TY - THES A1 - Gundermann, Ralf T1 - 3D-Simulation des Temperaturfeldes und der Gefügeumwandlung bei einer Laserstrahlschweißung T1 - 3D-simulation the temperature field and the material transformation at a laser beam welding N2 - Das FEM-Programmsystem „SYSWELD“ kommt für die Berechnung des Temperaturfeldes bei einer Laserstrahlschweißung zum Einsatz. Insbesondere sollen der Einfluss des Energieeintrages und die damit verbundene Gefügeumwandlung eines Feinkornbaustahles untersucht und Aussagen zur notwendigen Modellierungsgenauigkeit der Nahtgeometrie bzw. Netzverfeinerung getroffen werden. Im Einzelnen sind folgende Teilaufgaben zu lösen: - ausführliche Literaturrecherche zur numerischen Analyse von Schweißverbindungen insbesondere zu temperaturabhängigen Materialeigenschaften von Feinkornbaustählen, - Darstellung der Wärmequelle für das Laserstrahlschweißen, - Erprobung unterschiedlicher Netzvarianten für die FE-Analyse von instationären Temperaturfeldern, - Untersuchung zur Modellierungsgenauigkeit der Nahtgeometrie, - Parameterstudien zum Einfluss der Materialkennwerte und Gefügekinetik auf das Temperaturfeld sowie das Gefüge. N2 - The FEM-program "SYSWELD" comes for the calculation the temperature field at a laser beam welding to the employment. Particularly the influence of the energy deposit should explored and the with it joined material transformation of a fine grained steel and are met statements to the necessary modelling precision the weld geometry and mesh refinement. In the single following tasks are to be solved: - Comprehensive literature investigation to the numerical analysis of welding joints particularly to temperature dependent material properties of fine grained steels, - Display the heat source for the laser beam welding, - Test different mesh variants for the Fe-analysis of non-stationary temperature fields, - Investigation to the modelling precision on the weld geometry, - Investigation to the influence the material properties and material transformation on the temperature field as well as the material structure. KW - Laserschweißen KW - Finite-Elemente-Methode KW - Direkte numerische Simulation KW - Gefügeumwandlung KW - Feinkornbaustahl KW - Temperaturfeld KW - Laserstrahlschweißen KW - Aufheizraten KW - ZTU-Schaubild KW - laser beam KW - joint weld KW - fine grained steel Y1 - 2005 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:gbv:wim2-20111215-6680 N1 - Der Volltext-Zugang wurde im Zusammenhang mit der Klärung urheberrechtlicher Fragen mit sofortiger Wirkung gesperrt. ER - TY - JOUR A1 - Noh, Jung-Hwi A1 - Park, Jong-Heon T1 - A Calculation of Initial Cable Force for Ko-Ha Grand Bridge N2 - The primary objective of initial shape analysis of a cable stayed bridge is to calculate initial installation cable tension forces and to evaluate fabrication camber of main span and pylon providing the final longitudinal profile of the bridge at the end of construction. In addition, the initial cable forces depending on the alternation of the bridge’s shape can be obtained from the analysis, and will be used to provide construction safety during construction. In this research, we conducted numerical experiments for initial shape of Ko-ha bridge, which will be constructed in the near future, using three different typical methods such as continuous beam method, linear truss method, and IIMF (Introducing Initial Member Force) method KW - Finite-Elemente-Methode KW - Physikalisches Verfahren KW - Hängebrücke KW - cable stayed bridge KW - cable force KW - initial shape KW - initial equilibrium state Y1 - 2004 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:gbv:wim2-20111215-2459 ER - TY - CHAP A1 - Brehm, Maik A1 - Most, Thomas T1 - A Four-Node Plane EAS-Element for Stochastic Nonlinear Materials N2 - Iso-parametric finite elements with linear shape functions show in general a too stiff element behavior, called locking. By the investigation of structural parts under bending loading the so-called shear locking appears, because these elements can not reproduce pure bending modes. Many studies dealt with the locking problem and a number of methods to avoid the undesirable effects have been developed. Two well known methods are the >Assumed Natural Strain< (ANS) method and the >Enhanced Assumed Strain< (EAS) method. In this study the EAS method is applied to a four-node plane element with four EAS-parameters. The paper will describe the well-known linear formulation, its extension to nonlinear materials and the modeling of material uncertainties with random fields. For nonlinear material behavior the EAS parameters can not be determined directly. Here the problem is solved by using an internal iteration at the element level, which is much more efficient and stable than the determination via a global iteration. To verify the deterministic element behavior the results of common test examples are presented for linear and nonlinear materials. The modeling of material