model due to its non-homogeneous and non-linear material properties as well as its complex geometry. Finite element discrete one-dimensional Hill-based elements are largely used to simulate muscles in both passive and active states. There are, however, several shortfalls to utilizing one-dimensional elements, such as the impossibility to represent muscle physical mass and complex lines of action. Additionally, the use of one-dimensional elements restricts muscle insertion sites to a limited number of nodes causing unrealistic loading distributions in the bones. The behavior of various finite element muscle models was investigated and compared to manually calculated muscle behavior. An improved finite element muscle model consisting of shell elements and Hill-based contractile truss elements in series and parallel was ultimately developed. The muscles of the thigh were then modeled and integrated into an existing 50th percentile musculo-skeletal model of the knee-thigh-hip complex. Impact simulations representing full frontal car crashes were then conducted on the model and the pre-loading effects from active thigh muscles on the femur were investigated and compared to cadaver sled test data. It was found that the active muscles produced a pre-load femoral axial force that acted to slightly stabilize the rate of stress intensification on critical stress areas on the femur. Additionally, the active muscles served to direct the distribution of stress to more concentrated areas on the femoral neck. Furthermore, the pre-load femoral axial force suggests that a higher percentage of injuries to the knee-thigh-hip complex may be due to the effects of active muscles on the femur. "

Thin and slender structures are widely occurring both in nature and in human creations. Clever geometries of thin structures can produce strong constructions while requiring a minimal amount of material. Computer modeling and analysis of thin and slender structures have their own set of problems, stemming from assumptions made when deriving the governing equations. This thesis deals with the derivation of numerical methods suitable for approximating solutions to problems on thin geometries. It consists of an introduction and four papers. In the first paper we introduce a thread model for use in interactive simulation. Based on a three-dimensional beam model, a corotational approach is used for interactive simulation speeds in combination with adaptive mesh resolution to maintain accuracy. In the second paper we present a family of continuous piecewise linear finite elements for thin plate problems. Patchwise reconstruction of a discontinuous piecewise quadratic deflection field allows us touse a discontinuous Galerkin method for the plate problem. Assuming a criterion on the reconstructions is fulfilled we prove a priori error estimates in energy norm and L2-norm and provide numerical results to support our findings. The third paper deals with the biharmonic equation on a surface embedded in R3. We extend theory and formalism, developed for the approximation of solutions to the Laplace-Beltrami problem on an implicitly defined surface, to also cover the biharmonic problem. A priori error estimates for a continuous/discontinuous Galerkin method is proven in energy norm and L2-norm, and we support the theoretical results by numerical convergence studies for problems on a sphere and on a torus. In the fourth paper we consider finite element modeling of curved beams in R3. We let the geometry of the beam be implicitly defined by a vector distance function. Starting from the three-dimensional equations of linear elasticity, we derive a weak formulation for a linear curved beam expressed in global coordinates. Numerical results from a finite element implementation based on these equations are compared with classical results.

Research is performed to assess the viability of applying the least squares model to one-dimensional heat transfer and Euler-Bernoulli Beam Theory problems. Least squares models were developed for both the full and mixed forms of the governing one-dimensional heat transfer equation along weak form Galerkin models. Both least squares and weak form Galerkin models were developed for the first order and second order versions of the Euler-Bernoulli beams. Several numerical examples were presented for the heat transfer and Euler- Bernoulli beam theory. The examples for heat transfer included: a differential equation having the same form as the governing equation, heat transfer in a fin, heat transfer in a bar and axisymmetric heat transfer in a long cylinder. These problems were solved using both least squares models, and the full form weak form Galerkin model. With all four examples the weak form Galerkin model and the full form least squares model produced accurate results for the primary variables. To obtain accurate results with the mixed form least squares model it is necessary to use at least a quadratic polynominal. The least squares models with the appropriate approximation functions yielde more accurate results for the secondary variables than the weak form Galerkin. The examples presented for the beam problem include: a cantilever beam with linearly varying distributed load along the beam and a point load at the end, a simply supported beam with a point load in the middle, and a beam fixed on both ends with a distributed load varying cubically. The first two examples were solved using the least squares model based on the second order equation and a weak form Galerkin model based on the full form of the equation. The third problem was solved with the least squares model based on the second order equation. Both the least squares model and the Galerkin model calculated accurate results for the primary variables, while the least squares model was more accurate on the secondary variables. In general, the least-squares finite element models yield more acurate results for gradients of the solution than the traditional weak form Galkerkin finite element models. Extension of the present assessment to multi-dimensional problems and nonlinear provelms is awaiting attention.

