@misc{Gundermann2005, type = {Master Thesis}, author = {Gundermann, Ralf}, title = {3D-Simulation des Temperaturfeldes und der Gef{\"u}geumwandlung bei einer Laserstrahlschweißung}, doi = {10.25643/bauhaus-universitaet.668}, url = {http://nbn-resolving.de/urn:nbn:de:gbv:wim2-20111215-6680}, school = {Bauhaus-Universit{\"a}t Weimar}, year = {2005}, abstract = {Das FEM-Programmsystem „SYSWELD" kommt f{\"u}r die Berechnung des Temperaturfeldes bei einer Laserstrahlschweißung zum Einsatz. Insbesondere sollen der Einfluss des Energieeintrages und die damit verbundene Gef{\"u}geumwandlung eines Feinkornbaustahles untersucht und Aussagen zur notwendigen Modellierungsgenauigkeit der Nahtgeometrie bzw. Netzverfeinerung getroffen werden. Im Einzelnen sind folgende Teilaufgaben zu l{\"o}sen: - ausf{\"u}hrliche Literaturrecherche zur numerischen Analyse von Schweißverbindungen insbesondere zu temperaturabh{\"a}ngigen Materialeigenschaften von Feinkornbaust{\"a}hlen, - Darstellung der W{\"a}rmequelle f{\"u}r das Laserstrahlschweißen, - Erprobung unterschiedlicher Netzvarianten f{\"u}r die FE-Analyse von instation{\"a}ren Temperaturfeldern, - Untersuchung zur Modellierungsgenauigkeit der Nahtgeometrie, - Parameterstudien zum Einfluss der Materialkennwerte und Gef{\"u}gekinetik auf das Temperaturfeld sowie das Gef{\"u}ge.}, subject = {Laserschweißen}, language = {de} } @article{NohPark2004, author = {Noh, Jung-Hwi and Park, Jong-Heon}, title = {A Calculation of Initial Cable Force for Ko-Ha Grand Bridge}, doi = {10.25643/bauhaus-universitaet.245}, url = {http://nbn-resolving.de/urn:nbn:de:gbv:wim2-20111215-2459}, year = {2004}, abstract = {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}, subject = {Finite-Elemente-Methode}, language = {en} } @inproceedings{BrehmMost2003, author = {Brehm, Maik and Most, Thomas}, title = {A Four-Node Plane EAS-Element for Stochastic Nonlinear Materials}, doi = {10.25643/bauhaus-universitaet.282}, url = {http://nbn-resolving.de/urn:nbn:de:gbv:wim2-20111215-2825}, year = {2003}, abstract = {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.}, subject = {Nichtlineare Mechanik}, language = {en} } @inproceedings{HaefnerEckardtKoenke2003, author = {H{\"a}fner, Stefan and Eckardt, Stefan and K{\"o}nke, Carsten}, title = {A geometrical inclusion-matrix model for the finite element analysis of concrete at multiple scales}, doi = {10.25643/bauhaus-universitaet.301}, url = {http://nbn-resolving.de/urn:nbn:de:gbv:wim2-20111215-3018}, year = {2003}, abstract = {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.}, subject = {Beton}, language = {en} } @inproceedings{Montag1997, author = {Montag, U.}, title = {A New Efficient Concept for Elasto-plastic Simulations of Shell Responses}, doi = {10.25643/bauhaus-universitaet.436}, url = {http://nbn-resolving.de/urn:nbn:de:gbv:wim2-20111215-4364}, year = {1997}, abstract = {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.}, subject = {Schale}, language = {en} } @article{IbanezKraus, author = {Ibanez, Stalin and Kraus, Matthias}, title = {A Numerical Approach for Plastic Cross Cross-Sectional Analyses of Steel Members}, series = {ce/papers}, volume = {2021}, journal = {ce/papers}, number = {Volume 4, issue 2-4}, publisher = {Ernst \& Sohn, a Wiley brand}, address = {Berlin}, doi = {10.1002/cepa.1527}, url = {http://nbn-resolving.de/urn:nbn:de:gbv:wim2-20220112-45622}, pages = {2098 -- 2106}, abstract = {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.}, subject = {Stahlkonstruktion}, language = {en} } @article{VuBacNguyenXuanChenetal., author = {Vu-Bac, N. and Nguyen-Xuan, Hung and Chen, Lei and Lee, C.K. and Zi, Goangseup and Zhuang, Xiaoying and Liu, G.R. and Rabczuk, Timon}, title = {A phantom-node method with edge-based strain smoothing for linear elastic fracture mechanics}, series = {Journal of Applied Mathematics}, journal = {Journal of Applied Mathematics}, doi = {10.1155/2013/978026}, url = {http://nbn-resolving.de/urn:nbn:de:gbv:wim2-20170426-31676}, abstract = {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.}, subject = {Finite-Elemente-Methode}, language = {en} } @article{MironovPahl2004, author = {Mironov, Vadim and Pahl, Peter Jan}, title = {A Prismatic Finite Element for Accurate Arch Dam Analysis}, doi = {10.25643/bauhaus-universitaet.246}, url = {http://nbn-resolving.de/urn:nbn:de:gbv:wim2-20111215-2467}, year = {2004}, abstract = {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.}, subject = {Finite-Elemente-Methode}, language = {en} } @article{TalebiZiSilanietal., author = {Talebi, Hossein and Zi, Goangseup and Silani, Mohammad and Samaniego, Esteban and Rabczuk, Timon}, title = {A simple circular cell method for multilevel finite element analysis}, series = {Journal of Applied Mathematics}, journal = {Journal of Applied Mathematics}, doi = {10.1155/2012/526846}, url = {http://nbn-resolving.de/urn:nbn:de:gbv:wim2-20170426-31639}, abstract = {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.}, subject = {Finite-Elemente-Methode}, language = {en} } @inproceedings{Skrinar1997, author = {Skrinar, Matjaz}, title = {A simple FEM Beam Element with an Arbitrary Number of Cracks}, doi = {10.25643/bauhaus-universitaet.428}, url = {http://nbn-resolving.de/urn:nbn:de:gbv:wim2-20111215-4287}, year = {1997}, abstract = {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.}, subject = {Finite-Elemente-Methode}, language = {en} } @phdthesis{Eckardt2009, author = {Eckardt, Stefan}, title = {Adaptive heterogeneous multiscale models for the nonlinear simulation of concrete}, doi = {10.25643/bauhaus-universitaet.1416}, url = {http://nbn-resolving.de/urn:nbn:de:gbv:wim2-20100317-15023}, school = {Bauhaus-Universit{\"a}t Weimar}, year = {2009}, abstract = {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.}, subject = {Beton}, language = {en} } @article{LeeLee2004, author = {Lee, Kangkun and Lee, Kijang}, title = {Additional bending moment for shear-lag phenomenon in tube structures}, doi = {10.25643/bauhaus-universitaet.247}, url = {http://nbn-resolving.de/urn:nbn:de:gbv:wim2-20111215-2472}, year = {2004}, abstract = {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.}, subject = {Finite-Elemente-Methode}, language = {en} } @inproceedings{DaniunasKomkaWerner2000, author = {Daniunas, A. and Komka, A. and Werner, F.}, title = {ANALYSIS AND DETERMINATION OF STRENGTH IN PLASTIC STAGE OF FREE FORM STEEL SHAPES}, doi = {10.25643/bauhaus-universitaet.580}, url = {http://nbn-resolving.de/urn:nbn:de:gbv:wim2-20111215-5803}, year = {2000}, abstract = {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.}, subject = {Stahlkonstruktion}, language = {en} } @article{MostEckardt2004, author = {Most, Thomas and Eckardt, Stefan}, title = {Application of a hybrid parallelization technique to accelerate the numerical simulation of nonlinear mechanical problems}, doi = {10.25643/bauhaus-universitaet.259}, url = {http://nbn-resolving.de/urn:nbn:de:gbv:wim2-20111215-2599}, year = {2004}, abstract = {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.}, subject = {Framework }, language = {en} } @article{MelnikovSemenov2004, author = {Melnikov, B. E. and Semenov, Artem}, title = {Application of Multimodel Method of Elasto-Plastic Analysis for the Multilevel Computation of Structures}, doi = {10.25643/bauhaus-universitaet.248}, url = {http://nbn-resolving.de/urn:nbn:de:gbv:wim2-20111215-2487}, year = {2004}, abstract = {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.}, subject = {Finite-Elemente-Methode}, language = {en} } @phdthesis{Roos2001, author = {Roos, Dirk}, title = {Approximation und Interpolation von Grenzzustandsfunktionen zur Sicherheitsbewertung nichtlinearer Finite-Elemente-Strukturen}, doi = {10.25643/bauhaus-universitaet.71}, url = {http://nbn-resolving.de/urn:nbn:de:gbv:wim2-20040311-745}, school = {Bauhaus-Universit{\"a}t Weimar}, year = {2001}, abstract = {Die vorliegende Arbeit besch{\"a}ftigt 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 f{\"u}r jede Realisation der Zufallsvariablen. Die Strukturanalysen bilden jedoch den Hauptanteil am Berechnungsaufwand der Zuverl{\"a}ssigkeitsanalyse, so dass die Analyse von realistischen Strukturen mit nichtlinearem Verhalten durch die begrenzten Computer-Ressourcen stark eingeschr{\"a}nkt ist. Die klassischen Antwortfl{\"a}chenverfahren approximieren die Funktion der Strukturantwort oder aber die Grenzzustandsfunktion durch Polynome niedriger Ordnung. Dadurch ist f{\"u}r die Auswertung des Versagens-Kriteriums nur noch von Interesse, ob eine Realisation der Basisvariablen innerhalb oder außerhalb des von der Antwortfl{\"a}chenfunktion 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 {\"u}ber den Verlauf der Grenzzustandsfunktion, da die aufgefundenen St{\"u}tzstellen aus den vorangegangenen Simulationsl{\"a}ufen nicht ber{\"u}cksichtigt werden k{\"o}nnen. Aus diesem Grund erscheint eine Kombination beider Simulationsverfahren und eine Interpolation mittels einer Antwortfl{\"a}che geeignet, diese Probleme zu l{\"o}sen. Dies war die Motivation f{\"u}r die Entwicklung eines Verfahren der adaptiven Simulation der Einheitsvektoren und anschließender Interpolation der Grenzzustandsfunktion durch eine Antwortfl{\"a}chenfunktion. Dieses Vorgehen stellt besondere Anforderungen an die Antwortfl{\"a}chenfunktion. Diese muss flexibel genug sein, um stark nichtlineare Grenzzustandsfunktionen beliebig genau ann{\"a}hern zu k{\"o}nnen. Außerdem sollte die Anzahl der verarbeitbaren St{\"u}tzstellen nicht begrenzt sein. Auch ist zu ber{\"u}cksichtigen, dass die Ermittlung der St{\"u}tzstellen auf der Grenzzustandsfunktion nicht regelm{\"a}ßig 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 erf{\"u}llen 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 erf{\"u}llen diese Anforderungen.}, subject = {Tragwerk}, language = {de} } @phdthesis{Schorling1997, author = {Schorling, York}, title = {Beitrag zur Stabilit{\"a}tsuntersuchung von Strukturen mit r{\"a}umlich korrelierten geometrischen Imperfektionen}, doi = {10.25643/bauhaus-universitaet.29}, url = {http://nbn-resolving.de/urn:nbn:de:gbv:wim2-20040216-317}, school = {Bauhaus-Universit{\"a}t Weimar}, year = {1997}, abstract = {F{\"u}r geometrisch imperfekte Strukturen wird die Versagenswahrscheinlichkeit bez{\"u}glich Stabilit{\"a}tskriterien bestimmt. Eine probabilistische Beschreibung der geometrischen Imperfektionen erfolgt mit skalaren ortsdiskretisierten Zufallsfeldern. Die Stabilit{\"a}tsberechnungen werden mit der Finite Elemente Methode durchgef{\"u}hrt. Ausgangspunkt der Berechnung ist eine systematische Formulierung probabilistisch gewichteter Imperfektionsformen durch eine Eigenwertzerlegung der Kovarianzmatrix. Wenn mit einer strukturmechanisch orientierten Sensitivit{\"a}tsanalyse ein Unterraum zur n{\"a}herungsweisen Beschreibung des probabilistischen Strukturverhaltens gefunden wird, kann die Versagenswahrscheinlichkeit numerisch sehr effizient durch ein Interaktionsmodell bestimmt werden. Es zeigte sich, daß dies genau dann m{\"o}glich ist, wenn die Beulform merklich im Imperfektionsfeld enthalten ist. Die Imperfektionsform am Bemessungspunkt entspricht dann, unabh{\"a}ngig 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 m{\"o}glich.}, subject = {Tragwerk}, language = {de} } @phdthesis{Will1999, author = {Will, Johannes}, title = {Beitrag zur Standsicherheitsberechnung im gekl{\"u}fteten Fels in der Kontinuums- und Diskontinuumsmechanik unter Verwendung impliziter und expliziter Berechnungsstrategien}, doi = {10.25643/bauhaus-universitaet.58}, url = {http://nbn-resolving.de/urn:nbn:de:gbv:wim2-20040310-613}, school = {Bauhaus-Universit{\"a}t Weimar}, year = {1999}, subject = {Staumauer}, language = {de} } @article{ReichertOlneyLahmer, author = {Reichert, Ina and Olney, Peter and Lahmer, Tom}, title = {Combined approach for optimal sensor placement and experimental verification in the context of tower-like structures}, series = {Journal of Civil Structural Health Monitoring}, volume = {2021}, journal = {Journal of Civil Structural Health Monitoring}, number = {volume 11}, publisher = {Heidelberg}, address = {Springer}, doi = {10.1007/s13349-020-00448-7}, url = {http://nbn-resolving.de/urn:nbn:de:gbv:wim2-20210804-44701}, pages = {223 -- 234}, abstract = {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.}, subject = {Strukturmechanik}, language = {en} } @article{AtaollahiOshkourTalebiSeyedShirazietal., author = {Ataollahi Oshkour, Azim and Talebi, Hossein and Seyed Shirazi, Seyed Farid and Bayat, Mehdi and Yau, Yat Huang and Tarlochan, Faris and Abu Osman, Noor Azuan}, title = {Comparison of various functionally graded femoral prostheses by finite element analysis}, series = {Scientific World Journal}, journal = {Scientific World Journal}, doi = {10.1155/2014/807621}, url = {http://nbn-resolving.de/urn:nbn:de:gbv:wim2-20170413-31194}, abstract = {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.}, subject = {Finite-Elemente-Methode}, language = {en} } @phdthesis{Hanna, author = {Hanna, John}, title = {Computational Fracture Modeling and Design of Encapsulation-Based Self-Healing Concrete Using XFEM and Cohesive Surface Technique}, doi = {10.25643/bauhaus-universitaet.4746}, url = {http://nbn-resolving.de/urn:nbn:de:gbv:wim2-20221124-47467}, school = {Bauhaus-Universit{\"a}t Weimar}, pages = {125}, abstract = {Encapsulation-based self-healing concrete (SHC) is the most promising technique for providing a self-healing mechanism to concrete. This is due to its capacity to heal fractures effectively without human interventions, extending the operational life and lowering maintenance costs. The healing mechanism is created by embedding capsules containing the healing agent inside the concrete. The healing agent will be released once the capsules are fractured and the healing occurs in the vicinity of the damaged part. The healing efficiency of the SHC is still not clear and depends on several factors; in the case of microcapsules SHC the fracture of microcapsules is the most important aspect to release the healing agents and hence heal the cracks. This study contributes to verifying the healing efficiency of SHC and the fracture mechanism of the microcapsules. Extended finite element method (XFEM) is a flexible, and powerful discrete crack method that allows crack propagation without the requirement for re-meshing and has been shown high accuracy for modeling fracture in concrete. In this thesis, a computational fracture modeling approach of Encapsulation-based SHC is proposed based on the XFEM and cohesive surface technique (CS) to study the healing efficiency and the potential of fracture and debonding of the microcapsules or the solidified healing agents from the concrete matrix as well. The concrete matrix and a microcapsule shell both are modeled by the XFEM and combined together by CS. The effects of the healed-crack length, the interfacial fracture properties, and microcapsule size on the load carrying capability and fracture pattern of the SHC have been studied. The obtained results are compared to those obtained from the zero thickness cohesive element approach to demonstrate the significant accuracy and the validity of the proposed simulation. The present fracture simulation is developed to study the influence of the capsular clustering on the fracture mechanism by varying the contact surface area of the CS between the microcapsule shell and the concrete matrix. The proposed fracture simulation is expanded to 3D simulations to validate the 2D computational simulations and to estimate the accuracy difference ratio between 2D and 3D simulations. In addition, a proposed design method is developed to design the size of the microcapsules consideration of a sufficient volume of healing agent to heal the expected crack width. This method is based on the configuration of the unit cell (UC), Representative Volume Element (RVE), Periodic Boundary Conditions (PBC), and associated them to the volume fraction (Vf) and the crack width as variables. The proposed microcapsule design is verified through computational fracture simulations.