uncertainties is done by point-discretized random fields. To show the applicability of the element for stochastic finite element calculations Latin Hypercube Sampling was applied to investigate the stochastic hardening behavior of a cantilever beam with nonlinear material. The enhanced linear element can be applied as an alternative to higher-order finite elements where more nodes are necessary. The presented element formulation can be used in a similar manner to improve stochastic linear solid elements. KW - Nichtlineare Mechanik KW - Finite-Elemente-Methode KW - Zufallsvariable Y1 - 2003 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:gbv:wim2-20111215-2825 ER - TY - CHAP A1 - Häfner, Stefan A1 - Eckardt, Stefan A1 - Könke, Carsten T1 - A geometrical inclusion-matrix model for the finite element analysis of concrete at multiple scales N2 - This paper introduces a method to generate adequate inclusion-matrix geometries of concrete in two and three dimensions, which are independent of any specific numerical discretization. The article starts with an analysis on shapes of natural aggregates and discusses corresponding mathematical realizations. As a first prototype a two-dimensional generation of a mesoscale model is introduced. Particle size distribution functions are analysed and prepared for simulating an adequate three-dimensional representation of the aggregates within a concrete structure. A sample geometry of a three-dimensional test cube is generated and the finite element analysis of its heterogeneous geometry by a uniform mesh is presented. Concluding, aspects of a multiscale analysis are discussed and possible enhancements are proposed. KW - Beton KW - Dreidimensionales Modell KW - Finite-Elemente-Methode Y1 - 2003 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:gbv:wim2-20111215-3018 ER - TY - CHAP A1 - Montag, U. T1 - A New Efficient Concept for Elasto-plastic Simulations of Shell Responses N2 - For the analysis of arbitrary, by Finite Elements discretized shell structures, an efficient numerical simulation strategy with quadratic convergence including geometrically and physically nonlinear effects will be presented. In the beginning, a Finite-Rotation shell theory allowing constant shear deformations across the shell thickness is given in an isoparametric formulation. The assumed-strain concept enables the derivation of a locking-free finite element. The Layered Approach will be applied to ensure a sufficiently precise prediction of the propagation of plastic zones even throughout the shell thickness. The Riks-Wempner-Wessels global iteration scheme will be enhanced by a Line-Search procedure to ensure the tracing of nonlinear deformation paths with rather great load steps even in the post-peak range. The elastic-plastic material model includes isotropic hardening. A new Operator-Split return algorithm ensures considerably exact solution of the initial-value problem even for greater load steps. The combination with consistently linearized constitutive equations ensures quadratic convergence in a close neighbourhood to the exact solution. Finally, several examples will demonstrate accuracy and numerical efficiency of the developed algorithm. KW - Schale KW - Elastoplastizität KW - Finite-Elemente-Methode Y1 - 1997 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:gbv:wim2-20111215-4364 ER - TY - JOUR A1 - Ibanez, Stalin A1 - Kraus, Matthias T1 - A Numerical Approach for Plastic Cross Cross-Sectional Analyses of Steel Members JF - ce/papers N2 - Global structural analyses in civil engineering are usually performed considering linear-elastic material behavior. However, for steel structures, a certain degree of plasticization depending on the member classification may be considered. Corresponding plastic analyses taking material nonlinearities into account are effectively realized using numerical methods. Frequently applied finite elements of two and three-dimensional models evaluate the plasticity at defined nodes using a yield surface, i.e. by a yield condition, hardening rule, and flow rule. Corresponding calculations are connected to a large numerical as well as time-consuming effort and they do not rely on the theoretical background of beam theory, to which the regulations of standards mainly correspond. For that reason, methods using beam elements (one-dimensional) combined with cross-sectional analyses are commonly applied for steel members in terms of plastic zones theories. In these approaches, plasticization is in general assessed by means of axial stress only. In this paper, more precise numerical representation of the combined stress states, i.e. axial and shear stresses, is presented and results of the proposed approach are validated and discussed. KW - Stahlkonstruktion KW - Plastizität KW - Strukturanalyse KW - Stahlbauteil KW - Axialspannung KW - Finite-Elemente-Methode Y1 - 2021 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:gbv:wim2-20220112-45622 