In der vorliegenden Arbeit wird erstmals das QQDS-Magnetspektrometer für die höchstauflösende Ionenstrahlanalytik leichter Elemente am Helmholtz-Zentrum Dresden-Rossendorf umfassend vorgestellt. Zusätzlich werden sowohl alle auf die Analytik Einfluss nehmenden Parameter untersucht als auch Methoden und Modelle vorgestellt, wie deren Einfluss vermieden oder rechnerisch kompensiert werden kann. Die Schwerpunkte dieser Arbeit gliedern sich in fünf Bereiche. Der Erste ist der Aufbau und die Inbetriebnahme des QQDS-Magnetspektrometers, der zugehörige Streukammer mit allen Peripheriegeräten und des eigens für die höchstauflösende elastische Rückstoßanalyse entwickelten Detektors. Sowohl das umgebaute Spektrometer als auch der im Rahmen dieser Arbeit gebaute Detektor wurden speziell an experimentelle Bedingungen für die höchstauflösende Ionenstrahlanalytik leichter Elemente angepasst und erstmalig auf einen routinemäßigen Einsatz hin getestet. Der Detektor besteht aus zwei Komponenten. Zum einen befindet sich am hinteren Ende des Detektors eine Bragg-Ionisationskammer, die zur Teilchenidentifikation genutzt wird. Zum anderen dient ein Proportionalzähler, der eine Hochwiderstandsanode besitzt und direkt hinter dem Eintrittsfenster montiert ist, zur Teilchenpositionsbestimmung im Detektor. Die folgenden zwei Schwerpunkte beinhalten grundlegende Untersuchungen zur Ionen-Festkörper-Wechselwirkung. Durch die Verwendung eines Magnetspektrometers ist die Messung der Ladungszustandsverteilung der herausgestreuten Teilchen direkt nach einem binären Stoß sowohl möglich als auch für die Analyse notwendig. Aus diesem Grund werden zum einen die Ladungszustände gemessen und zum anderen mit existierenden Modellen verglichen. Außerdem wird ein eigens entwickeltes Modell vorgestellt und erstmals im Rahmen dieser Arbeit angewendet, welches den ladungszustandsabhängigen Energieverlust bei der Tiefenprofilierung berücksichtigt. Es wird gezeigt, dass ohne die Anwendung dieses Modells die Tiefenprofile nicht mit den quantitativen Messungen mittels konventioneller Ionenstrahlanalytikmethoden und mit der Dickenmessung mittels Transmissionselektronenmikroskopie übereinstimmen, und damit falsche Werte liefern würden. Der zweite für die Thematik wesentliche Aspekt der Ionen-Festkörper-Wechselwirkung, sind die Probenschäden und -modifikationen, die während einer Schwerionen-bestrahlung auftreten. Dabei wird gezeigt, dass bei den hier verwendeten Energien sowohl elektronisches Sputtern als auch elektronisch verursachtes Grenzflächendurchmischen eintreten. Das elektronische Sputtern kann durch geeignete Strahlparameter für die meisten Proben ausreichend minimiert werden. Dagegen ist der Einfluss der Grenzflächendurchmischung meist signifikant, so dass dieser analysiert und in der Auswertung berücksichtigt werden muss. Schlussfolgernd aus diesen Untersuchungen ergibt sich für die höchstauflösende Ionenstrahlanalytik leichter Elemente am Rossendorfer 5-MV Tandembeschleuniger, dass die geeignetsten Primärionen Chlor mit einer Energie von 20 MeV sind. In Einzelfällen, wie zum Beispiel der Analyse von Bor, muss die Energie jedoch auf 6,5 MeV reduziert werden, um das elektronische Sputtern bei der notwendigen Fluenz unterhalb der Nachweisgrenze zu halten. Der vierte Schwerpunkt ist die Untersuchung von sowohl qualitativen als auch quantitativen Einflüssen bestimmter Probeneigenschaften, wie beispielsweise Oberflächenrauheit, auf die Form des gemessenen Energiespektrums beziehungsweise auf das analysierte Tiefenprofil. Die Kenntnis der Rauheit einer Probe an der Oberfläche und an den Grenzflächen ist für die Analytik unabdingbar. Als Resultat der genannten Betrachtungen werden die Einflüsse von Probeneigenschaften und Ionen-Festkörper-Wechselwirkungen auf die Energie- beziehungsweise Tiefenauflösung des Gesamtsystems beschrieben, berechnet und mit der konventionellen Ionenstrahlanalytik verglichen. Die Möglichkeiten der höchstauflösenden Ionenstrahlanalytik werden zudem mit den von anderen Gruppen veröffentlichten Komplementärmethoden gegenübergestellt. Der fünfte und letzte Schwerpunkt ist die Analytik leichter Elemente in ultradünnen Schichten unter Berücksichtigung aller in dieser Arbeit vorgestellten Modelle, wie die Reduzierung des Einflusses von Strahlschäden oder die Quantifizierung der Elemente im dynamischen Ladungszustandsnichtgleichgewicht. Es wird die Tiefenprofilierung von Mehrschichtsystemen, bestehend aus SiO2-Si3N4Ox-SiO2 auf Silizium, von Ultra-Shallow-Junction Bor-Implantationsprofilen und von ultradünnen Oxidschichten, wie zum Beispiel High-k-Materialien, demonstriert