}, subject = {Beton}, language = {en} } @article{LegatiukWeiszPatrault, author = {Legatiuk, Dmitrii and Weisz-Patrault, Daniel}, title = {Coupling of Complex Function Theory and Finite Element Method for Crack Propagation Through Energetic Formulation: Conformal Mapping Approach and Reduction to a Riemann-Hilbert Problem}, series = {Computational Methods and Function Theory}, volume = {2021}, journal = {Computational Methods and Function Theory}, publisher = {Springer}, address = {Heidelberg}, doi = {10.1007/s40315-021-00403-7}, url = {http://nbn-resolving.de/urn:nbn:de:gbv:wim2-20210805-44763}, pages = {1 -- 23}, abstract = {In this paper we present a theoretical background for a coupled analytical-numerical approach to model a crack propagation process in two-dimensional bounded domains. The goal of the coupled analytical-numerical approach is to obtain the correct solution behaviour near the crack tip by help of the analytical solution constructed by using tools of complex function theory and couple it continuously with the finite element solution in the region far from the singularity. In this way, crack propagation could be modelled without using remeshing. Possible directions of crack growth can be calculated through the minimization of the total energy composed of the potential energy and the dissipated energy based on the energy release rate. Within this setting, an analytical solution of a mixed boundary value problem based on complex analysis and conformal mapping techniques is presented in a circular region containing an arbitrary crack path. More precisely, the linear elastic problem is transformed into a Riemann-Hilbert problem in the unit disk for holomorphic functions. Utilising advantages of the analytical solution in the region near the crack tip, the total energy could be evaluated within short computation times for various crack kink angles and lengths leading to a potentially efficient way of computing the minimization procedure. To this end, the paper presents a general strategy of the new coupled approach for crack propagation modelling. Additionally, we also discuss obstacles in the way of practical realisation of this strategy.}, subject = {Angewandte Mathematik}, language = {en} } @article{KaklauskasCervenkaCervenka2004, author = {Kaklauskas, Gintaris and Cervenka, Vladimir and Cervenka, Jan}, title = {Deflection Calculation of RC Beams: Finite Element Software versus Design Code Methods}, doi = {10.25643/bauhaus-universitaet.249}, url = {http://nbn-resolving.de/urn:nbn:de:gbv:wim2-20111215-2498}, year = {2004}, abstract = {The paper investigates accuracy of deflection predictions made by the finite element package ATENA and design code methods ACI and EC2. Deflections have been calculated for a large number of experimental reinforced concrete beams reported by three investigators. Statistical parameters have been established for each of the technique at different load levels, separately for the beams with small and moderate reinforcement ratio.}, subject = {Finite-Elemente-Methode}, language = {en} } @article{EirinhevskyDikhnyakEirichevskyetal.1997, author = {{\^E}irinhevsky, V. V. and D{\^i}khnyak, B. M. and {\^E}irichevsky, R. V. and {\^E}{\^i}zub, Y. G.}, title = {Determination of the Temperature of Dissipative Warming and Parameters of Fracture in Elastomers with using of Singular Finite Elements}, doi = {10.25643/bauhaus-universitaet.547}, url = {http://nbn-resolving.de/urn:nbn:de:gbv:wim2-20111215-5471}, year = {1997}, abstract = {For modeling of singular fields of stresses and deformations in elasters with a crack is offered to use of three-dimesional a special finite element. Weak compessible of elasters is taken into account on the basis of threefold approximation of fields of displacements, deformations and function of volume change. At intensive cyclic loading of the elastomer constructions with a crack it is necessary to take into account warming and large deformations at the crack top. The stress-deformed state elasters with a crack is determined from the decision of a nonlinear problem by a modified method Newton-Kantorovich. Account stress intensity factors for a rectangular plate with a various arrangement of a through crack is executed. Process of development of a surface crack and dissipative warming in prismatic a element of shift is investigated.}, subject = {Elastomer}, language = {en} } @article{PickHeimsundMilbradt2004, author = {Pick, Tobias and Heimsund, Bjoern-Ove and Milbradt, Peter}, title = {Development and Analysis of Sparse Matrix Concepts for Finite Element Approximation on general Cells}, doi = {10.25643/bauhaus-universitaet.250}, url = {http://nbn-resolving.de/urn:nbn:de:gbv:wim2-20111215-2500}, year = {2004}, abstract = {In engineering and computing, the finite element approximation is one of the most well-known computational solution techniques. It is a great tool to find solutions for mechanic, fluid mechanic and ecological problems. Whoever works with the finite element method will need to solve a large system of linear equations. There are different ways to find a solution. One way is to use a matrix decomposition technique such as LU or QR. The other possibility is to use an iterative solution algorithm like Conjugate Gradients, Gauß-Seidel, Multigrid Methods, etc. This paper will focus on iterative solvers and the needed storage techniques...}, subject = {Finite-Elemente-Methode}, language = {en} } @inproceedings{DuckeEcksteinMontag2000, author = {Ducke, M. and Eckstein, U. and Montag, U.}, title = {Die Eisenbahnbr{\"u}cken des Lehrter Bahnhofs in Berlin - Ein ganzheitliches FE-Berechnungskonzept}, doi = {10.25643/bauhaus-universitaet.581}, url = {http://nbn-resolving.de/urn:nbn:de:gbv:wim2-20111215-5812}, year = {2000}, abstract = {Der Komplexit{\"a}t moderner Br{\"u}ckenbauwerke scheinen die verwendeten Berechungsmodelle oft nicht angemessen. Tragwerksberechnungen basieren in vielen F{\"a}llen noch auf der Vorgehensweise, das Br{\"u}ckenbauwerk in Einzelbauteile zu zerlegen und mit unterschiedlichen Teilmodellen zu behandeln. Das erscheint, auch vor dem Hintergrund st{\"a}ndig wachsender Rechnerleistung, nicht mehr zeitgem{\"a}ß. Dies gilt zum Beispiel auch f{\"u}r die g{\"a}ngige Praxis, fl{\"a}chenhafte Br{\"u}cken{\"u}berbauten mit Balkenmodellen zu berechnen. Der vorliegende Beitrag stellt ein ganzheitliches Berech-nungskonzept vor, welches auf der Basis eines einzigen FE-Modells die Berechnung des Gesamtbauwerks erlaubt. Damit wird f{\"u}r alle Bauteile neben der Zustandsgr{\"o}ßenberechnung auch die Bemessung von Stahl- und Spannbetonbauteilen bis hin zu Nachweisen wie zur Beschr{\"a}nkung der Rissbreite gef{\"u}hrt. Die Anwendung dieses Berechnungskonzeptes wird am Beispiel der Eisenbahn{\"u}berf{\"u}hrung des neuen Lehrter Bahn-hofs in Berlin gezeigt. Das verwendete FE-Modell umfasst Baugrund, Fundamente, Stahl- bzw. Gußstahlunterkonstruktion sowie den Stahl- bzw. Spannbeton{\"u}berbau. Besonderheiten sind unter anderem die Modellierung des plattenbalkenartigen {\"U}berbaus durch exzentrische, vorspannbare Schalenelemente und das getrennte Vorhalten von tragwerks- und lastbezogenen Eingabefiles. Damit gelingt die sequentielle Erfassung unterschiedlicher Bettungsmoduli zur Simulation statischer und dynamischer Beanspruchungen, die Ber{\"u}cksichtigung des Anspannens und der Interaktion zwischen vorgespannten Stahlverb{\"a}nden zur Aufnahme von Horizontallasten sowie die Ber{\"u}cksichtigung unterschiedlicher statischer Systeme bei der Herstellung des Spannbeton{\"u}berbaus.}, subject = {Berlin}, language = {de} } @inproceedings{ZolotovAkimov2003, author = {Zolotov, Alexander B. and Akimov, Pavel}, title = {Discrete-continual Finite Element Method of Analysis for Three-dimensional Curvilinear Structures}, doi = {10.25643/bauhaus-universitaet.384}, url = {http://nbn-resolving.de/urn:nbn:de:gbv:wim2-20111215-3848}, year = {2003}, abstract = {This paper is devoted to discrete-continual finite element method (DCFEM) of analysis for three-dimensional curvilinear structures. Operational and variational formulations of the problem in the ring coordinate system are presented. The discrete-continual design model for structures with constant physical and geometrical parameters in longitudinal direction is offered on the basis of so-called curvilinear discrete-continual finite elements. Element coordinate system, approximation of nodal unknowns, construction of element nodal load vector are under consideration. Element system of differential equations is formulated with use of special generalized block-structured stiffness matrix of discrete-continual finite element. Local differential relations are formulated. Resultant multipoint boundary problem for system of ordinary differential equations is given. Method of analytical solution of multipoint boundary problems in structural analysis is offered as well. Its major peculiarities include universality, computer-oriented algorithm involving theory of distributions, computational stability, optimal conditionality of resultant systems, partial Jordan decomposition of matrix of coefficients, eliminating necessity of calculation of root vectors. Brief information concerning developed software is provided.}, subject = {Raumtragwerk}, language = {de} } @inproceedings{BurghardtMeissner2000, author = {Burghardt, Michael and Meißner, Udo F.}, title = {Dreidimensionale Finite-Element-Baugrundmodelle f{\"u}r Ingeniuerprobleme}, doi = {10.25643/bauhaus-universitaet.575}, url = {http://nbn-resolving.de/urn:nbn:de:gbv:wim2-20111215-5750}, year = {2000}, abstract = {Bei komplexen Gr{\"u}ndungskonstruktionen sind Planungsfehler durch eine konsistente Modellierung vermeidbar. Manuelle Berechnungsmethoden erm{\"o}glichen im allgemeinen ein dreidimensionales Vorgehen nicht. Numerische Berechnungsmethoden, wie z.B. die Finite-Element-Methode, sind ein optimales Werkzeug zur ganzheitlichen Simulation des Problems. Die f{\"u}r die Finite-Element-Analyse notwendige Diskretisierung komplexer Bau- grundstrukturen ist manuell nicht zu bew{\"a}ltigen. Der vorliegende Beitrag zeigt wie ein Finite-Element-Modell automatisch aus einem geotechnischen Modell unter Ber{\"u}cksichtigung der spezifischen Anforderungen der Baugrund-Tragwerk-Struktur und des Bauablaufes erzeugt werden kann. Hierbei wird die Ber{\"u}cksichtigung der geometrischen und der mechanischen Besonderheiten bei der Netzgenerierung dargestellt.}, subject = {Baugrund}, language = {de} } @inproceedings{GabbertGrochlaKoeppe1997, author = {Gabbert, U. and Grochla, J. and K{\"o}ppe, H.}, title = {Dynamic-explicit finite element simulation of complex problems in civil engineering by parallel computing}, doi = {10.25643/bauhaus-universitaet.425}, url = {http://nbn-resolving.de/urn:nbn:de:gbv:wim2-20111215-4259}, year = {1997}, abstract = {The paper deals with the simulation of the non-linear and time dependent behaviour of complex structures in engineering. Such simulations have to provide high accuracy in the prediction of deformations and stability, by taking into account the long term influences of the non-linear behaviour of the material as well as the large deformation and contact conditions. The limiting factors of the computer simulation are the computer run time and the memory requirement during solving large scale problems. To overcome these problems we use a dynamic-explicit time integration procedure for the solution of the semi-discrete equations of motion, which is very suited for parallel processing. In the paper at first we give a brief review of the theoretical background of the mechanical modelling and the dynamic-explicit technique for the solution of the semi-discrete equations of motion. Then the concept of parallel processing will be discussed . A test example concludes the paper.}, subject = {Tragwerk}, language = {en} } @misc{Ullrich2005, type = {Master Thesis}, author = {Ullrich, Carmen}, title = {Dynamische Analyse der Sprottetalbr{\"u}cke}, doi = {10.25643/bauhaus-universitaet.726}, url = {http://nbn-resolving.de/urn:nbn:de:gbv:wim2-20111215-7268}, school = {Bauhaus-Universit{\"a}t Weimar}, year = {2005}, abstract = {Die vorliegende Arbeit besch{\"a}ftigt sich mit der dynamischen Analyse der Sprottetalbr{\"u}cke infolge aufgetretener Asphaltsch{\"a}den. Sie beinhaltet die Erstellung eines FE-Modells, der Darstellung der theoretischen Grundlagen der Dynamik sowie die Auswertung von berechneten Eigenformen und Asphaltspannungen unter Ber{\"u}cksichtigung der derzeit g{\"u}ltigen Normen.}, subject = {Finite-Elemente-Methode}, language = {de} } @article{KwakKim2004, author = {Kwak, Hyo-Gyoung and Kim, Jin-Kook}, title = {Efficient Shoring System in RC Frame Structures}, doi = {10.25643/bauhaus-universitaet.251}, url = {http://nbn-resolving.de/urn:nbn:de:gbv:wim2-20111215-2511}, year = {2004}, abstract = {In this paper, systematic analyses for the shoring systems installed to support the applied loads during construction are performed on the basis of the numerical approach. On the basis of a rigorous time-dependent analysis, structural behaviors of reinforced concrete (RC) frame structures according to the changes in design variables such as the types of shoring systems, shore stiffness and shore spacing are analyzed and discussed. The time-dependent deformations of concrete such as creep and shrinkage and construction sequences of frame structures are also taken into account to minimize the structural instability and to reach to an improved design of shoring system because these effects may increase the axial forces delivered to the shores. In advance, the influence of the column shortening effect, generally mentioned in a tall building structure, is analyzed. From many parametric studies, it has been finally concluded that the most effective shoring system in RC frame structures is 2S1R (two shores and one reshore) regardless of the changes in design variables.