UR - https://onlinelibrary.wiley.com/doi/full/10.1002/cepa.1527 VL - 2021 IS - Volume 4, issue 2-4 SP - 2098 EP - 2106 PB - Ernst & Sohn, a Wiley brand CY - Berlin ER - TY - JOUR A1 - Vu-Bac, N. A1 - Nguyen-Xuan, Hung A1 - Chen, Lei A1 - Lee, C.K. A1 - Zi, Goangseup A1 - Zhuang, Xiaoying A1 - Liu, G.R. A1 - Rabczuk, Timon T1 - A phantom-node method with edge-based strain smoothing for linear elastic fracture mechanics JF - Journal of Applied Mathematics N2 - This paper presents a novel numerical procedure based on the combination of an edge-based smoothed finite element (ES-FEM) with a phantom-node method for 2D linear elastic fracture mechanics. In the standard phantom-node method, the cracks are formulated by adding phantom nodes, and the cracked element is replaced by two new superimposed elements. This approach is quite simple to implement into existing explicit finite element programs. The shape functions associated with discontinuous elements are similar to those of the standard finite elements, which leads to certain simplification with implementing in the existing codes. The phantom-node method allows modeling discontinuities at an arbitrary location in the mesh. The ES-FEM model owns a close-to-exact stiffness that is much softer than lower-order finite element methods (FEM). Taking advantage of both the ES-FEM and the phantom-node method, we introduce an edge-based strain smoothing technique for the phantom-node method. Numerical results show that the proposed method achieves high accuracy compared with the extended finite element method (XFEM) and other reference solutions. KW - Finite-Elemente-Methode KW - Steifigkeit KW - Bruchmechanik KW - Riss Y1 - 2013 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:gbv:wim2-20170426-31676 ER - TY - JOUR A1 - Mironov, Vadim A1 - Pahl, Peter Jan T1 - A Prismatic Finite Element for Accurate Arch Dam Analysis N2 - The displacements and stresses in arch dams and their abutments are frequently determined with 20-node brick elements. The elements are distorted near the contact plane between the wall and the abutment. A cantilever beam testbed has been developed to investigate the consequences of this distortion. It is shown that the deterioration of the accuracy in the computed stresses is significant. A compatible 18-node wedge element with linear stress variation is developed as an alternative to the brick element. The shape of this element type is readily adapted to the shape of the contact plane. It is shown that the accuracy of the computed stresses in the vicinity of the contact plane is improved significantly by the use of wedge elements. KW - Finite-Elemente-Methode KW - Physikalisches Verfahren KW - Dammbau Y1 - 2004 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:gbv:wim2-20111215-2467 ER - TY - JOUR A1 - Talebi, Hossein A1 - Zi, Goangseup A1 - Silani, Mohammad A1 - Samaniego, Esteban A1 - Rabczuk, Timon T1 - A simple circular cell method for multilevel finite element analysis JF - Journal of Applied Mathematics N2 - A simple multiscale analysis framework for heterogeneous solids based on a computational homogenization technique is presented. The macroscopic strain is linked kinematically to the boundary displacement of a circular or spherical representative volume which contains the microscopic information of the material. The macroscopic stress is obtained from the energy principle between the macroscopic scale and the microscopic scale. This new method is applied to several standard examples to show its accuracy and consistency of the method proposed. KW - Finite-Elemente-Methode KW - Feststoff Y1 - 2012 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:gbv:wim2-20170426-31639 ER - TY - CHAP A1 - Skrinar, Matjaz T1 - A simple FEM Beam Element with an Arbitrary Number of Cracks N2 - To fulfil safety requirements the changes in the static and/or dynamic behaviour of the structure must be analysed with great care. These changes are often caused by local reduction of the stiffness of the structure caused by the irregularities in the structure, as for example cracks. In simple structures such analysis can be performed directly, by solving equations of motion, but for more complex structures a different approach, usually numerical, must be applied. The problem of crack implementation into the structure behaviour has been studied by many authors who have usually modelled the crack as a massless rotational spring of suitable stiffness placed at the beam at the location where the crack occurs. Recently, the numerical procedure for the computation of the stiffness matrix for a beam element with a single transverse crack has been replaced with the element stiffness matrix written in fully symbolic form. A detailed comparison of the results obtained by using 200 2D finite elements with those obtained with a single cracked beam element has confirmed the usefulness of such element. KW - Finite-Elemente-Methode KW - Rissbildung