In this thesis the QQDS magnetic spectrometer that is used for high resolution ion beam analysis (IBA) of light elements at the Helmholtz-Zentrum Dresden-Rossendorf is presented for the first time. In addition all parameters are investigated that influence the analysis. Methods and models are presented with which the effects can be minimised or calculated. There are five focal points of this thesis. The first point is the construction and commissioning of the QQDS magnetic spectrometer, the corresponding scattering chamber with all the peripherals and the detector, which is specially developed for high resolution elastic recoil detection. Both the reconstructed spectrometer and the detector were adapted to the specific experimental conditions needed for high-resolution Ion beam analysis of light elements and tested for routine practice. The detector consists of two compo-nents. At the back end of the detector a Bragg ionization chamber is mounted, which is used for the particle identification. At the front end, directly behind the entrance window a proportional counter is mounted. This proportional counter includes a high-resistance anode. Thus, the position of the particles is determined in the detector. The following two points concern fundamental studies of ion-solid interaction. By using a magnetic spectrometer the charge state distribution of the particles scattered from the sample after a binary collision is both possible and necessary for the analysis. For this reason the charge states are measured and compared with existing models. In addition, a model is developed that takes into account the charge state dependent energy loss. It is shown that without the application of this model the depth profiles do not correspond with the quantitative measurements by conventional IBA methods and with the thickness obtained by transmission electron microscopy. The second fundamental ion-solid interaction is the damage and the modification of the sample that occurs during heavy ion irradiation. It is shown that the used energies occur both electronic sputtering and electronically induced interface mixing. Electronic sputtering is minimised by using optimised beam parameters. For most samples the effect is below the detection limit for a fluence sufficient for the analysis. However, the influence of interface mixing is so strong that it has to be included in the analysis of the layers of the depth profiles. It is concluded from these studies that at the Rossendorf 5 MV tandem accelerator chlorine ions with an energy of 20 MeV deliver the best results. In some cases, such as the analysis of boron, the energy must be reduced to 6.5 MeV in order to retain the electronic sputtering below the detection limit. The fourth focus is the study of the influence of specific sample properties, such as surface roughness, on the shape of a measured energy spectra and respectively on the analysed depth profile. It is shown that knowledge of the roughness of a sample at the surface and at the interfaces for the analysis is needed. In addition, the contribution parameters limiting the depth resolution are calculated and compared with the conventional ion beam analysis. Finally, a comparison is made between the high-resolution ion beam analysis and complementary methods published by other research groups. The fifth and last focus is the analysis of light elements in ultra thin layers. All models presented in this thesis to reduce the influence of beam damage are taken into account. The dynamic non-equilibrium charge state is also included for the quantification of elements. Depth profiling of multilayer systems is demonstrated for systems consisting of SiO2-Si3N4Ox-SiO2 on silicon, boron implantation profiles for ultra shallow junctions and ultra thin oxide layers, such as used as high-k materials