}, subject = {Finite-Elemente-Methode}, language = {en} } @inproceedings{Tzanev1997, author = {Tzanev, D.}, title = {Entwurf eines objektorientierten Modells zur Analyse von Schalentragwerken}, doi = {10.25643/bauhaus-universitaet.439}, url = {http://nbn-resolving.de/urn:nbn:de:gbv:wim2-20111215-4397}, year = {1997}, abstract = {In der vorliegenden Arbeit werden dickwandige Schalentragwerke unter statischen Belastungen betrachtet. Die Schale besteht aus verschiedenen Zonen und in jeder Zone wird die Schalenmittelflaeche mittels eines eigenen Geometriegleichungssystems definiert. Das Verzerrungsfeld hat allen 6 unabhaengigen Komponenten unter der Annahme, dass die Querschnittsfasern, die normal zu der Mittelflaeche der unbelasteten Schale sind, geradelinig bleiben. Ein dreidimensionales isoparametrisches finites Element wird vorgeschlagen. Die Berechnung wird mit der Hilfe der Makroelemententechnik durchgefuehrt. In der Arbeit werden die wesentliche Parameter der Schalengeometrie, sowie auch entsprechendes Anteil von Klassen des konstruktiven Modells, definiert. Ein konstruktives Informationsmodell und ein FEM-Informationsmodell, werden entwickelt. Die Informationsverbindungen zwischen den beiden Modellen werden definiert. Diese objektorientierten Modelle werden in Programmiersprache Microsoft Visual C++ v.4.0 unter Windows 95 implementiert. Als numerisches Beispiel wird ein Bogenmauertragwerk betrachtet.}, subject = {Bogenstaumauer}, language = {de} } @article{Lahmer, author = {Lahmer, Tom}, title = {FEM-Based determination of real and complex elastic, dielectric, and piezoelectric moduli in piezoceramic materials}, series = {IEEE Transactions on Ultrasonics, Ferroelectrics, and Frequency Control}, journal = {IEEE Transactions on Ultrasonics, Ferroelectrics, and Frequency Control}, doi = {10.25643/bauhaus-universitaet.3608}, url = {http://nbn-resolving.de/urn:nbn:de:gbv:wim2-20171030-36083}, abstract = {We propose an enhanced iterative scheme for the precise reconstruction of piezoelectric material parameters from electric impedance and mechanical displacement measurements. It is based on finite-element simulations of the full three-dimensional piezoelectric equations, combined with an inexact Newton or nonlinear Landweber iterative inversion scheme. We apply our method to two piezoelectric materials and test its performance. For the first material, the manufacturer provides a full data set; for the second one, no material data set is available. For both cases, our inverse scheme, using electric impedance measurements as input data, performs well.}, subject = {Finite-Elemente-Methode}, language = {en} } @inproceedings{BergerGraeffWeinberg1997, author = {Berger, Hans and Graeff-Weinberg, K.}, title = {FEM-Detailuntersuchungen an Tragwerken unter Einsatz von pNh-{\"U}bergangselementen}, doi = {10.25643/bauhaus-universitaet.426}, url = {http://nbn-resolving.de/urn:nbn:de:gbv:wim2-20111215-4267}, year = {1997}, abstract = {Detailuntersuchungen an Tragwerken f{\"u}hren bei FE-Berechnungen immer wieder auf das Problem einer geeigneten Netzgestaltung. W{\"a}hrend in weiten Bereichen ein grobes Netz ausreicht, muß an kritischen Stellen ein sehr feines Netz gew{\"a}hlt werden, um gerade dort hinreichend genaue Ergebnisse zu erhalten. Bei der Realisierung lokaler Netzverdichtungen stellt die Gestaltung des {\"U}bergangs vom groben zum feinen Netz das Hauptproblem dar. Im Beitrag wird hierzu eine Familie von FE-{\"U}bergangselementen vorgestellt, mit denen sich eine voll-kompatible Kopplung von wenigen großen Elementen mit vielen kleinen Elementen bereits {\"u}ber nur eine Stufe erzielen l{\"a}ßt. Diese neu entwickelten sogenannten pNh-Elemente erm{\"o}glichen an einer oder mehreren Seiten den Anschluß von N kleineren Elementen (Elementseiten f{\"u}r h-Verfeinerung). Das wird durch N st{\"u}ckweise definierte Ansatzfunktionen an den entsprechenden Seiten erreicht, wobei die Teilung nicht {\"a}quidistant sein braucht. Dar{\"u}ber hinaus ist es m{\"o}glich, Elemente unterschiedlichen Polynomgrades p an den Standardseiten und den Verfeinerungsseiten anzuschließen. Der praktische Einsatz der {\"U}bergangselemente setzt geeignete automatische oder halbautomatische Netzgeneratoren voraus, die diese Elemente einbeziehen. Im Rahmen einer substrukturorientierten Modellierung l{\"a}ßt sich dies besonders g{\"u}nstig realisieren. Im Beitrag wird gezeigt, wie durch Zerlegung des Gesamtmodells in Bereiche mit grobem Netz, mit {\"U}bergangsnetz und mit feinem Netz, eine effektive Generierung der Netzverdichtungen zu erreichen ist. An einem praktischen Beispiel aus dem Bauingenieurwesen werden die Vorteile des vorgestellten {\"U}bergangselementkonzeptes umfassend demonstriert.}, subject = {Tragwerk}, language = {de} } @article{MilbradtSchierbaumSchwoeppe2004, author = {Milbradt, Peter and Schierbaum, Jochen and Schw{\"o}ppe, Axel}, title = {Finite Cell-Elements of Higher Order}, doi = {10.25643/bauhaus-universitaet.252}, url = {http://nbn-resolving.de/urn:nbn:de:gbv:wim2-20111215-2524}, year = {2004}, abstract = {The method of the finite elements is an adaptable numerical procedure for interpolation as well as for the numerical approximation of solutions of partial differential equations. The basis of these procedure is the formulation of suitable finite elements and element decompositions of the solution space. Classical finite elements are based on triangles or quadrangles in the two-dimensional space and tetrahedron or hexahedron in the threedimensional space. The use of arbitrary-dimensional convex and non-convex polyhedrons as the geometrical basis of finite elements increases the flexibility of generating finite element decompositions substantially and is sometimes the only way to get a clear decomposition...}, subject = {Finite-Elemente-Methode}, language = {en} } @inproceedings{MilbradtSchwoeppe2003, author = {Milbradt, Peter and Schw{\"o}ppe, Axel}, title = {Finite Element Approximation auf der Basis geometrischer Zellen}, doi = {10.25643/bauhaus-universitaet.333}, url = {http://nbn-resolving.de/urn:nbn:de:gbv:wim2-20111215-3333}, year = {2003}, abstract = {Die Methode der Finiten Elemente ist ein numerisches Verfahren zur Interpolation vorgegebener Werte und zur numerischen Approximation von L{\"o}sungen station{\"a}rer oder instation{\"a}rer partieller Differentialgleichungen bzw. Systemen partieller Differentialgleichungen. Grundlage dieser Verfahren ist die Formulierung geeigneter Finiter Elemente und Finiter Element Zerlegungen. Finite Elemente besitzen in der Regel eine geometrische Basis bestehend aus Strecken im eindimensionalen, Drei- oder Vierecken im zweidimensionalen und Tetra- oder Hexaedern im dreidimensionalen euklidischen Raum, eine Menge von Freiheitsgraden und eine Basis von Funktionen. Die geometrische Basis eines Finiten Elements wird verallgemeinert als geometrische Zelle formuliert. Diese geschlossene geometrische Formulierung f{\"u}hrt zu einer geometrieunabh{\"a}ngigen Definition der Basisfunktionen eines Finiten Elements in den Zellkoordinaten der geometrischen Zelle. Finite Elemente auf der Basis geometrischer Zellen werden als Bestandteile Finiter Element Zerlegungen in Finiten Element Interpolationen und Finiten Element Approximationen verwendet. Die Finiten Element Approximationen werden am Beispiel der 2-dimensionalen Diffusionsgleichung {\"u}ber das Standard-Galerkin-Verfahren ermittelt.}, subject = {Finite-Elemente-Methode}, language = {de} } @phdthesis{Habtemariam, author = {Habtemariam, Abinet Kifle}, title = {Generalized Beam Theory for the analysis of thin-walled circular pipe members}, doi = {10.25643/bauhaus-universitaet.4572}, url = {http://nbn-resolving.de/urn:nbn:de:gbv:wim2-20220127-45723}, school = {Bauhaus-Universit{\"a}t Weimar}, pages = {188}, abstract = {The detailed structural analysis of thin-walled circular pipe members often requires the use of a shell or solid-based finite element method. Although these methods provide a very good approximation of the deformations, they require a higher degree of discretization which causes high computational costs. On the other hand, the analysis of thin-walled circular pipe members based on classical beam theories is easy to implement and needs much less computation time, however, they are limited in their ability to approximate the deformations as they cannot consider the deformation of the cross-section. This dissertation focuses on the study of the Generalized Beam Theory (GBT) which is both accurate and efficient in analyzing thin-walled members. This theory is based on the separation of variables in which the displacement field is expressed as a combination of predetermined deformation modes related to the cross-section, and unknown amplitude functions defined on the beam's longitudinal axis. Although the GBT was initially developed for long straight members, through the consideration of complementary deformation modes, which amend the null transverse and shear membrane strain assumptions of the classical GBT, problems involving short members, pipe bends, and geometrical nonlinearity can also be analyzed using GBT. In this dissertation, the GBT formulation for the analysis of these problems is developed and the application and capabilities of the method are illustrated using several numerical examples. Furthermore, the displacement and stress field results of these examples are verified using an equivalent refined shell-based finite element model. The developed static and dynamic GBT formulations for curved thin-walled circular pipes are based on the linear kinematic description of the curved shell theory. In these formulations, the complex problem in pipe bends due to the strong coupling effect of the longitudinal bending, warping and the cross-sectional ovalization is handled precisely through the derivation of the coupling tensors between the considered GBT deformation modes. Similarly, the geometrically nonlinear GBT analysis is formulated for thin-walled circular pipes based on the nonlinear membrane kinematic equations. Here, the initial linear and quadratic stress and displacement tangent stiffness matrices are built using the third and fourth-order GBT deformation mode coupling tensors. Longitudinally, the formulation of the coupled GBT element stiffness and mass matrices are presented using a beam-based finite element formulation. Furthermore, the formulated GBT elements are tested for shear and membrane locking problems and the limitations of the formulations regarding the membrane locking problem are discussed.}, subject = {Finite-Elemente-Methode}, language = {en} } @phdthesis{Haefner2006, author = {H{\"a}fner, Stefan}, title = {Grid-based procedures for the mechanical analysis of heterogeneous solids}, doi = {10.25643/bauhaus-universitaet.858}, url = {http://nbn-resolving.de/urn:nbn:de:gbv:wim2-20070830-9185}, school = {Bauhaus-Universit{\"a}t Weimar}, year = {2006}, abstract = {The importance of modern simulation methods in the mechanical analysis of heterogeneous solids is presented in detail. Thereby the problem is noted that even for small bodies the required high-resolution analysis reaches the limits of today's computational power, in terms of memory demand as well as acceptable computational effort. A further problem is that frequently the accuracy of geometrical modelling of heterogeneous bodies is inadequate. The present work introduces a systematic combination and adaption of grid-based methods for achieving an essentially higher resolution in the numerical analysis of heterogeneous solids. Grid-based methods are as well primely suited for developing efficient and numerically stable algorithms for flexible geometrical modeling. A key aspect is the uniform data management for a grid, which can be utilized to reduce the effort and complexity of almost all concerned methods. A new finite element program, called Mulgrido, was just developed to realize this concept consistently and to test the proposed methods. Several disadvantages which generally result from grid discretizations are selectively corrected by modified methods. The present work is structured into a geometrical model, a mechanical model and a numerical model. The geometrical model includes digital image-based modeling and in particular several methods for the theory-based generation of inclusion-matrix models. Essential contributions refer to variable shape, size distribution, separation checks and placement procedures of inclusions. The mechanical model prepares the fundamentals of continuum mechanics, homogenization and damage modeling for the following numerical methods. The first topic of the numerical model introduces to a special version of B-spline finite elements. These finite elements are entirely variable in the order k of B-splines. For homogeneous bodies this means that the approximation quality can arbitrarily be scaled. In addition, the multiphase finite element concept in combination with transition zones along material interfaces yields a valuable solution for heterogeneous bodies. As the formulation is element-based, the storage of a global stiffness matrix is superseded such that the memory demand can essentially be reduced. This is possible in combination with iterative solver methods which represent the second topic of the numerical model. Here, the focus lies on multigrid methods where the number of required operations to solve a linear equation system only increases linearly with problem size. Moreover, for badly conditioned problems quite an essential improvement is achieved by preconditioning. The third part of the numerical model discusses certain aspects of damage simulation which are closely related to the proposed grid discretization. The strong efficiency of the linear analysis can be maintained for damage simulation. This is achieved by a damage-controlled sequentially linear iteration scheme. Finally a study on the effective material behavior of heterogeneous bodies is presented. Especially the influence of inclusion shapes is examined. By means of altogether more than one hundred thousand random geometrical arrangements, the effective material behavior is statistically analyzed and assessed.}, subject = {B-Spline}, language = {en} } @inproceedings{GurtovyPiskunov2000, author = {Gurtovy, O. G. and Piskunov, V. G.