Y1 - 1997 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:gbv:wim2-20111215-4287 ER - TY - THES A1 - Eckardt, Stefan T1 - Adaptive heterogeneous multiscale models for the nonlinear simulation of concrete N2 - The nonlinear behavior of concrete can be attributed to the propagation of microcracks within the heterogeneous internal material structure. In this thesis, a mesoscale model is developed which allows for the explicit simulation of these microcracks. Consequently, the actual physical phenomena causing the complex nonlinear macroscopic behavior of concrete can be represented using rather simple material formulations. On the mesoscale, the numerical model explicitly resolves the components of the internal material structure. For concrete, a three-phase model consisting of aggregates, mortar matrix and interfacial transition zone is proposed. Based on prescribed grading curves, an efficient algorithm for the generation of three-dimensional aggregate distributions using ellipsoids is presented. In the numerical model, tensile failure of the mortar matrix is described using a continuum damage approach. In order to reduce spurious mesh sensitivities, introduced by the softening behavior of the matrix material, nonlocal integral-type material formulations are applied. The propagation of cracks at the interface between aggregates and mortar matrix is represented in a discrete way using a cohesive crack approach. The iterative solution procedure is stabilized using a new path following constraint within the framework of load-displacement-constraint methods which allows for an efficient representation of snap-back phenomena. In several examples, the influence of the randomly generated heterogeneous material structure on the stochastic scatter of the results is analyzed. Furthermore, the ability of mesoscale models to represent size effects is investigated. Mesoscale simulations require the discretization of the internal material structure. Compared to simulations on the macroscale, the numerical effort and the memory demand increases dramatically. Due to the complexity of the numerical model, mesoscale simulations are, in general, limited to small specimens. In this thesis, an adaptive heterogeneous multiscale approach is presented which allows for the incorporation of mesoscale models within nonlinear simulations of concrete structures. In heterogeneous multiscale models, only critical regions, i.e. regions in which damage develops, are resolved on the mesoscale, whereas undamaged or sparsely damage regions are modeled on the macroscale. A crucial point in simulations with heterogeneous multiscale models is the coupling of sub-domains discretized on different length scales. The sub-domains differ not only in the size of the finite elements but also in the constitutive description. In this thesis, different methods for the coupling of non-matching discretizations - constraint equations, the mortar method and the arlequin method - are investigated and the application to heterogeneous multiscale models is presented. Another important point is the detection of critical regions. An adaptive solution procedure allowing the transfer of macroscale sub-domains to the mesoscale is proposed. In this context, several indicators which trigger the model adaptation are introduced. Finally, the application of the proposed adaptive heterogeneous multiscale approach in nonlinear simulations of concrete structures is presented. N2 - Das nichtlineare Materialverhalten von Beton ist durch die Entwicklung von Mikrorissen innerhalb der heterogenen Materialstruktur gekennzeichnet. In dieser Arbeit wird ein Mesoskalenmodell entwickelt, welches die einzelnen Bestandteile der Materialstruktur explizit auflöst und somit die Simulation dieser Mikrorisse erlaubt. Dadurch können die wirklichen physikalischen Vorgänge, welche das komplexe nichtlineare Verhalten von Beton verursachen, durch relativ einfache Materialformulierungen abgebildet werden. Für Beton wird auf der Mesoskala ein 3-Phasenmodell vorgeschlagen, bestehend aus groben Zuschlägen, Mörtelmatrix und Übergangszone zwischen Zuschlag und Matrix. In diesem Zusammenhang wird ein effizienter Algorithmus vorgestellt, welcher ausgehend von einer gegebenen Sieblinie dreidimensionale Kornstrukturen mittels Ellipsoiden simuliert. Im Mesoskalenmodell wird das Zugversagen der Mörtelmatrix durch einen Kontinuumsansatz beschrieben. Um Netzabhängigkeiten, welche durch das Entfestigungsverhalten des Materials hervorgerufen werden, zu reduzieren, kommen nichtlokale Materialformulierungen zum Einsatz. Risse innerhalb der Übergangszone zwischen Zuschlag und Matrix werden, basierend auf einem kohäsiven Modell, mittels eines diskreten Rissansatzes abgebildet. Die Verwendung einer neuen Nebenbedingung innerhalb der Last-Verschiebungs-Zwangsmethode führt zu einer Stabilisierung des iterativen Lösungverfahrens, so dass eine effiziente Simulation von Snap-back Phänomenen möglich