碩士
國立成功大學
土木工程學系
89
ABSTRACT The development of interface element is an important subject for finite element method. It plays an important role to transit forces and displacement between different elements or materials. How to deal with the interface between solid elements and beam element by an efficient method is helpful for engineering. In the present years, some scholars devoted to establish some interface elements to connect two different elements, but most of them only can connect one by one. Those methods may transit forces and displacement precisely, but they are still inconvenient in mesh generation. We know Finite Element Method is an efficient and precise numerical method but its mesh generation is inconvenient especially when the mesh is complex. In this thesis we want to introduce an efficient method to connect beam element and solid elements. We hope this method not only get sufficient accuracy but also can reduce the procedure of mesh generation. In this thesis the procedure of this numerical method will be described. Both static and dynamic analysis will be discussed in this thesis, so this method can solve not only static but also dynamic problem. The advantages and constrains about this method will be discussed.

M. Tech. (Department of Mechanical Engineering, Faculty of Engineering and Technology), Vaal University of Technology
A project investigating the behaviour of an assembled preloaded rotor was performed for an M-Tech qualification in the Mechanical Engineering Department. Pre-Stressing of mechanical structures is widely applied to improve their performance, and in this project the behaviour of an assembled preloaded rotor was investigated. An Impact Test was done on the structure to see if induced stresses originated by a set of bolts which keep the discs system together, would influence the natural dynamic response or the rotor. Tendencies in the natural response were investigated. Analytical models like the Finite Element Beam model and the Solid Finite Element model were studied in order to find a represntative description of this particular structure's dynamic behaviour after pre-tension. From the experimental results it was apparent that the slenderness of the pre-tensioned sector influences the natural frequency. The solid finite element model appears to be the most applicable model to present the assembled rotor-disk system as a continuous shaft. Furthermore, modelling and predictions for a typical rotor and similar assembled structures can be generated from the findings.

In composite beam design, headed stud shear connectors are commonly used to transfer longitudinal shear forces across the steel¿concrete interface. Present knowledge of the load¿slip behavior and the shear capacity of the shear stud in composite beam are limited to data obtained from the experimental push-off tests. For this purpose, an effective numerical model using the finite element method to simulate the push-off test was proposed. The model has been validated against test results and compared with data given in the current Code of Practices, i.e., BS5950, EC4, and AISC. Parametric studies using this model were preformed to investigate variations in concrete strength and shear stud diameter. The finite element model provided a better understanding to the different modes of failure observed during experimental testing and hence shear capacity of headed shear studs in solid concrete slabs