}, title = {HIGH-PRECISION MODELING AND FINITE-ELEMENT INVESTIGATION OF ELASTOPLASTIC DEFORMATION OF NON-ISOTROPIC THICK SANDWICH PLATES AND SHELLS}, doi = {10.25643/bauhaus-universitaet.584}, url = {http://nbn-resolving.de/urn:nbn:de:gbv:wim2-20111215-5848}, year = {2000}, abstract = {There was suggested a phenomenological modified quadratic condition of the beginning of plasticity for plastic and quasifragile orthotropic materials. Limiting surface in the shape of a paraboloid with an axis bend over hydrostatic axis corresponds to the condition. The equations of theory of current with the isotropic and anisotropic hardenings, associated with the suggested yield condition, modified into the version of determining equations of strain theory of plasticity are received. These defining equations formed the basis of highlyprecise non-classic continual (along thickness) theory of non-linear deformation of thick sandwich plates and sloping shells. In the approximations along the cross coordinate the specificity of flexural and non-flexural deformations is taken into account. The necessity of introducing the approximations of higher order, as well as accounting for the cross compression while decreasing of the relatively cross normal and shear layer rigidness is shown. The specifications, obtained in comparison with the known physically nonlinear specified model of the bending of plates with orthotropic layers are distinguished. An effective procedure of linearization of the solving equations and getting the solutions in frames of the discrete-continual scheme of the finite-element method is suggested. The approximations of higher order let to model the appearance of the cracs of layers being split by the introducing of slightly hard thin layers into the finite element, not violating the idea of continuality of theory. Calculation of a threelayer plate with rigid face diaphragms on the contour is considered}, subject = {Platte}, language = {en} } @misc{Kurukuri2005, type = {Master Thesis}, author = {Kurukuri, Srihari}, title = {Homogenization of Damaged Concrete Mesostructures using Representative Volume Elements - Implementation and Application to SLang}, doi = {10.25643/bauhaus-universitaet.667}, url = {http://nbn-resolving.de/urn:nbn:de:gbv:wim2-20111215-6670}, school = {Bauhaus-Universit{\"a}t Weimar}, year = {2005}, abstract = {This master thesis explores an important and under-researched topic on the so-called bridging of length scales (from >meso< to >macro<), with the concept of homogenization in which the careful characterization of mechanical response requires that the developed material model >bridge< the representations of events that occur at two different scales. The underlying objective here is to efficiently incorporate material length scales in the classical continuum plasticity/damage theories through the concept of homogenization theory. The present thesis is devoted to computational modeling of heterogeneous materials, primarily to matrix-inclusion type of materials. Considerations are focused predominantly on the elastic and damage behavior as a response to quasistatic mechanical loading. Mainly this thesis focuses to elaborate a sound numerical homogenization model which accounts for the prediction of overall properties with the application of different types of boundary conditions namely: periodic, homogeneous and mixed type of boundary conditions over two-dimensional periodic and non-periodic RVEs and three-dimensional non-periodic RVEs. Identification of the governing mechanisms and assessing their effect on the material behavior leads one step further. Bringing together this knowledge with service requirements allows for functional oriented materials design. First, this thesis gives attention on providing the theoretical basic mechanisms involved in homogenization techniques and a survey will be made on existing analytical methods available in literature. Second, the proposed frameworks are implemented in the well known finite element software programs ANSYS and SLang. Simple and efficient algorithms in FORTRAN are developed for automated microstructure generation using RSA algorithm in order to perform a systematic numerical testing of microstructures of composites. Algorithms are developed to generate constraint equations in periodic boundary conditions and different displacements applied spatially over the boundaries of the RVE in homogeneous boundary conditions. Finally, nonlinear simulations are performed at mesolevel, by considering continuum scalar damage behavior of matrix material with the linear elastic behavior of aggregates with the assumption of rigid bond between constituents.}, subject = {Schadensmechanik}, language = {en} } @phdthesis{Schwedler, author = {Schwedler, Michael}, title = {Integrated structural analysis using isogeometric finite element methods}, doi = {10.25643/bauhaus-universitaet.2737}, url = {http://nbn-resolving.de/urn:nbn:de:gbv:wim2-20170130-27372}, school = {Bauhaus-Universit{\"a}t Weimar}, pages = {209}, abstract = {The gradual digitization in the architecture, engineering, and construction industry over the past fifty years led to an extremely heterogeneous software environment, which today is embodied by the multitude of different digital tools and proprietary data formats used by the many specialists contributing to the design process in a construction project. Though these projects become increasingly complex, the demands on financial efficiency and the completion within a tight schedule grow at the same time. The digital collaboration of project partners has been identified as one key issue in successfully dealing with these challenges. Yet currently, the numerous software applications and their respective individual views on the design process severely impede that collaboration. An approach to establish a unified basis for the digital collaboration, regardless of the existing software heterogeneity, is a comprehensive digital building model contributed to by all projects partners. This type of data management known as building information modeling (BIM) has many benefits, yet its adoption is associated with many difficulties and thus, proceeds only slowly. One aspect in the field of conflicting requirements on such a digital model is the cooperation of architects and structural engineers. Traditionally, these two disciplines use different abstractions of reality for their models that in consequence lead to incompatible digital representations thereof. The onset of isogeometric analysis (IGA) promised to ease the discrepancy in design and analysis model representations. Yet, that initial focus quickly shifted towards using these methods as a more powerful basis for numerical simulations. Furthermore, the isogeometric representation alone is not capable of solving the model abstraction problem. It is thus the intention of this work to contribute to an improved digital collaboration of architects and engineers by exploring an integrated analysis approach on the basis of an unified digital model and solid geometry expressed by splines. In the course of this work, an analysis framework is developed that utilizes such models to automatically conduct numerical simulations commonly required in construction projects. In essence, this allows to retrieve structural analysis results from BIM models in a fast and simple manner, thereby facilitating rapid design iterations and profound design feedback. The BIM implementation Industry Foundation Classes (IFC) is reviewed with regard to its capabilities of representing the unified model. The current IFC schema strongly supports the use of redundant model data, a major pitfall in digital collaboration. Additionally, it does not allow to describe the geometry by volumetric splines. As the pursued approach builds upon a unique model for both, architectural and structural design, and furthermore requires solid geometry, necessary schema modifications are suggested. Structural entities are modeled by volumetric NURBS patches, each of which constitutes an individual subdomain that, with regard to the analysis, is incompatible with the remaining full model. The resulting consequences for numerical simulation are elaborated in this work. The individual subdomains have to be weakly coupled, for which the mortar method is used. Different approaches to discretize the interface traction fields are implemented and their respective impact on the analysis results is evaluated. All necessary coupling conditions are automatically derived from the related geometry model. The weak coupling procedure leads to a linear system of equations in saddle point form, which, owed to the volumetric modeling, is large in size and, the associated coefficient matrix has, due to the use of higher degree basis functions, a high bandwidth. The peculiarities of the system require adapted solution methods that generally cause higher numerical costs than the standard procedures for symmetric, positive-definite systems do. Different methods to solve the specific system are investigated and an efficient parallel algorithm is finally proposed. When the structural analysis model is derived from the unified model in the BIM data, it does in general initially not meet the requirements on the discretization that are necessary to obtain sufficiently accurate analysis results. The consequently necessary patch refinements must be controlled automatically to allowfor an entirely automatic analysis procedure. For that purpose, an empirical refinement scheme based on the geometrical and possibly mechanical properties of the specific entities is proposed. The level of refinement may be selectively manipulated by the structural engineer in charge. Furthermore, a Zienkiewicz-Zhu type error estimator is adapted for the use with isogeometric analysis results. It is shown that also this estimator can be used to steer an adaptive refinement procedure.}, subject = {Finite-Elemente-Methode}, language = {en} } @phdthesis{Nanthakumar, author = {Nanthakumar, S.S.}, title = {Inverse and optimization problems in piezoelectric materials using Extended Finite Element Method and Level sets}, doi = {10.25643/bauhaus-universitaet.2709}, url = {http://nbn-resolving.de/urn:nbn:de:gbv:wim2-20161128-27095}, school = {Bauhaus-Universit{\"a}t Weimar}, abstract = {Piezoelectric materials are used in several applications as sensors and actuators where they experience high stress and electric field concentrations as a result of which they may fail due to fracture. Though there are many analytical and experimental works on piezoelectric fracture mechanics. There are very few studies about damage detection, which is an interesting way to prevent the failure of these ceramics. An iterative method to treat the inverse problem of detecting cracks and voids in piezoelectric structures is proposed. Extended finite element method (XFEM) is employed for solving the inverse problem as it allows the use of a single regular mesh for large number of iterations with different flaw geometries. Firstly, minimization of cost function is performed by Multilevel Coordinate Search (MCS) method. The XFEM-MCS methodology is applied to two dimensional electromechanical problems where flaws considered are straight cracks and elliptical voids. Then a numerical method based on combination of classical shape derivative and level set method for front propagation used in structural optimization is utilized to minimize the cost function. The results obtained show that the XFEM-level set methodology is effectively able to determine the number of voids in a piezoelectric structure and its corresponding locations. The XFEM-level set methodology is improved to solve the inverse problem of detecting inclusion interfaces in a piezoelectric structure. The material interfaces are implicitly represented by level sets which are identified by applying regularisation using total variation penalty terms. The formulation is presented for three dimensional structures and inclusions made of different materials are detected by using multiple level sets. The results obtained prove that the iterative procedure proposed can determine the location and approximate shape of material subdomains in the presence of higher noise levels. Piezoelectric nanostructures exhibit size dependent properties because of surface elasticity and surface piezoelectricity. Initially a study to understand the influence of surface elasticity on optimization of nano elastic beams is performed. The boundary of the nano structure is implicitly represented by a level set function, which is considered as the design variable in the optimization process. Two objective functions, minimizing the total potential energy of a nanostructure subjected to a material volume constraint and minimizing the least square error compared to a target displacement, are chosen for the numerical examples. The numerical examples demonstrate the importance of size and aspect ratio in determining how surface effects impact the optimized topology of nanobeams. Finally a conventional cantilever energy harvester with a piezoelectric nano layer is analysed. The presence of surface piezoelectricity in nano beams and nano plates leads to increase in electromechanical coupling coefficient. Topology optimization of these piezoelectric structures in an energy harvesting device to further increase energy conversion using appropriately modified XFEM-level set algorithm is performed .