wird. Anhand von Beispielen wird gezeigt, dass Mesoskalenmodelle die stochastische Streuung von Ergebnissen und Maßstabseffekte abbilden können. Da auf der Mesoskala die Diskretisierung der inneren Materialstruktur erforderlich ist, steigt im Vergleich zu Simulationen auf der Makroskala der numerische Aufwand erheblich. Aufgrund der Komplexität des numerischen Modells sind Mesoskalensimulationen in der Regel auf kleine Probekörper beschränkt. In dieser Arbeit wird ein adaptiver heterogener Mehrskalenansatz vorgestellt, welcher die Verwendung von Mesoskalenmodellen in nichtlinearen Simulationen von Betonstrukturen erlaubt. In heterogenen Mehrskalenmodellen werden nur kritische Bereiche auf der Mesoskala aufgelöst, während ungeschädigte Bereiche auf der Makroskala abgebildet werden. Ein wichtiger Aspekt in Simulationen mit heterogenen Mehrskalenmodellen ist die Kopplung der auf unterschiedlichen Längenskalen diskretisierten Teilgebiete. Diese unterscheiden sich nicht nur in der Größe der finiten Elemente sondern auch in der Beschreibung des Materials. Verschiedene Methoden zur Kopplung nicht übereinstimmender Vernetzungen - Kopplungsgleichungen, die Mortar-Methode und die Arlequin-Methode - werden untersucht und ihre Anwendung in heterogenen Mehrskalenmodellen wird gezeigt. Ein weiterer wichtiger Aspekt ist die Bestimmung kritischer Regionen. Eine adaptive Lösungsstrategie wird entwickelt, welche die Umwandlung von Makroskalengebieten auf die Mesoskala erlaubt. In diesem Zusammenhang werden Indikatoren vorgestellt, die eine Modellanpassung auslösen. Anhand nichtlinearer Simulationen von Betonstrukturen wird die Anwendung des vorgestellten adaptiven heterogenen Mehrskalenansatzes demonstriert. T2 - Adaptive heterogene Mehrskalenmodelle zur nichtlinearen Simulation von Beton T3 - ISM-Bericht // Institut für Strukturmechanik, Bauhaus-Universität Weimar - 2010,1 KW - Beton KW - Mehrskalenanalyse KW - Finite-Elemente-Methode KW - Nichtlineare Finite-Elemente-Methode KW - Schadensmechanik KW - Mehrskalenmodell KW - Adaptives Verfahren KW - concrete KW - multiscale method KW - finite element method KW - continuum damage mechanics KW - adaptive simulation Y1 - 2009 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:gbv:wim2-20100317-15023 ER - TY - JOUR A1 - Lee, Kangkun A1 - Lee, Kijang T1 - Additional bending moment for shear-lag phenomenon in tube structures N2 - Framed-tube system with multiple internal tubes is analysed using an orthotropic box beam analogy approach in which each tube is individually modelled by a box beam that accounts for the flexural and shear deformations, as well as the shear-lag effects. A simple numerical modeling technique is proposed for estimating the shear-lag phenomenon in tube structures with multiple internal tubes. The proposed method idealizes the framed-tube structures with multiple internal tubes as equivalent multiple tubes, each composed of four equivalent orthotropic plate panels. The numerical analysis is based on the minimum potential energy principle in conjunction with the variational approach. The shear-lag phenomenon of such structures is studied taking into account the additional bending moments in the tubes. A detailed work is carried out through the numerical analysis of the additional bending moment. The moment factor is further introduced to identify the shear lag phenomenon along with the additional moment. KW - Finite-Elemente-Methode KW - Physikalisches Verfahren KW - Hochhaus Y1 - 2004 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:gbv:wim2-20111215-2472 ER - TY - CHAP A1 - Daniunas, A. A1 - Komka, A. A1 - Werner, F. T1 - ANALYSIS AND DETERMINATION OF STRENGTH IN PLASTIC STAGE OF FREE FORM STEEL SHAPES N2 - The steel structure design codes require to check up the member strength when evaluating plastic deformations. The model of perfectly plastic material is accepted. The strength criteria for simple cross-sections (I section, etc.) of steel members are given in design codes. The analytical strength criteria for steel cross-sections and numerical approaches based on stepwise procedure are investigated in many articles. Another way for checking the carrying capacity of cross-sections is the use of methods that are applied for defining strain-deformed state of elastic perfectly plastic systems. In this paper non-iterative methods are suggested for checking strength of cross-sections. Carrying capacity of cross section is verified according to extremum principle of plastic fail under monotonically loading and the strain-deformed state of cross-section is defined according to extremum energy principals of elastic potential of residual stresses and complementary work of residual displacements. The mathematical expressions of these principals for discrete cross-section are formulated as problems of convex mathematical programming. The cross-section of steel member using finite element method is divided into free form plane elements. The