In der vorliegenden Arbeit wird erstmals das QQDS-Magnetspektrometer für die höchstauflösende Ionenstrahlanalytik leichter Elemente am Helmholtz-Zentrum Dresden-Rossendorf umfassend vorgestellt. Zusätzlich werden sowohl alle auf die Analytik Einfluss nehmenden Parameter untersucht als auch Methoden und Modelle vorgestellt, wie deren Einfluss vermieden oder rechnerisch kompensiert werden kann. Die Schwerpunkte dieser Arbeit gliedern sich in fünf Bereiche. Der Erste ist der Aufbau und die Inbetriebnahme des QQDS-Magnetspektrometers, der zugehörige Streukammer mit allen Peripheriegeräten und des eigens für die höchstauflösende elastische Rückstoßanalyse entwickelten Detektors. Sowohl das umgebaute Spektrometer als auch der im Rahmen dieser Arbeit gebaute Detektor wurden speziell an experimentelle Bedingungen für die höchstauflösende Ionenstrahlanalytik leichter Elemente angepasst und erstmalig auf einen routinemäßigen Einsatz hin getestet. Der Detektor besteht aus zwei Komponenten. Zum einen befindet sich am hinteren Ende des Detektors eine Bragg-Ionisationskammer, die zur Teilchenidentifikation genutzt wird. Zum anderen dient ein Proportionalzähler, der eine Hochwiderstandsanode besitzt und direkt hinter dem Eintrittsfenster montiert ist, zur Teilchenpositionsbestimmung im Detektor. Die folgenden zwei Schwerpunkte beinhalten grundlegende Untersuchungen zur Ionen-Festkörper-Wechselwirkung. Durch die Verwendung eines Magnetspektrometers ist die Messung der Ladungszustandsverteilung der herausgestreuten Teilchen direkt nach einem binären Stoß sowohl möglich als auch für die Analyse notwendig. Aus diesem Grund werden zum einen die Ladungszustände gemessen und zum anderen mit existierenden Modellen verglichen. Außerdem wird ein eigens entwickeltes Modell vorgestellt und erstmals im Rahmen dieser Arbeit angewendet, welches den ladungszustandsabhängigen Energieverlust bei der Tiefenprofilierung berücksichtigt. Es wird gezeigt, dass ohne die Anwendung dieses Modells die Tiefenprofile nicht mit den quantitativen Messungen mittels konventioneller Ionenstrahlanalytikmethoden und mit der Dickenmessung mittels Transmissionselektronenmikroskopie übereinstimmen, und damit falsche Werte liefern würden. Der zweite für die Thematik wesentliche Aspekt der Ionen-Festkörper-Wechselwirkung, sind die Probenschäden und -modifikationen, die während einer Schwerionen-bestrahlung auftreten. Dabei wird gezeigt, dass bei den hier verwendeten Energien sowohl elektronisches Sputtern als auch elektronisch verursachtes Grenzflächendurchmischen eintreten. Das elektronische Sputtern kann durch geeignete Strahlparameter für die meisten Proben ausreichend minimiert werden. Dagegen ist der Einfluss der Grenzflächendurchmischung meist signifikant, so dass dieser analysiert und in der Auswertung berücksichtigt werden muss. Schlussfolgernd aus diesen Untersuchungen ergibt sich für die höchstauflösende Ionenstrahlanalytik leichter Elemente am Rossendorfer 5-MV Tandembeschleuniger, dass die geeignetsten Primärionen Chlor mit einer Energie von 20 MeV sind. In Einzelfällen, wie zum Beispiel der Analyse von Bor, muss die Energie jedoch auf 6,5 MeV reduziert werden, um das elektronische Sputtern bei der notwendigen Fluenz unterhalb der Nachweisgrenze zu halten. Der vierte Schwerpunkt ist die Untersuchung von sowohl qualitativen als auch quantitativen Einflüssen bestimmter Probeneigenschaften, wie beispielsweise Oberflächenrauheit, auf die Form des gemessenen Energiespektrums beziehungsweise auf das analysierte Tiefenprofil. Die Kenntnis der Rauheit einer Probe an der Oberfläche und an den Grenzflächen ist für die Analytik unabdingbar. Als Resultat der genannten Betrachtungen werden die Einflüsse von Probeneigenschaften und Ionen-Festkörper-Wechselwirkungen auf die Energie- beziehungsweise Tiefenauflösung des Gesamtsystems beschrieben, berechnet und mit der konventionellen Ionenstrahlanalytik verglichen. Die Möglichkeiten der höchstauflösenden Ionenstrahlanalytik werden zudem mit den von anderen Gruppen veröffentlichten Komplementärmethoden gegenübergestellt. Der fünfte und letzte Schwerpunkt ist die Analytik leichter Elemente in ultradünnen Schichten unter Berücksichtigung aller in dieser Arbeit vorgestellten Modelle, wie die Reduzierung des Einflusses von Strahlschäden oder die Quantifizierung der Elemente im dynamischen Ladungszustandsnichtgleichgewicht. Es wird die Tiefenprofilierung von Mehrschichtsystemen, bestehend aus SiO2-Si3N4Ox-SiO2 auf Silizium, von Ultra-Shallow-Junction Bor-Implantationsprofilen und von ultradünnen Oxidschichten, wie zum Beispiel High-k-Materialien, demonstriert.