}, subject = {Finite-Elemente-Methode}, language = {de} } @phdthesis{Hossain, author = {Hossain, Md Naim}, title = {Isogeometric analysis based on Geometry Independent Field approximaTion (GIFT) and Polynomial Splines over Hierarchical T-meshes}, doi = {10.25643/bauhaus-universitaet.4037}, url = {http://nbn-resolving.de/urn:nbn:de:gbv:wim2-20191129-40376}, school = {Bauhaus-Universit{\"a}t Weimar}, pages = {157}, abstract = {This thesis addresses an adaptive higher-order method based on a Geometry Independent Field approximatTion(GIFT) of polynomial/rationals plines over hierarchical T-meshes(PHT/RHT-splines). In isogeometric analysis, basis functions used for constructing geometric models in computer-aided design(CAD) are also employed to discretize the partial differential equations(PDEs) for numerical analysis. Non-uniform rational B-Splines(NURBS) are the most commonly used basis functions in CAD. However, they may not be ideal for numerical analysis where local refinement is required. The alternative method GIFT deploys different splines for geometry and numerical analysis. NURBS are utilized for the geometry representation, while for the field solution, PHT/RHT-splines are used. PHT-splines not only inherit the useful properties of B-splines and NURBS, but also possess the capabilities of local refinement and hierarchical structure. The smooth basis function properties of PHT-splines make them suitable for analysis purposes. While most problems considered in isogeometric analysis can be solved efficiently when the solution is smooth, many non-trivial problems have rough solutions. For example, this can be caused by the presence of re-entrant corners in the domain. For such problems, a tensor-product basis (as in the case of NURBS) is less suitable for resolving the singularities that appear since refinement propagates throughout the computational domain. Hierarchical bases and local refinement (as in the case of PHT-splines) allow for a more efficient way to resolve these singularities by adding more degrees of freedom where they are necessary. In order to drive the adaptive refinement, an efficient recovery-based error estimator is proposed in this thesis. The estimator produces a recovery solution which is a more accurate approximation than the computed numerical solution. Several two- and three-dimensional numerical investigations with PHT-splines of higher order and continuity prove that the proposed method is capable of obtaining results with higher accuracy, better convergence, fewer degrees of freedom and less computational cost than NURBS for smooth solution problems. The adaptive GIFT method utilizing PHT-splines with the recovery-based error estimator is used for solutions with discontinuities or singularities where adaptive local refinement in particular domains of interest achieves higher accuracy with fewer degrees of freedom. This method also proves that it can handle complicated multi-patch domains for two- and three-dimensional problems outperforming uniform refinement in terms of degrees of freedom and computational cost.}, subject = {Finite-Elemente-Methode}, language = {en} } @phdthesis{LopezZermeno, author = {L{\´o}pez Zerme{\~n}o, Jorge Alberto}, title = {Isogeometric and CAD-based methods for shape and topology optimization: Sensitivity analysis, B{\´e}zier elements and phase-field approaches}, doi = {10.25643/bauhaus-universitaet.4710}, url = {http://nbn-resolving.de/urn:nbn:de:gbv:wim2-20220831-47102}, school = {Bauhaus-Universit{\"a}t Weimar}, abstract = {The Finite Element Method (FEM) is widely used in engineering for solving Partial Differential Equations (PDEs) over complex geometries. To this end, it is required to provide the FEM software with a geometric model that is typically constructed in a Computer-Aided Design (CAD) software. However, FEM and CAD use different approaches for the mathematical description of the geometry. Thus, it is required to generate a mesh, which is suitable for FEM, based on the CAD model. Nonetheless, this procedure is not a trivial task and it can be time consuming. This issue becomes more significant for solving shape and topology optimization problems, which consist in evolving the geometry iteratively. Therefore, the computational cost associated to the mesh generation process is increased exponentially for this type of applications. The main goal of this work is to investigate the integration of CAD and CAE in shape and topology optimization. To this end, numerical tools that close the gap between design and analysis are presented. The specific objectives of this work are listed below: • Automatize the sensitivity analysis in an isogeometric framework for applications in shape optimization. Applications for linear elasticity are considered. • A methodology is developed for providing a direct link between the CAD model and the analysis mesh. In consequence, the sensitivity analysis can be performed in terms of the design variables located in the design model. • The last objective is to develop an isogeometric method for shape and topological optimization. This method should take advantage of using Non-Uniform Rational B-Splines (NURBS) with higher continuity as basis functions. Isogeometric Analysis (IGA) is a framework designed to integrate the design and analysis in engineering problems. The fundamental idea of IGA is to use the same basis functions for modeling the geometry, usually NURBS, for the approximation of the solution fields. The advantage of integrating design and analysis is two-fold. First, the analysis stage is more accurate since the system of PDEs is not solved using an approximated geometry, but the exact CAD model. Moreover, providing a direct link between the design and analysis discretizations makes possible the implementation of efficient sensitivity analysis methods. Second, the computational time is significantly reduced because the mesh generation process can be avoided. Sensitivity analysis is essential for solving optimization problems when gradient-based optimization algorithms are employed. Automatic differentiation can compute exact gradients, automatically by tracking the algebraic operations performed on the design variables. For the automation of the sensitivity analysis, an isogeometric framework is used. Here, the analysis mesh is obtained after carrying out successive refinements, while retaining the coarse geometry for the domain design. An automatic differentiation (AD) toolbox is used to perform the sensitivity analysis. The AD toolbox takes the code for computing the objective and constraint functions as input. Then, using a source code transformation approach, it outputs a code for computing the objective and constraint functions, and their sensitivities as well. The sensitivities obtained from the sensitivity propagation method are compared with analytical sensitivities, which are computed using a full isogeometric approach. The computational efficiency of AD is comparable to that of analytical sensitivities. However, the memory requirements are larger for AD. Therefore, AD is preferable if the memory requirements are satisfied. Automatic sensitivity analysis demonstrates its practicality since it simplifies the work of engineers and designers. Complex geometries with sharp edges and/or holes cannot easily be described with NURBS. One solution is the use of unstructured meshes. Simplex-elements (triangles and tetrahedra for two and three dimensions respectively) are particularly useful since they can automatically parameterize a wide variety of domains. In this regard, unstructured B{\´e}zier elements, commonly used in CAD, can be employed for the exact modelling of CAD boundary representations. In two dimensions, the domain enclosed by NURBS curves is parameterized with B{\´e}zier triangles. To describe exactly the boundary of a two-dimensional CAD model, the continuity of a NURBS boundary representation is reduced to C^0. Then, the control points are used to generate a triangulation such that the boundary of the domain is identical to the initial CAD boundary representation. Thus, a direct link between the design and analysis discretizations is provided and the sensitivities can be propagated to the design domain. In three dimensions, the initial CAD boundary representation is given as a collection of NURBS surfaces that enclose a volume. Using a mesh generator (Gmsh), a tetrahedral mesh is obtained. The original surface is reconstructed by modifying the location of the control points of the tetrahedral mesh using B{\´e}zier tetrahedral elements and a point inversion algorithm. This method offers the possibility of computing the sensitivity analysis using the analysis mesh. Then, the sensitivities can be propagated into the design discretization. To reuse the mesh originally generated, a moving B{\´e}zier tetrahedral mesh approach was implemented. A gradient-based optimization algorithm is employed together with a sensitivity propagation procedure for the shape optimization cases. The proposed shape optimization approaches are used to solve some standard benchmark problems in structural mechanics. The results obtained show that the proposed approach can compute accurate gradients and evolve the geometry towards optimal solutions. In three dimensions, the moving mesh approach results in faster convergence in terms of computational time and avoids remeshing at each optimization step. For considering topological changes in a CAD-based framework, an isogeometric phase-field based shape and topology optimization is developed. In this case, the diffuse interface of a phase-field variable over a design domain implicitly describes the boundaries of the geometry. The design variables are the local values of the phase-field variable. The descent direction to minimize the objective function is found by using the sensitivities of the objective function with respect to the design variables. The evolution of the phase-field is determined by solving the time dependent Allen-Cahn equation. Especially for topology optimization problems that require C^1 continuity, such as for flexoelectric structures, the isogeometric phase field method is of great advantage. NURBS can achieve the desired continuity more efficiently than the traditional employed functions. The robustness of the method is demonstrated when applied to different geometries, boundary conditions, and material configurations. The applications illustrate that compared to piezoelectricity, the electrical performance of flexoelectric microbeams is larger under bending. In contrast, the electrical power for a structure under compression becomes larger with piezoelectricity.}, subject = {CAD}, language = {en} } @article{KashiyamaHamadaTaniguchi2004, author = {Kashiyama, Kazuo and Hamada, Hidetaka and Taniguchi, Takeo}, title = {Large Scale Finite Element Simulation and Modeling Using GIS/CAD for Environmental Flows in Urban Area}, doi = {10.25643/bauhaus-universitaet.267}, url = {http://nbn-resolving.de/urn:nbn:de:gbv:wim2-20111215-2675}, year = {2004}, abstract = {A large-scale computer modeling and simulation method is presented for environmental flows in urban area. Several GIS and CAD data were used for the preparation of shape model and an automatic mesh generation method based on Delaunay method was developed. Parallel finite element method based on domain decomposition method was employed for the numerical simulation of natural phenomena. The present method was applied to the simulation of flood flow and wind flow in urban area. The present method is shown to be a useful planning and design tool for the natural disasters and the change of environments.}, subject = {Geoinformationssystem}, language = {en} } @article{GalffyWellmannJelicHartmann2004, author = {Galffy, Mozes and Wellmann Jelic, Andres and Hartmann, Dietrich}, title = {Lifetime-oriented modelling of vortex-induced across-wind vibrations on bridge tie rods}, doi = {10.25643/bauhaus-universitaet.253}, url = {http://nbn-resolving.de/urn:nbn:de:gbv:wim2-20111215-2536}, year = {2004}, abstract = {The influence of vortex-induces vibrations on vertical tie rods has been proved as a determinant load factor in the lifetime-oriented dimensioning of arched steel bridges. Particularly, the welded connection plates between the suspenders and the arches often exhibit cracks induced primarily rods. In this context, the synchronization of the vortex-shedding to the rod motion in a critical wind velocity range, the so-called lock-in effect, is of essential interest.}, subject = {Finite-Elemente-Methode}, language = {en} } @phdthesis{Kessler2018, author = {Keßler, Andrea}, title = {Matrix-free voxel-based finite element method for materials with heterogeneous microstructures}, doi = {10.25643/bauhaus-universitaet.3844}, url = {http://nbn-resolving.de/urn:nbn:de:gbv:wim2-20190116-38448}, school = {Bauhaus-Universit{\"a}t Weimar}, pages = {113}, year = {2018}, abstract = {Modern image detection techniques such as micro computer tomography (μCT), magnetic resonance imaging (MRI) and scanning electron microscopy (SEM) provide us with high resolution images of the microstructure of materials in a non-invasive and convenient way. They form the basis for the geometrical models of high-resolution analysis, so called image-based analysis. However especially in 3D, discretizations of these models reach easily the size of 100 Mill. degrees of freedoms and require extensive hardware resources in terms of main memory and computing power to solve the numerical model. Consequently, the focus of this work is to combine and adapt numerical solution methods to reduce the memory demand first and then the computation time and therewith enable an execution of the image-based analysis on modern computer desktops. Hence, the numerical model is a straightforward grid discretization of the voxel-based (pixels with a third dimension) geometry which omits the boundary detection algorithms and allows reduced storage of the finite element data structure and a matrix-free solution algorithm. This in turn reduce the effort of almost all applied grid-based solution techniques and results in memory efficient and numerically stable algorithms for the microstructural models. Two variants of the matrix-free algorithm are presented. The efficient iterative solution method of conjugate gradients is used with matrix-free applicable preconditioners such as the Jacobi and the especially suited multigrid method. The jagged material boundaries of the voxel-based mesh are smoothed through embedded boundary elements which contain different material information at the integration point and are integrated sub-cell wise though without additional boundary detection. The efficiency of the matrix-free methods can be retained.}, subject = {Dissertation}, language = {en} } @inproceedings{PopovaDatchevaIankov2003, author = {Popova, E. D. and Datcheva, Maria and Iankov, Roumen}, title = {Mechanical Models with Interval Parameters}, doi = {10.25643/bauhaus-universitaet.348}, url = {http://nbn-resolving.de/urn:nbn:de:gbv:wim2-20111215-3482}, year = {2003}, abstract = {In this paper we consider modelling of composite material with inclusions where the elastic material properties of both matrix and inclusions are uncertain and vary within prescribed bounds. Such mechanical systems, involving interval uncertainties and modelled by finite element method, can be described by parameter dependent systems of linear interval equations and process variables depending on the system solution. A newly developed hybrid interval approach for solving parametric interval linear systems is applied to the considered model and the results are compared to other interval methods. The hybrid approach provides very sharp bounds for the process variables - element strains and stresses. The sources for overestimation when dealing with interval computations are demonstrated. Based on the element strains and stresses, we introduce a definition for the values of nodal strains and stresses by using a set-theoretic approach.