constant distribution of stresses along the finite element is accepted. The relationships of finite elements for static formulation of the problem are formed so, that kinematics formulation relationships could be obtained in a formal way using the theory of duality. Numerical examples of determination of cross-section strength, composition of interactive curves and composition of moment-curvature curves for different axial force levels are presented. KW - Stahlkonstruktion KW - Plastische Deformation KW - Mathematisches Modell KW - Finite-Elemente-Methode Y1 - 2000 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:gbv:wim2-20111215-5803 ER - TY - JOUR A1 - Most, Thomas A1 - Eckardt, Stefan T1 - Application of a hybrid parallelization technique to accelerate the numerical simulation of nonlinear mechanical problems N2 - This paper presents the combination of two different parallelization environments, OpenMP and MPI, in one numerical simulation tool. The computation of the system matrices and vectors is parallelized with OpenMP and the solution of the system of equations is done with the MPIbased solver MUMPS. The efficiency of both algorithms is shown on several linear and nonlinear examples using the Finite Element Method and a meshless discretization technique. KW - Framework KW - API KW - Parallelverarbeitung KW - Finite-Elemente-Methode Y1 - 2004 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:gbv:wim2-20111215-2599 ER - TY - JOUR A1 - Melnikov, B. E. A1 - Semenov, Artem T1 - Application of Multimodel Method of Elasto-Plastic Analysis for the Multilevel Computation of Structures N2 - Creation of hierarchical sequence of the plastic and viscoplastic models according to different levels of structure approximations is considered. Developed strategy of multimodel analysis, which consists of creation of the inelastic models library, determination of selection criteria system and caring out of multivariant sequential clarifying computations, is described. Application of the multimodel approach in numerical computations has demonstrated possibility of reliable prediction of stress-strain response under wide variety of combined nonproportional loading. KW - Finite-Elemente-Methode KW - Physikalisches Verfahren KW - Elastoplastizität Y1 - 2004 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:gbv:wim2-20111215-2487 ER - TY - THES A1 - Roos, Dirk T1 - Approximation und Interpolation von Grenzzustandsfunktionen zur Sicherheitsbewertung nichtlinearer Finite-Elemente-Strukturen T1 - Reliability analysis using approximation and interpolation of nonlinear finite element limit state functions N2 - Die vorliegende Arbeit beschäftigt sich mit der Berechnung der Sicherheit von Strukturen mit sowohl geometrisch als auch physikalisch nichtlinearem Verhalten. Die Berechnung der Versagenswahrscheinlichkeit einer Struktur mit Hilfe von Monte-Carlo-Simulationsmethoden erfordert, dass die Funktion der Strukturantwort implizit berechnet wird, zum Beispiel durch nichtlineare Strukturanalysen für jede Realisation der Zufallsvariablen. Die Strukturanalysen bilden jedoch den Hauptanteil am Berechnungsaufwand der Zuverlässigkeitsanalyse, so dass die Analyse von realistischen Strukturen mit nichtlinearem Verhalten durch die begrenzten Computer-Ressourcen stark eingeschränkt ist. Die klassischen Antwortflächenverfahren approximieren die Funktion der Strukturantwort oder aber die Grenzzustandsfunktion durch Polynome niedriger Ordnung. Dadurch ist für die Auswertung des Versagens-Kriteriums nur noch von Interesse, ob eine Realisation der Basisvariablen innerhalb oder außerhalb des von der Antwortflächenfunktion gebildeten Raumes liegt - die Strukturanalyse kann dann entfallen. Bei stark nichtlinearen Grenzzustandsfunktionen versagt die polynomiale Approximation. Das directional sampling neigt bei Problemen mit vielen Zufallsvariablen zu einem systematischen Fehler. Das adaptive importance directional sampling dagegen beseitigt diesen Fehler, verschenkt jedoch Informationen über den Verlauf der Grenzzustandsfunktion, da die aufgefundenen Stützstellen aus den vorangegangenen Simulationsläufen nicht berücksichtigt werden können. Aus diesem Grund erscheint eine Kombination beider Simulationsverfahren und eine Interpolation mittels einer Antwortfläche geeignet, diese Probleme zu lösen. Dies war die Motivation für die Entwicklung eines Verfahren der adaptiven Simulation der Einheitsvektoren und anschließender Interpolation der Grenzzustandsfunktion durch eine Antwortflächenfunktion. Dieses Vorgehen stellt besondere Anforderungen an die Antwortflächenfunktion. Diese muss flexibel genug sein, um stark nichtlineare Grenzzustandsfunktionen beliebig genau annähern zu können. Außerdem sollte die Anzahl der verarbeitbaren Stützstellen nicht begrenzt sein. Auch ist zu berücksichtigen, dass die Ermittlung der Stützstellen auf der Grenzzustandsfunktion nicht regelmäßig erfolgt. Die in dieser Arbeit entwickelten Methoden