In this thesis the QQDS magnetic spectrometer that is used for high resolution ion beam analysis (IBA) of light elements at the Helmholtz-Zentrum Dresden-Rossendorf is presented for the first time. In addition all parameters are investigated that influence the analysis. Methods and models are presented with which the effects can be minimised or calculated. There are five focal points of this thesis. The first point is the construction and commissioning of the QQDS magnetic spectrometer, the corresponding scattering chamber with all the peripherals and the detector, which is specially developed for high resolution elastic recoil detection. Both the reconstructed spectrometer and the detector were adapted to the specific experimental conditions needed for high-resolution Ion beam analysis of light elements and tested for routine practice. The detector consists of two compo-nents. At the back end of the detector a Bragg ionization chamber is mounted, which is used for the particle identification. At the front end, directly behind the entrance window a proportional counter is mounted. This proportional counter includes a high-resistance anode. Thus, the position of the particles is determined in the detector. The following two points concern fundamental studies of ion-solid interaction. By using a magnetic spectrometer the charge state distribution of the particles scattered from the sample after a binary collision is both possible and necessary for the analysis. For this reason the charge states are measured and compared with existing models. In addition, a model is developed that takes into account the charge state dependent energy loss. It is shown that without the application of this model the depth profiles do not correspond with the quantitative measurements by conventional IBA methods and with the thickness obtained by transmission electron microscopy. The second fundamental ion-solid interaction is the damage and the modification of the sample that occurs during heavy ion irradiation. It is shown that the used energies occur both electronic sputtering and electronically induced interface mixing. Electronic sputtering is minimised by using optimised beam parameters. For most samples the effect is below the detection limit for a fluence sufficient for the analysis. However, the influence of interface mixing is so strong that it has to be included in the analysis of the layers of the depth profiles. It is concluded from these studies that at the Rossendorf 5 MV tandem accelerator chlorine ions with an energy of 20 MeV deliver the best results. In some cases, such as the analysis of boron, the energy must be reduced to 6.5 MeV in order to retain the electronic sputtering below the detection limit. The fourth focus is the study of the influence of specific sample properties, such as surface roughness, on the shape of a measured energy spectra and respectively on the analysed depth profile. It is shown that knowledge of the roughness of a sample at the surface and at the interfaces for the analysis is needed. In addition, the contribution parameters limiting the depth resolution are calculated and compared with the conventional ion beam analysis. Finally, a comparison is made between the high-resolution ion beam analysis and complementary methods published by other research groups. The fifth and last focus is the analysis of light elements in ultra thin layers. All models presented in this thesis to reduce the influence of beam damage are taken into account. The dynamic non-equilibrium charge state is also included for the quantification of elements. Depth profiling of multilayer systems is demonstrated for systems consisting of SiO2-Si3N4Ox-SiO2 on silicon, boron implantation profiles for ultra shallow junctions and ultra thin oxide layers, such as used as high-k materials.