}, subject = {Verbundwerkstoff}, language = {en} } @phdthesis{Jia, author = {Jia, Yue}, title = {Methods based on B-splines for model representation, numerical analysis and image registration}, doi = {10.25643/bauhaus-universitaet.2484}, url = {http://nbn-resolving.de/urn:nbn:de:gbv:wim2-20151210-24849}, school = {Bauhaus-Universit{\"a}t Weimar}, pages = {200}, abstract = {The thesis consists of inter-connected parts for modeling and analysis using newly developed isogeometric methods. The main parts are reproducing kernel triangular B-splines, extended isogeometric analysis for solving weakly discontinuous problems, collocation methods using superconvergent points, and B-spline basis in image registration applications. Each topic is oriented towards application of isogeometric analysis basis functions to ease the process of integrating the modeling and analysis phases of simulation. First, we develop reproducing a kernel triangular B-spline-based FEM for solving PDEs. We review the triangular B-splines and their properties. By definition, the triangular basis function is very flexible in modeling complicated domains. However, instability results when it is applied for analysis. We modify the triangular B-spline by a reproducing kernel technique, calculating a correction term for the triangular kernel function from the chosen surrounding basis. The improved triangular basis is capable to obtain the results with higher accuracy and almost optimal convergence rates. Second, we propose an extended isogeometric analysis for dealing with weakly discontinuous problems such as material interfaces. The original IGA is combined with XFEM-like enrichments which are continuous functions themselves but with discontinuous derivatives. Consequently, the resulting solution space can approximate solutions with weak discontinuities. The method is also applied to curved material interfaces, where the inverse mapping and the curved triangular elements are considered. Third, we develop an IGA collocation method using superconvergent points. The collocation methods are efficient because no numerical integration is needed. In particular when higher polynomial basis applied, the method has a lower computational cost than Galerkin methods. However, the positions of the collocation points are crucial for the accuracy of the method, as they affect the convergent rate significantly. The proposed IGA collocation method uses superconvergent points instead of the traditional Greville abscissae points. The numerical results show the proposed method can have better accuracy and optimal convergence rates, while the traditional IGA collocation has optimal convergence only for even polynomial degrees. Lastly, we propose a novel dynamic multilevel technique for handling image registration. It is application of the B-spline functions in image processing. The procedure considered aims to align a target image from a reference image by a spatial transformation. The method starts with an energy function which is the same as a FEM-based image registration. However, we simplify the solving procedure, working on the energy function directly. We dynamically solve for control points which are coefficients of B-spline basis functions. The new approach is more simple and fast. Moreover, it is also enhanced by a multilevel technique in order to prevent instabilities. The numerical testing consists of two artificial images, four real bio-medical MRI brain and CT heart images, and they show our registration method is accurate, fast and efficient, especially for large deformation problems.}, subject = {Finite-Elemente-Methode}, language = {en} } @article{MortazaviPereiraJiangetal., author = {Mortazavi, Bohayra and Pereira, Luiz Felipe C. and Jiang, Jin-Wu and Rabczuk, Timon}, title = {Modelling heat conduction in polycrystalline hexagonal boron-nitride films}, series = {Scientific Reports}, journal = {Scientific Reports}, doi = {10.1038/srep13228}, url = {http://nbn-resolving.de/urn:nbn:de:gbv:wim2-20170425-31534}, abstract = {We conducted extensive molecular dynamics simulations to investigate the thermal conductivity of polycrystalline hexagonal boron-nitride (h-BN) films. To this aim, we constructed large atomistic models of polycrystalline h-BN sheets with random and uniform grain configuration. By performing equilibrium molecular dynamics (EMD) simulations, we investigated the influence of the average grain size on the thermal conductivity of polycrystalline h-BN films at various temperatures. Using the EMD results, we constructed finite element models of polycrystalline h-BN sheets to probe the thermal conductivity of samples with larger grain sizes. Our multiscale investigations not only provide a general viewpoint regarding the heat conduction in h-BN films but also propose that polycrystalline h-BN sheets present high thermal conductivity comparable to monocrystalline sheets.}, subject = {W{\"a}rmeleitf{\"a}higkeit}, language = {en} } @inproceedings{EbertBucher2000, author = {Ebert, Matthias and Bucher, Christian}, title = {Modelling of changing of dynamic and static parameters of damaged R/C}, doi = {10.25643/bauhaus-universitaet.582}, url = {http://nbn-resolving.de/urn:nbn:de:gbv:wim2-20111215-5825}, year = {2000}, abstract = {Dynamic testing for damage assessment as non-destructive method has attracted growing in-terest for systematic inspections and maintenance of civil engineering structures. In this con-text the paper presents the Stochastic Finite Element (SFE) Modeling of the static and dy-namic results of own four point bending experiments with R/C beams. The beams are dam-aged by an increasing load. Between the load levels the dynamic properties are determined. Calculated stiffness loss factors for the displacements and the natural frequencies show differ-ent histories. A FE Model for the beams is developed with a discrete crack formulation. Cor-related random fields are used for structural parameters stiffness and tension strength. The idea is to simulate different crack evolutions. The beams have the same design parameters, but because of the stochastic material properties their undamaged state isn't yet the same. As the structure is loaded a stochastic first crack occurs on the weakest place of the structure. The further crack evolution is also stochastic. These is a great advantage compared with de-terministic formulations. To reduce the computational effort of the Monte Carlo simulation of this nonlinear problem the Latin-Hypercube sampling technique is applied. From the results functions of mean value and standard deviation of displacements and frequencies are calcu-lated. Compared with the experimental results some qualitative phenomena are good de-scribed by the model. Differences occurs especially in the dynamic behavior of the higher load levels. Aim of the investigations is to assess the possibilities of dynamic testing under consideration of effects from stochastic material properties}, subject = {Stahlbetonbauteil}, language = {en} } @inproceedings{vanRooyenOlivier2004, author = {van Rooyen, G.C. and Olivier, A. H.}, title = {Notes on structural analysis in a distributed collaboratory}, doi = {10.25643/bauhaus-universitaet.145}, url = {http://nbn-resolving.de/urn:nbn:de:gbv:wim2-20111215-1451}, year = {2004}, abstract = {The worldwide growth of communication networks and associated technologies provide the basic infrastructure for new ways of executing the engineering process. Collaboration amongst team members seperated in time and location is of particular importance. Two broad themes can be recognized in research pertaining to distributed collaboration. One theme focusses on the technical and technological aspects of distributed work, while the other emphasises human aspects thereof. The case of finite element structural analysis in a distributed collaboratory is examined in this paper. An approach is taken which has its roots in human aspects of the structural analysis task. Based on experience of how structural engineers currently approach and execute this task while utilising standard software designed for use on local workstations only, criteria are stated for a software architechture that could support collaborative structural analysis. Aspects of a pilot application and the results of qualitative performance measurements are discussed.}, subject = {Ingenieurbau}, language = {en} } @inproceedings{KirichukKoeppler1997, author = {Kirichuk, A. and K{\"o}ppler, H.}, title = {Numerical Algorithms and Computer Modeling for nonlinear Analysis of Shell Structures}, doi = {10.25643/bauhaus-universitaet.438}, url = {http://nbn-resolving.de/urn:nbn:de:gbv:wim2-20111215-4382}, year = {1997}, abstract = {The dynamic behaviour of shells, which are widely used in construction and mechanical engineering as critical components of machinery and 3-D structures, under static and dynamic loadings is described by system of deep nonlinear differential equations. Solution of these equations can be received with assistance of technique basing on a modern numerical algorithms and computer modeling.. The system of nonlinear differential equations of vibration of the shells is proposed taking into account the inertia forces in the tangential and normal directions. Its solution is based on combination of parameter prolongation method, finite-difference method and the Newton-Kantorovich iterative algorithm that allows plotting the loading trajectories and determination of bifurcation points on them. Package of Applied Programs >SEVSOR< is a computation means to be used in research of deformation, stability and vibration in thin axically-symmetric shells of complicated shape Input data include information on shell geometry, physical and mechanical properties, bearing conditions, types of loadings and load application. Frame output of motion forms in real time or either in decelerated or accelerated time scales for creating cartoons or video films is used for analysis of the compound dynamic processes in shell-type structures.}, subject = {Schale}, language = {en} } @misc{Habtemariam, type = {Master Thesis}, author = {Habtemariam, Abinet Kifle}, title = {Numerical Demolition Analysis of a Slender Guyed Antenna Mast}, doi = {10.25643/bauhaus-universitaet.4460}, url = {http://nbn-resolving.de/urn:nbn:de:gbv:wim2-20210723-44609}, school = {Bauhaus-Universit{\"a}t Weimar}, pages = {75}, abstract = {The main purpose of the thesis is to ensure the safe demolition of old guyed antenna masts that are located in different parts of Germany. The major problem in demolition of this masts is the falling down of the masts in unexpected direction because of buckling problem. The objective of this thesis is development of a numerical models using finite element method (FEM) and assuring a controlled collapse by coming up with different time setups for the detonation of explosives which are responsible for cutting down the cables. The result of this thesis will avoid unexpected outcomes during the demolition processes and prevent risk of collapsing of the mast over near by structures.}, subject = {Abbruch}, language = {en} } @phdthesis{Zacharias, author = {Zacharias, Christin}, title = {Numerical Simulation Models for Thermoelastic Damping Effects}, doi = {10.25643/bauhaus-universitaet.4735}, url = {http://nbn-resolving.de/urn:nbn:de:gbv:wim2-20221116-47352}, school = {Bauhaus-Universit{\"a}t Weimar}, pages = {191}, abstract = {Finite Element Simulations of dynamically excited structures are mainly influenced by the mass, stiffness, and damping properties of the system, as well as external loads. The prediction quality of dynamic simulations of vibration-sensitive components depends significantly on the use of appropriate damping models. Damping phenomena have a decisive influence on the vibration amplitude and the frequencies of the vibrating structure. However, developing realistic damping models is challenging due to the multiple sources that cause energy dissipation, such as material damping, different types of friction, or various interactions with the environment. This thesis focuses on thermoelastic damping, which is the main cause of material damping in homogeneous materials. The effect is caused by temperature changes due to mechanical strains. In vibrating structures, temperature gradients arise in adjacent tension and compression areas. Depending on the vibration frequency, they result in heat flows, leading to increased entropy and the irreversible transformation of mechanical energy into thermal energy. The central objective of this thesis is the development of efficient simulation methods to incorporate thermoelastic damping in finite element analyses based on modal superposition. The thermoelastic loss factor is derived from the structure's mechanical mode shapes and eigenfrequencies. In subsequent analyses that are performed in the time and frequency domain, it is applied as modal damping. Two approaches are developed to determine the thermoelastic loss in thin-walled plate structures, as well as three-dimensional solid structures. The realistic representation of the dissipation effects is verified by comparing the simulation results with experimentally determined data. Therefore, an experimental setup is developed to measure material damping, excluding other sources of energy dissipation. The three-dimensional solid approach is based on the determination of the generated entropy and therefore the generated heat per vibration cycle, which is a measure for thermoelastic loss in relation to the total strain energy. For thin plate structures, the amount of bending energy in a modal deformation is calculated and summarized in the so-called Modal Bending Factor (MBF). The highest amount of thermoelastic loss occurs in the state of pure bending. Therefore, the MBF enables a quantitative classification of the mode shapes concerning the thermoelastic damping potential. The results of the developed simulations are in good agreement with the experimental results and are appropriate to predict thermoelastic loss factors. Both approaches are based on modal superposition with the advantage of a high computational efficiency. Overall, the modeling of thermoelastic damping represents an important component in a comprehensive damping model, which is necessary to perform realistic simulations of vibration processes.