der lokalen Interpolation der Grenzzustandsfunktion durch Normalen-Hyperebenen bzw. sekantialen Hyperebenen und der sowohl lokalen als auch globalen Interpolation durch gewichtete Radien erfüllen diese Anforderungen. ungen. dieser Arbeit entwickelten Methoden der lokalen Interpolation der Grenzzustandsfunktion durch Normalen-Hyperebenen bzw. sekantialen Hyperebenen und der sowohl lokalen als auch globalen Interpolation durch gewichtete Radien erfüllen diese Anforderungen. N2 - The objective is the analysis of the structural reliability of nonlinear finite element systems. Normally, the limit state of a structural system is described implicitly, e.g. through an algorithmic procedure within finite element analysis. Alternatively, the original limit state function can be approximated by a response surface function. One of the major advantages of the response surface method lies in its potential to selectively determine the number of structural analyses of the support points. By such means the computational effort can be substantially reduced. On the other hand, the global approximation schemes widely used in the application of the response surface method can be quite misleading due to the lack of information in certain regions of the random variable space. It is therefore required to avoid such undesirable interpolation errors at reasonable computational effort. The polynomial approximations are not quite flexible. They always need a predefined number of limit state check points in unimportant directions in order to avoid any approximation problems. On this account the maximum number of limit state check points is limited, too. The study presents an approach to polyhedral and weighted modeling of convex and concave failure surfaces intended to provide reasonably accurate estimates of failure probabilities while maintaining computational efficiency. In particular, these response surfaces can be adaptively refined to consistently increase the accuracy of the estimated failure probability. This is achieved by a combination of random search strategies (based on the adaptive directional sampling approach) as well as deterministic search refinement together with local and global interpolation schemes. The main advantage of these methods is their flexibility for the approximation of highly nonlinear limit state functions. In this sense, the proposed methods are very robust and efficient. KW - Tragwerk KW - Nichtlineares System KW - Tragfähigkeit KW - Mechanisches Versagen KW - Zuverlässigkeitstheorie KW - Finite-Elemente-Methode KW - Sicherheit KW - Antwortflächenverfahren KW - structural reliability KW - response surface method KW - finite elements Y1 - 2001 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:gbv:wim2-20040311-745 ER - TY - THES A1 - Schorling, York T1 - Beitrag zur Stabilitätsuntersuchung von Strukturen mit räumlich korrelierten geometrischen Imperfektionen N2 - Für geometrisch imperfekte Strukturen wird die Versagenswahrscheinlichkeit bezüglich Stabilitätskriterien bestimmt. Eine probabilistische Beschreibung der geometrischen Imperfektionen erfolgt mit skalaren ortsdiskretisierten Zufallsfeldern. Die Stabilitätsberechnungen werden mit der Finite Elemente Methode durchgeführt. Ausgangspunkt der Berechnung ist eine systematische Formulierung probabilistisch gewichteter Imperfektionsformen durch eine Eigenwertzerlegung der Kovarianzmatrix. Wenn mit einer strukturmechanisch orientierten Sensitivitätsanalyse ein Unterraum zur näherungsweisen Beschreibung des probabilistischen Strukturverhaltens gefunden wird, kann die Versagenswahrscheinlichkeit numerisch sehr effizient durch ein Interaktionsmodell bestimmt werden. Es zeigte sich, daß dies genau dann möglich ist, wenn die Beulform merklich im Imperfektionsfeld enthalten ist. Die Imperfektionsform am Bemessungspunkt entspricht dann, unabhängig vom Lastniveau, gerade der Beulform. Wenn die Beulform im Imperfektionsfeld einen untergeordneten Beitrag liefert, erscheint eine Reduktion des stochastischen Problems auf wenige Zufallsvariablen dagegen nicht möglich. N2 - The thesis presents a concept for reliability analysis of geometrical imperfect structures with respect to static stability criteria. The geometrical imperfections are modeled as Gaussian random fields. The structural analysis is based on the Finite Element Method. A spectral decomposition of the covariance matrix, enables to formulate independent probabilistically weighted imperfections shapes, which may be analyzed by means of structural mechanics. Reliability calculations with procedures such as the response surface method require the reduction of the random variable space. Examples proved that a suitable definition of a subspace of the random variable space is possible, if the buckling shapes are sufficiently included in the random field. In this case the imperfection shape is-independent of the load level-identical to the buckling shape. In contrast if the buckling shapes