Abstract A line-to-line beam contact formulation in the framework of the absolute nodal coordinate formulation (ANCF) is introduced in this paper. Higher- and lower-order ANCF beam elements employ the introduced beam contact formulation. The higher- and lower-order ANCF beam elements are compared in terms of their accuracy and performance in a large deformation contact problem. Efficiency of numerical integration of contact energy variation contribution to the system’s equations of motion is studied. The contacting elements’ surfaces of the ANCF beam elements are parameterized by segmentation of integration over the contact patch. Numerical results investigate the accuracy, robustness and efficiency of the developed line-to-line contact formulation by comparing against a solid element type using commercial finite element code. According to the numerical results, the higher-order ANCF beam element’s solution is closer than the lower-order ANCF beam element’s in accordance with the reference solution provided by a solid element type using commercial finite element code ABAQUS. Furthermore, the higher-order beam element is found to be more efficient than the lower-order beam with respect to the numerical integration of the contact energy variation. Expectedly, the higher-order ANCF beam element is able to capture the cross-section deformation in a large deformation contact problem, while the lower-order element fails to exhibit such cross-sectional deformation.

Abstract In this work, a numerically hybrid model is presented for the lattice structures to reduce the computational cost of the simulations. This approach consists of utilization of solid elements for the junctions and beam elements for the microbeams connecting the corresponding junctions to each other. To take into account the geometric defects, for each microbeam of the lattice structures, an ellipse is fitted to capture the effect of shape variation and roughness. Having the parameters of the ellipses, the lattice structures are constructed in Spaceclaim (ANSYS) using the geometrical hybrid approach. When the global response of the structure is linear, the results from the hybrid models are in good agreement with the ones from the 3D models. However, the hybrid models have difficulty to converge when the effect of large deformation and local plasticity are considerable in the BCCZ structures. For BCCZ lattice structures, the results are not affected by the junction’s size. This is also valid for BCC lattice structures as long as the ratio of the junction’s size to the diameter of the microbeams is greater than 2.

Discrete Element Method (DEM) is an explicit numerical scheme to model the mechanical response of solid and particulate media. In our paper, we are introducing Quadrilateral Discrete Element Method (QDEM) for the simulation of the separation of elements in fixed beam subjected to impact load. QDEM results are compared with other DEM results available in literature. Impact loads include two cases: (a) a half sine wave and (b) a penetrator hitting the fixed beam. Separation criteria used for the discrete elements is maximum principal stress failure criteria. In QDEM, convergence study for the response of fixed beam is obtained using MATLAB platform. Validation of quadrilateral elements in fixed beam is being carried out by comparing the results with empirical formula available in literature for the impact analysis.

The objective of this paper is to present results of a study designed to determine conversion factors to allow designers and analysts calculate natural frequencies of vibrating prismatic beams of arbitrary dimensions using simpler beam elements instead of expensive 3D solid elements. Prismatic beams subject to the most commonly encountered boundary conditions were modeled using beam elements and solid elements. The resulting natural frequencies were calculated and validated and the corresponding conversion factors were determined.

Abstract Literaturally, the local-global finite element analysis technique plays a very important role in the area array packaging. This technique applies a finite element based method to calculate the geometrical data and elastic/plastic material properties of the equivalent beam model that is used to elastically and plastically simulate the 3-D local model. In this study, the underlying goal is to propose an improved equivalent model for the use in the local/global analysis, and most importantly, provide a systematic procedure in approaching this equivalent model. In addition, the choice of the equivalent beam model (i.e., either solid circular beam or the thin-walled circular pipe) will be also extensively investigated. Since the configuration of the solder joint is far from being close to a “beam-like” structure, defining the corresponding equivalent beam exists a great level of difficulties. Hence, in order to remove the possible difficulties, a comparatively effective way is proposed by incorporating the analytical derivations and optimization approaches. To this end, one practical application is presented to substantiate the proposed methodology.