}, subject = {Werkstoffd{\"a}mpfung}, language = {en} } @inproceedings{MilbradtRose2000, author = {Milbradt, Peter and Rose, Martin}, title = {Numerische Approximation makroskopischer Verkehrsmodelle mit der Methode der Finiten Elemente}, doi = {10.25643/bauhaus-universitaet.604}, url = {http://nbn-resolving.de/urn:nbn:de:gbv:wim2-20111215-6046}, year = {2000}, abstract = {Makroskopische Verkehrsmodelle sind ein wesentliches Hilfsmittel bei der Beurteilung und Steuerung von Verkehrsfl{\"u}ssen auf Hauptverkehrsadern. F{\"u}r die notwendige Beeinflussung des Verkehrsablaufs werden Online-Messungen und prognostische numerische Simulationen ben{\"o}tigt. F{\"u}r die Simulationen bieten sich makroskopische Verkehrsmodelle an, die den Verkehr als kontinuierliche Fahrzeugstr{\"o}meabbilden. Aufgrund der Analogie zu den Modellen der Str{\"o}mungsmechanik lassen sich die numerischen Verfahren aus diesem Bereich auch zur L{\"o}sung makroskopischer Verkehrsmodelle verwenden. Es wird eine Finite-Elemente-Approximation f{\"u}r die numerische Umsetzung makroskopischer Verkehrsmodelle vorgestellt. Exemplarisch wird sie am Verkehrsmodell von Kerner und Konh{\"a}user erl{\"a}utert. Dieses und andere makroskopische Verkehrsmodelle wurden bisher mit der Methode der Finiten Differenzen gel{\"o}st. Die vorgestellte Approximation entspricht einem Petrov-Galerkin-Verfahren, bei dem der Fehler eines Standard-Galerkin-Verfahrens mit Hilfe eines Upwinding-Koeffizienten minimiert wird. Die Wahl des Upwinding-Koeffizienten ist {\"u}bertragbar und basiert ausschließlich auf dem Charakter der zugrundeliegenden Gleichungen. Die Ergebnisse zeigen typische Ph{\"a}nomene eines Verkehrsablaufs wie die Entstehung von Stop-and-Go-Wellen oder Staus. Die Finite-Elemente-Methode erweist sich f{\"u}r unter-schiedlichste Verkehrsmodelle als ausgesprochen stabil.}, subject = {Verkehrsleitsystem}, language = {de} } @inproceedings{SchlegelRautenstrauch2000, author = {Schlegel, Roger and Rautenstrauch, Karl}, title = {Numerische Simulation von Mauerwerk als Kontinuum}, doi = {10.25643/bauhaus-universitaet.610}, url = {http://nbn-resolving.de/urn:nbn:de:gbv:wim2-20111215-6106}, year = {2000}, abstract = {Im vorliegenden Beitrag wird ein in das FE-Programmsystem ANSYS implementiertes elastoplastisches Berechnungsmodell zur nichtlinearen, r{\"a}umlichen Untersuchung von Mauerwerkstrukturen vorgestellt. Die Modellierung des heterogenen Baustoffs Mauerwerk erfolgt mit Hilfe eines verschmierten Ersatzkontinuums. Das anisotrope Materialverhalten wird sowohl hinsichtlich der Spannungs-Dehnungsbeziehung als auch bei der Beschreibung der Festigkeit ber{\"u}cksichtigt. Durch die Verwendung einer zusammengesetzten Fließbedingung ist es m{\"o}glich, das Versagen der einzelnen Mauerwerkkomponenten Stein und M{\"o}rtelfugen und des Verbundes zu ber{\"u}cksichtigen. Dadurch ist die Anwendbarkeit des Modells f{\"u}r mehrere Mauerwerksarten gegeben. Die hierf{\"u}r verwendeten Materialparameter sind aus einfachen Kleink{\"o}rperversuchen bestimmbar oder innerhalb gewisser Grenzen aus empirischen Formeln berechenbar. Die notwendige Beschr{\"a}nkung der Anzahl der Materialparameter sichert die praktische Anwendbarkeit des entwickelten Berechnungsmodells. Die numerische Umsetzung des hier verwendeten impliziten Berechnungsverfahrens l{\"a}sst sich in eine lokale und eine globale Iterationsebene gliedern. Die lokale Iteration am Integrationspunkt dient der Spannungsr{\"u}ckf{\"u}hrung. Dabei sind die Besonderheiten der Verarbeitung mehrfl{\"a}chiger Fließfiguren zu beachten. Die globale Iteration auf Systemebene sichert die Umlagerung des Residuums. Mit der Nachrechnung von Versuchsergebnissen soll das entwickelte Modell verifiziert und seine physikalische Leistungsf{\"a}higkeit eingesch{\"a}tzt werden.}, subject = {Mauerwerk}, language = {de} } @misc{Li2006, author = {Li, Fei}, title = {Numerische Untersuchungen zu Temperaturfeldern und Eigenspannungen einer MAG-geschweißten Stumpfnaht an austenitisch-ferritischem Stahl X2CrNiMoN22-5-3}, doi = {10.25643/bauhaus-universitaet.786}, url = {http://nbn-resolving.de/urn:nbn:de:gbv:wim2-20111215-7862}, year = {2006}, abstract = {Auf der Basis der Literaturrecherche wird in dieser Arbeit eine 5-lagige MAG-geschweißte Stumpfnaht an austenitisch-ferritischen Stahl X2CrNiMoN22-5-3 (Duplex-Stahl 1.4462) mit dem FE-Programm „SYSWELD®" simuliert. Die Berech-nungen der Temperaturfelder werden unter der Ber{\"u}cksichtigung sowohl von tempe-raturunabh{\"a}ngigen als auch temperaturabh{\"a}ngigen thermophysikalischen Material-eigenschaften am drei-dimensionalen und zwei-dimensionalen Modell durchgef{\"u}hrt. Die berechneten Temperatur-Zeit-Verl{\"a}ufe und Gef{\"u}geumwandlungen beim MAG-Schweißen der Stumpfnaht werden hinsichtlich der Einfl{\"u}sse und Ver{\"a}nderun-gen analysiert und die ermittelten Abk{\"u}hlzeiten t12/8 werden f{\"u}r jede Schweißlage bewertet. Anschließend werden die Berechnungen des Eigenspannungszustandes f{\"u}r einzelne Schweißlagen untersucht.}, subject = {Duplexstahl}, language = {de} } @inproceedings{BaitschHartmann2004, author = {Baitsch, Matthias and Hartmann, Dietrich}, title = {Object Oriented Finite Element Analysis for Structural Optimization using p-Elements}, doi = {10.25643/bauhaus-universitaet.108}, url = {http://nbn-resolving.de/urn:nbn:de:gbv:wim2-20111215-1089}, year = {2004}, abstract = {The optimization of continuous structures requires careful attention to discretization errors. Compared to ordinary low order formulation (h-elements) in conjunction with an adaptive mesh refinement in each optimization step, the use of high order finite elements (so called p-elements) has several advantages. However, compared to the h-method a higher order finite element analysis program poses higher demands from a software engineering point of view. In this article the basics of an object oriented higher order finite element system especially tailored to the use in structural optimization is presented. Besides the design of the system, aspects related to the employed implementation language Java are discussed.}, subject = {Konzipieren }, language = {en} } @article{LaemmerBurghardtMeissner1997, author = {L{\"a}mmer, Lutz and Burghardt, Michael and Meißner, Udo F.}, title = {Parallele Netzgenerierung}, doi = {10.25643/bauhaus-universitaet.531}, url = {http://nbn-resolving.de/urn:nbn:de:gbv:wim2-20111215-5315}, year = {1997}, abstract = {Bei der Berechnung von statischen oder dynamischen Problemen mit Hilfe der Methode der Finiten Elemente ist eine Diskretisierung des zu berechnenden Gebietes notwendig. Bei einer sinnvollen Modellierung des Gebietes ist die Elementgr{\"o}ße meist nicht konstant, sondern ist an kritischen Stellen kleiner. Die Vorgaben hierf{\"u}r k{\"o}nnen einerseits aus Erfahrungen des Anwenders, andererseits aus einer Fehlerabsch{\"a}tzung einer vorangegangenen FE-Berechnung resultieren [5]. Soll die FE-Berechnung auf einem Parallelrechner geschehen, ist eine Partitionierung des Gebietes, d.h. eine Zuordnung der Elemente zu den Prozessoren, notwendig. Bei dem hier beschriebenen Ansatz werden nun im Gegensatz zu den {\"u}blichen Verfahren erst die Eingangsdaten f{\"u}r den Netzgenerator umgewandelt und dann das Elementnetz direkt auf dem Parallelrecher gleichzeitig auf allen Prozessoren erzeugt. Eine Aufteilung der Elemente auf die Prozessoren entsteht als Nebenprodukt der Netzaufteilung. Die entstehenden Teilgebietsgrenzen werden geometrisch minimiert. Die Lastbalance der Netzaufteilung sowie der FE-Rechnung wird durch ein ann{\"a}hernd gleiche Anzahl der Elemente je Partition gew{\"a}hrleistet. Als Eingabedaten wird eine Beschreibung des Gebietes durch Polygonz{\"u}ge, sowie einer Netzdichtefunktion, z.B. durch Punkte mit Angaben {\"u}ber die angestrebte Elementgr{\"o}ße, ben{\"o}tigt.}, subject = {Finite-Elemente-Methode}, language = {de} } @phdthesis{Msekh, author = {Msekh, Mohammed Abdulrazzak}, title = {Phase Field Modeling for Fracture with Applications to Homogeneous and Heterogeneous Materials}, doi = {10.25643/bauhaus-universitaet.3229}, url = {http://nbn-resolving.de/urn:nbn:de:gbv:wim2-20170615-32291}, school = {Bauhaus-Universit{\"a}t Weimar}, pages = {190}, abstract = {The thesis presents an implementation including different applications of a variational-based approach for gradient type standard dissipative solids. Phase field model for brittle fracture is an application of the variational-based framework for gradient type solids. This model allows the prediction of different crack topologies and states. Of significant concern is the application of theoretical and numerical formulation of the phase field modeling into the commercial finite element software Abaqus in 2D and 3D. The fully coupled incremental variational formulation of phase field method is implemented by using the UEL and UMAT subroutines of Abaqus. The phase field method considerably reduces the implementation complexity of fracture problems as it removes the need for numerical tracking of discontinuities in the displacement field that are characteristic of discrete crack methods. This is accomplished by replacing the sharp discontinuities with a scalar damage phase field representing the diffuse crack topology wherein the amount of diffusion is controlled by a regularization parameter. The nonlinear coupled system consisting of the linear momentum equation and a diffusion type equation governing the phase field evolution is solved simultaneously via a Newton- Raphson approach. Post-processing of simulation results to be used as visualization module is performed via an additional UMAT subroutine implemented in the standard Abaqus viewer. In the same context, we propose a simple yet effective algorithm to initiate and propagate cracks in 2D geometries which is independent of both particular constitutive laws and specific element technology and dimension. It consists of a localization limiter in the form of the screened Poisson equation with, optionally, local mesh refinement. A staggered scheme for standard equilibrium and screened Cauchy equations is used. The remeshing part of the algorithm consists of a sequence of mesh subdivision and element erosion steps. Element subdivision is based on edge split operations using a given constitutive quantity (either damage or void fraction). Mesh smoothing makes use of edge contraction as function of a given constitutive quantity such as the principal stress or void fraction. To assess the robustness and accuracy of this algorithm, we use both quasi-brittle benchmarks and ductile tests. Furthermore, we introduce a computational approach regarding mechanical loading in microscale on an inelastically deforming composite material. The nanocomposites material of fully exfoliated clay/epoxy is shaped to predict macroscopic elastic and fracture related material parameters based on their fine-scale features. Two different configurations of polymer nanocomposites material (PNCs) have been studied. These configurations are fully bonded PNCs and PNCs with an interphase zone formation between the matrix and the clay reinforcement. The representative volume element of PNCs specimens with different clay weight contents, different aspect ratios, and different interphase zone thicknesses are generated by adopting Python scripting. Different constitutive models are employed for the matrix, the clay platelets, and the interphase zones. The brittle fracture behavior of the epoxy matrix and the interphase zones material are modeled using the phase field approach, whereas the stiff silicate clay platelets of the composite are designated as a linear elastic material. The comprehensive study investigates the elastic and fracture behavior of PNCs composites, in addition to predict Young's modulus, tensile strength, fracture toughness, surface energy dissipation, and cracks surface area in the composite for different material parameters, geometry, and interphase zones properties and thicknesses.}, subject = {Finite-Elemente-Methode}, language = {en} } @article{BanihaniRabczukAlmomani, author = {Banihani, Suleiman and Rabczuk, Timon and Almomani, Thakir}, title = {POD for real-time simulation of hyperelastic soft biological tissue using the point collocation method of finite spheres}, series = {Mathematical Problems in Engineering}, journal = {Mathematical Problems in Engineering}, doi = {10.1155/2013/386501}, url = {http://nbn-resolving.de/urn:nbn:de:gbv:wim2-20170413-31203}, abstract = {The point collocation method of finite spheres (PCMFS) is used to model the hyperelastic response of soft biological tissue in real time within the framework of virtual surgery simulation. The proper orthogonal decomposition (POD) model order reduction (MOR) technique was used to achieve reduced-order model of the problem, minimizing computational cost. The PCMFS is a physics-based meshfree numerical technique for real-time simulation of surgical procedures where the approximation functions are applied directly on the strong form of the boundary value problem without the need for integration, increasing computational efficiency. Since computational speed has a significant role in simulation of surgical procedures, the proposed technique was able to model realistic nonlinear behavior of organs in real time. Numerical results are shown to demonstrate the effectiveness of the new methodology through a comparison between full and reduced analyses for several nonlinear problems. It is shown that the proposed technique was able to achieve good agreement with the full model; moreover, the computational and data storage costs were significantly reduced.}, subject = {Chirurgie}, language = {en} } @inproceedings{Milbradt2003, author = {Milbradt, Peter}, title = {Stabilisierte Finite Elemente in der Hydrodynamik}, doi = {10.25643/bauhaus-universitaet.332}, url = {http://nbn-resolving.de/urn:nbn:de:gbv:wim2-20111215-3327}, year = {2003}, abstract = {Hydro- und morphodynamischen Prozesse in Binnengew{\"a}ssern und im K{\"u}stennahbereich erzeugen hochkomplexe Ph{\"a}nomene. Zur Beurteilung der Entwicklung von K{\"u}stenzohnen, von Flussbetten sowie von Eingriffen des Menschen in Form von Schutzbauwerken sind geeignete numerische Modellwerkzeuge notwendig. Es wird ein holistischer Modellansatz zur Approximation gekoppelter Seegangs-, Str{\"o}mungs- und Morphodynamischer Prozesse auf der Basis stabilisierter Finiter Elemente vorgestellt. Der Großteil der Modellgleichungen der Hydro- und Morphodynamik sind Transportgleichungen. Dem Transportcharakter dieser Gleichungen entsprechend wird ein stabilisiertes Finites Element Verfahren auf Dreiecken vorgestellt. Die vorgestellte Approximation entspricht einem streamline upwinding Petrov-Galerkin-Verfahrens f{\"u}r vektorwertige mehrdimensionale Probleme, bei dem der Fehler eines Standard-Galerkin-Verfahrens mit Hilfe eines Upwinding-Koeffizienten minimiert wird. Die Wahl des Upwinding-Koeffizienten ist {\"u}bertragbar auf andere Problemklassen und basiert ausschließlich auf dem Charakter der zugrundeliegene Das Modell wurde f{\"u}r Seegangs- und Str{\"o}mungs-Untersuchungen im Jade-Weser-{\"A}stuar an der deutschen Nordseek{\"u}ste eingesetzt.