are not included in the random field, the structure shows a wide banded behavior. Consequently a reduction of the variable space and the application of an interaction models is then not feasible for the determination of the failure probabilty. KW - Tragwerk KW - Formabweichung KW - Stabilität KW - Beulung KW - Zuverlässigkeit KW - Finite-Elemente-Methode KW - Imperfektion KW - Berechnung KW - Stochastik KW - Zufallsfeld Y1 - 1997 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:gbv:wim2-20040216-317 ER - TY - THES A1 - Will, Johannes T1 - Beitrag zur Standsicherheitsberechnung im geklüfteten Fels in der Kontinuums- und Diskontinuumsmechanik unter Verwendung impliziter und expliziter Berechnungsstrategien T1 - Structural safety analysis for jointed rock with continuum and discontinuum mechanics in implizit and explizit codes KW - Staumauer KW - Standsicherheit KW - Klüftung KW - Finite-Elemente-Methode KW - Diskrete-Elemente-Methode KW - Kontinuumsmechanik KW - Diskontinuumsmechanik KW - jointed rock KW - continuum mechanics KW - diskontinuum mechanics Y1 - 1999 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:gbv:wim2-20040310-613 ER - TY - JOUR A1 - Reichert, Ina A1 - Olney, Peter A1 - Lahmer, Tom T1 - Combined approach for optimal sensor placement and experimental verification in the context of tower-like structures JF - Journal of Civil Structural Health Monitoring N2 - When it comes to monitoring of huge structures, main issues are limited time, high costs and how to deal with the big amount of data. In order to reduce and manage them, respectively, methods from the field of optimal design of experiments are useful and supportive. Having optimal experimental designs at hand before conducting any measurements is leading to a highly informative measurement concept, where the sensor positions are optimized according to minimal errors in the structures’ models. For the reduction of computational time a combined approach using Fisher Information Matrix and mean-squared error in a two-step procedure is proposed under the consideration of different error types. The error descriptions contain random/aleatoric and systematic/epistemic portions. Applying this combined approach on a finite element model using artificial acceleration time measurement data with artificially added errors leads to the optimized sensor positions. These findings are compared to results from laboratory experiments on the modeled structure, which is a tower-like structure represented by a hollow pipe as the cantilever beam. Conclusively, the combined approach is leading to a sound experimental design that leads to a good estimate of the structure’s behavior and model parameters without the need of preliminary measurements for model updating. KW - Strukturmechanik KW - Finite-Elemente-Methode KW - tower-like structures KW - experimental validation KW - mean-squared error KW - fisher-information matrix Y1 - 2020 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:gbv:wim2-20210804-44701 UR - https://link.springer.com/article/10.1007/s13349-020-00448-7 VL - 2021 IS - volume 11 SP - 223 EP - 234 PB - Heidelberg CY - Springer ER - TY - JOUR A1 - Ataollahi Oshkour, Azim A1 - Talebi, Hossein A1 - Seyed Shirazi, Seyed Farid A1 - Bayat, Mehdi A1 - Yau, Yat Huang A1 - Tarlochan, Faris A1 - Abu Osman, Noor Azuan T1 - Comparison of various functionally graded femoral prostheses by finite element analysis JF - Scientific World Journal N2 - This study is focused on finite element analysis of a model comprising femur into which a femoral component of a total hip replacement was implanted. The considered prosthesis is fabricated from a functionally graded material (FGM) comprising a layer of a titanium alloy bonded to a layer of hydroxyapatite. The elastic modulus of the FGM was adjusted in the radial, longitudinal, and longitudinal-radial directions by altering the volume fraction gradient exponent. Four cases were studied, involving two different methods of anchoring the prosthesis to the spongy bone and two cases of applied loading. The results revealed that the FG prostheses provoked more SED to the bone. The FG prostheses carried less stress, while more stress was induced to the bone and cement. Meanwhile, less shear interface stress was stimulated to the prosthesis-bone interface in the noncemented FG prostheses. The cement-bone interface carried more stress compared to the prosthesis-cement interface. Stair climbing induced more harmful effects to the implanted femur components compared to the normal walking by causing more stress. Therefore, stress shielding, developed stresses, and interface stresses in the THR components could be adjusted through the controlling stiffness of the FG prosthesis by managing volume fraction gradient exponent. KW - Finite-Elemente-Methode KW - Hüftgelenk KW - Funktioneller Gradientenwerkstoff Y1 - 2014 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:gbv:wim2-20170413-31194 ER -