The accurate modeling of a rotor system is essential for effective design and troubleshooting in rotating machinery. The beam-type finite element (FE) may be inadequate for modeling a rotor or support structure with complex shapes. In addition, the isolated support impedance methods may be inaccurate for modeling the support structure that has modes that are highly coupled between bearings and directions at the bearing locations. The solid FE method is a good replacement of the beam FE and support impedance approaches. However, a drawback for this method is the significant amount of computation time required to obtain accurate solutions due to the large number of nodes in the solid FE analysis. The authors present an improved approach to analyze the coupled rotor-support dynamics, by modeling the rotor with solid elements and utilizing transfer functions (TFs) to represent the flexible support. A state-space model is then employed to perform general rotordynamic analyses. The solid FE rotor model includes the gyroscopic effects and the asymmetric and cross-coupled stiffness coefficients of the bearing. A series of rational TFs are used to simulate dynamic characteristics of the support structure, including the cross-coupling between degrees of freedom (DOFs). These TFs are derived by curve-fitting the frequency response functions (FRFs) of the solid FE support model at the bearing locations. The impact of the polynomial degree of the TF on the unbalance response analysis is discussed, and a general rule is proposed to select an adequate polynomial degree. To validate the proposed modeling approach, a comprehensive comparison among the complete solid FE rotor-support model and the solid FE rotor model with the TFs representing the flexible support (the reduced state-space model) are presented. Comparisons are made between natural frequencies, critical speeds, unbalance response, logarithmic decrement (log dec), and computation time. The results of these comparisons show that the reduced state-space rotor-support model provides a dynamically accurate approximation of the solid FE rotor-support model in terms of general rotordynamic analyses. Moreover, the computation time for the proposed modeling approach is reduced to 2.5 minutes, compared to 14 minutes for the complete solid FE modeling. The reduction of the computation time may vary with different number of DOFs of the rotor model and the support structure model. In addition, the modes up to 100,000 cpm are compared among the beam rotor with the solid FE support model, the solid FE rotor with the super-element support model, and the reduced state-space model. The results show that the reduced state-space model is more accurate in predicting high-frequency modes than the beam rotor-support and super-element support models. Further, the proposed approach with the state-space model is useful for applications in vibration control and active magnetic bearing (AMB) systems.

Finite element methods are used increasingly to predict weld residual stresses. This is a relatively complex use of the finite element method, and it is important that its practitioners are able to demonstrate their ability to produce accurate predictions. Extensively characterised benchmark problems are a vital tool in achieving this. However, existing benchmarks are relatively complex and not suitable for analysis by novice weld modellers. This paper describes two benchmarks based upon a simple beam specimen with a single autogenous weld bead laid along its top edge. This geometry may be analysed using either 3D or 2D FE models and employing either block-dumped or moving heat source techniques. The first, simpler, benchmark is manufactured from AISI 316 steel, which does not undergo solid state phase transformation, while the second, more complex, benchmark is manufactured from SA508 Cl 3 steel, which undergoes solid state phase transformation during welding. A number of such beams were manufactured using an automated TIG process, and instrumented with thermocouples and strain gauges to record the transient temperature and strain response during welding. The resulting residual stresses were measured using diverse techniques, and showed markedly different distributions in the austenitic and ferritic beams. The paper presents the information necessary to perform and validate finite element weld residual stress simulations in both the simple austenitic beam and the more complex ferritic beam, and provides performance measures for the austenitic beam problem.

This work presents a novel technique for enforcing the beam-to-shell, beam-to-solid, and shell-to-solid family of constraints in explicit finite element formulations. The limitations of classical multipoint constraint approaches are examined at length, with robustness and accuracy examined through numerical examples. Novel formulation of the new constraint method is presented, and its implementation in the explicit finite element computational cycle discussed. The results of some illustrative test cases employing the newly proposed method are given, showing excellent accuracy even in the presence of large rotations. When compared to existing works, the salient features of the current method are in evidence.

Prefabricated modular steel (PFMS) construction is a more efficient and safe method of constructing a high-quality building with less waste material and labour dependency than traditional steel construction. It is indeed critical to have a precise and valuable intermodular joining system that allows for efficient load transfer, safe handling, and optimal use of modular units' strength. Thus, the purpose of this study was to develop joints using tension bolts and solid tenons welded into the gusset plate (GP). These joints ensured rigid and secure connectivity in both horizontal and vertical directions for the modular units. Using the three-dimensional (3D) finite element (FE) analysis software ABAQUS, the study investigated the nonlinear lateral structural performance of the joint and two-storey modular steel building (MSB). The solid element FE models of joints were then simplified by introducing connectors and beam elements to enhance computational efficiency. Numerous parameters indicated that column tenons were important in determining the joint's structural performance. Moreover, with a standard deviation (SD) of 0.025, the developed connectors and beam element models accurately predicted the structural behaviour of the joints. As a result of their simplification, these joints demonstrated effective load distribution, seismic performance, and ductility while reducing computational time, effort, and complexity. The validity of the FE analysis was then determined by comparing the results to the thirteen joint bending tests performed in the reference.