}, subject = {Hydrodynamik}, language = {de} } @article{KrausCrişanWittor, author = {Kraus, Matthias and Cri{\c{s}}an, Nicolae-Andrei and Wittor, Bj{\"o}rn}, title = {Stability Study of Cantilever-Beams - Numerical Analysis and Analytical Calculation (LTB)}, series = {ce/papers}, volume = {2021}, journal = {ce/papers}, number = {Volume 4, issue 2-4}, publisher = {Ernst \& Sohn, a Wiley brand}, address = {Berlin}, doi = {10.1002/cepa.1539}, url = {http://nbn-resolving.de/urn:nbn:de:gbv:wim2-20220112-45637}, pages = {2199 -- 2206}, abstract = {According to Eurocode, the computation of bending strength for steel cantilever beams is a straightforward process. The approach is based on an Ayrton-Perry formula adaptation of buckling curves for steel members in compression, which involves the computation of an elastic critical buckling load for considering the instability. NCCI documents offer a simplified formula to determine the critical bending moment for cantilevers beams with symmetric cross-section. Besides the NCCI recommendations, other approaches, e.g. research literature or Finite-Element-Analysis, may be employed to determine critical buckling loads. However, in certain cases they render different results. Present paper summarizes and compares the abovementioned analytical and numerical approaches for determining critical loads and it exemplarily analyses corresponding cantilever beam capacities using numerical approaches based on plastic zones theory (GMNIA).}, subject = {Tr{\"a}ger}, language = {en} } @phdthesis{Ghasemi, author = {Ghasemi, Hamid}, title = {Stochastic optimization of fiber reinforced composites considering uncertainties}, doi = {10.25643/bauhaus-universitaet.2704}, url = {http://nbn-resolving.de/urn:nbn:de:gbv:wim2-20161117-27042}, school = {Bauhaus-Universit{\"a}t Weimar}, pages = {140}, abstract = {Briefly, the two basic questions that this research is supposed to answer are: 1. Howmuch fiber is needed and how fibers should be distributed through a fiber reinforced composite (FRC) structure in order to obtain the optimal and reliable structural response? 2. How do uncertainties influence the optimization results and reliability of the structure? Giving answer to the above questions a double stage sequential optimization algorithm for finding the optimal content of short fiber reinforcements and their distribution in the composite structure, considering uncertain design parameters, is presented. In the first stage, the optimal amount of short fibers in a FRC structure with uniformly distributed fibers is conducted in the framework of a Reliability Based Design Optimization (RBDO) problem. Presented model considers material, structural and modeling uncertainties. In the second stage, the fiber distribution optimization (with the aim to further increase in structural reliability) is performed by defining a fiber distribution function through a Non-Uniform Rational BSpline (NURBS) surface. The advantages of using the NURBS surface as a fiber distribution function include: using the same data set for the optimization and analysis; high convergence rate due to the smoothness of the NURBS; mesh independency of the optimal layout; no need for any post processing technique and its non-heuristic nature. The output of stage 1 (the optimal fiber content for homogeneously distributed fibers) is considered as the input of stage 2. The output of stage 2 is the Reliability Index (b ) of the structure with the optimal fiber content and distribution. First order reliability method (in order to approximate the limit state function) as well as different material models including Rule of Mixtures, Mori-Tanaka, energy-based approach and stochastic multi-scales are implemented in different examples. The proposed combined model is able to capture the role of available uncertainties in FRC structures through a computationally efficient algorithm using all sequential, NURBS and sensitivity based techniques. The methodology is successfully implemented for interfacial shear stress optimization in sandwich beams and also for optimization of the internal cooling channels in a ceramic matrix composite. Finally, after some changes and modifications by combining Isogeometric Analysis, level set and point wise density mapping techniques, the computational framework is extended for topology optimization of piezoelectric / flexoelectric materials.}, subject = {Finite-Elemente-Methode}, language = {en} } @article{KeJianMing2004, author = {Ke, Chen and Jian Ming, Lu}, title = {Study of Analysis System for Bridge Test}, doi = {10.25643/bauhaus-universitaet.254}, url = {http://nbn-resolving.de/urn:nbn:de:gbv:wim2-20111215-2547}, year = {2004}, abstract = {Analysis System for Bridge Test (Chinese name abbr.: QLJC) is an application software specially designed for bridge test to analyze the static and dynamic character of bridge structures, calculate efficiency ratio of load test, pick up the results of observation points and so on. In this paper, research content, system design, calculation theory, characteristics and practical application of QLJC is introduced in detail.}, subject = {Finite-Elemente-Methode}, language = {en} } @article{TolokTolokGomenyuk1997, author = {Tolok, V. A. and Tolok, A. V. and Gomenyuk, S. I.}, title = {The instrumental System of Mechanics Problems Analysis of the deformed Solid Body}, doi = {10.25643/bauhaus-universitaet.536}, url = {http://nbn-resolving.de/urn:nbn:de:gbv:wim2-20111215-5361}, year = {1997}, abstract = {In the abstract proposed is the Instrumental System of mechanics problems analysis of the deformed solid body. It supplies the researcher with the possibility to describe the input data on the object under analyses and the problem scheme based upon the variational principles within one task. The particular feature of System is possibility to describe the information concerning the object of any geometrical shape and the computation sheme according to the program defined for purpose. The Methods allow to compute the tasks with indefinite functional and indefinite geometry of the object (or the set of objects). The System provides the possibility to compute the tasks with indefinite sheme based upon the Finite Element Method (FEM). The restrictions of the System usage are therefore determined by the restrictions of the FEM itself. It contrast to other known programms using FEM (ANSYS, LS-DYNA and etc) described system possesses more universality in defining input data and choosing computational scheme. Builtin is an original Subsytem of Numerical Result Analuses. It possesses the possibility to visualise all numerical results, build the epures of the unknown variables, etc. The Subsystem is approved while solving two- and three-dimensional problems of Elasticiti and Plasticity, under the conditions of Geometrical Unlinearity. Discused are Contact Problems of Statics and Dynamics.}, subject = {Festk{\"o}rpermechanik}, language = {en} } @inproceedings{BernsteinRichter2003, author = {Bernstein, Swanhild and Richter, Matthias}, title = {The Use of Genetic Algorithms in Finite Element Model Identification}, doi = {10.25643/bauhaus-universitaet.276}, url = {http://nbn-resolving.de/urn:nbn:de:gbv:wim2-20111215-2769}, year = {2003}, abstract = {A realistic and reliable model is an important precondition for the simulation of revitalization tasks and the estimation of system properties of existing buildings. Thereby, the main focus lies on the parameter identification, the optimization strategies and the preparation of experiments. As usual structures are modeled by the finite element method. This as well as other techniques are based on idealizations and empiric material properties. Within one theory the parameters of the model should be approximated by gradually performed experiments and their analysis. This approximation method is performed by solving an optimization problem, which is usually non-convex, of high dimension and possesses a non-differentiable objective function. Therefore we use an optimization procedure based on genetic algorithms which was implemented by using the program package SLang...}, subject = {Finite-Elemente-Methode}, language = {en} } @article{GanevMarinov1997, author = {Ganev, T. and Marinov, M.}, title = {Towards Optimal Designing of thin elastic Plates with a specific free Oscillations Frequency}, doi = {10.25643/bauhaus-universitaet.537}, url = {http://nbn-resolving.de/urn:nbn:de:gbv:wim2-20111215-5375}, year = {1997}, abstract = {Thin elastic plates are the basic constructional elements and are very often subjected to dynamic effects especially in the machine-building structures. Their saving design of resonance conditions of operation is an extremely complicated task which cannot be solved analytically. In the present report an efficient and sufficiently general method for optimal design of thin plates is worked out on the basis of energy resonance method of Wilder, the method of the finite elements for dynamic research and the methods of parameter optimization. By means of these methods various limitations and requirements put by the designer to the plates can be taken into account. A programme module for numerical investigation of the weight variation of the plate depending on the taken variable of the designed thickness at different supporting conditions is developed. The reasons for the considerable quantity and quality difference between the obtained optimal designs are also analysed.}, subject = {Platte}, language = {en} } @article{KaapkeMilbradt2004, author = {Kaapke, Kai and Milbradt, Peter}, title = {Voronoi-based finite volume method for transport problems}, doi = {10.25643/bauhaus-universitaet.255}, url = {http://nbn-resolving.de/urn:nbn:de:gbv:wim2-20111215-2558}, year = {2004}, abstract = {Transport problems, as, for instance, the transport of sediment in hydraulic engineering and the transport of harmful substances through porous media, play an important role in many fields of civil engineering. Other examples include the dissipation of heat or sound as well as the simulation of traffic with macroscopic models. The contribution explains the analysis of the applicability of Voronoi-based finite volume methods for the approximation of solutions of transport problems. A special concern is the discretisation of the transport equation. Current limitations of the method as well as ideas for stabilisation are explained with examples.}, subject = {Finite-Elemente-Methode}, language = {en} } @inproceedings{KoepplerRoosBurkhardt1997, author = {K{\"o}ppler, H. and Roos, Dirk and Burkhardt, Gerhard}, title = {Zur Berechnung vielschichtiger Schalen mit orthotropen Schichten}, doi = {10.25643/bauhaus-universitaet.437}, url = {http://nbn-resolving.de/urn:nbn:de:gbv:wim2-20111215-4379}, year = {1997}, abstract = {Wirklichkeitsnahe Erfassung und Beschreibung des Trag- und Verformungsverhaltens von Strukturen baulicher Anlagen hat in den letzten Jahrzehnten st{\"a}ndig an Bedeutung gewonnen. Konstruktionen im Hoch- und Industriebau werden zunehmend multifunktional genutzt - die >Grenzen< zwischen Bauwerk und Tragwerk, zwischen H{\"u}ll- und Tragkonstruktion l{\"o}sen sich auf. Werden raumabschließende Elemente (W{\"a}nde, Decken, D{\"a}cher) gleichzeitig als Tragelemente und w{\"a}rme- und schalld{\"a}mmende Konstruktionen ausgef{\"u}hrt, so entstehen beispielsweise Sandwichplatten, deren Schichten sehr stark differierende Materialeigenschaften aufweisen. Beim Aufbau des FEM-Modells f{\"u}r vielschichtige Schalen k{\"o}nnen die Form{\"a}nderungshypothesen f{\"u}r jede Schicht einzeln als auch f{\"u}r die Schale insgesamt gegeben werden. Im ersten Fall ist der Knotenfreiheitsgrad von der Schichtenzahl abh{\"a}ngig, im zweiten Fall nicht. Im weiteren wird eine Form{\"a}nderungshypothese f{\"u}r das Schichtenpaket angenommen. Ausgegangen wird von den Gleichungen der 3D-Elastizit{\"a}tstheorie. Die Ber{\"u}cksichtigung der Querkraftschubverformungen ergibt die M{\"o}glichkeit einer ad{\"a}quaten Beschreibung der Verformungen sowohl d{\"u}nner Schalen als auch von Schalen mittlerer Dicke; die Berechnung der Kr{\"u}mmungen und der LAMEschen Parameter der Bezugsfl{\"a}che zu umgehen, was f{\"u}r komplizierte Schalenformen eine selbst{\"a}ndige Aufgabe ist; eines nat{\"u}rlichen {\"U}bergangs von homogenen zu geschichteten Schalen. Das vielschichtige isoparametrische Schalen-FE wird vorgestellt, seine Implementierung in das in Entwicklung befindliche Programmsystem SLANG wird vorbereitet.}, subject = {Schale}, language = {de} } @inproceedings{Schutte2000, author = {Schutte, Gerrit}, title = {Zur Ermittlung von Spannungen am Rand eines elastischen Kontinuums}, doi = {10.25643/bauhaus-universitaet.613}, url = {http://nbn-resolving.de/urn:nbn:de:gbv:wim2-20111215-6135}, year = {2000}, abstract = {F{\"u}r den Entwurf von Ingenieurbauten ist eine zuverl{\"a}ssige Prognose {\"u}ber den Spannungsverlauf im Bauwerk und auf dessen Rand von großer Bedeutung. Eine geschlossene L{\"o}sung der elastischen Bestimmungsgleichungen des Bauwerks ist in der Regel nicht verf{\"u}gbar. Es wird daher unter Verwendung der Methode der gewichteten Reste eine schwache Form der Gleichungen abgeleitet, die zu einem gemischten Arbeitsprinzip f{\"u}hrt. Das zugeh{\"o}rige Finite-Elemente-Modell erlaubt es Spannungen am Rand des Bauwerks zu ermitteln, die im Gleichgewicht zu den angreifenden Lasten stehen.}, subject = {Kontinuum}, language = {de} } @phdthesis{Lehmkuhl2004, author = {Lehmkuhl, Hansj{\"o}rg}, title = {Zur praktischen Anwendung numerischer Analysemethoden f{\"u}r Stabilit{\"a}tsprobleme}, doi = {10.25643/bauhaus-universitaet.676}, url = {http://nbn-resolving.de/urn:nbn:de:gbv:wim2-20051013-7102}, school = {Bauhaus-Universit{\"a}t Weimar}, year = {2004}, abstract = {In der t{\"a}glichen Ingenieurpraxis werden in zunehmenden Maße numerische Analysen im Rahmen der Finite-Elemente-Methode auch zur Untersuchung stabilit{\"a}tsgef{\"a}hrdeter Strukturen eingesetzt. F{\"u}r die aktuelle Praxis, insbesondere im konstruktiven Stahlbau, ist jedoch festzustellen, dass zwischen der fortgeschrittenen Theorie und dem Niveau der praktischen Anwendung numerischer Stabilit{\"a}tsanalysen eine große Kluft besteht. Aus praktischer Sicht erscheint es unumg{\"a}nglich, die weiter wachsende Diskrepanz zwischen den umfangreichen theoretischen M{\"o}glichkeiten und der gegenw{\"a}rtigen Praxis abzubauen. Damit steht der praktisch t{\"a}tige Ingenieur vor der Aufgabe, sein Wissen auf dem Gebiet numerischer Stabilit{\"a}tsanalysen zu vertiefen und bereits vorhandene FE-Programme um Berechnungsalgorithmen f{\"u}r umfassende numerische Stabilit{\"a}tsanalysen zu erweitern. Daf{\"u}r werden in der Arbeit die Grundlagen einer FEM- orientierten modernen Stabilit{\"a}tstheorie einheitlich und aus Sicht einer praktischen Anwendung aufbereitet. Die Darstellung von realisierten programmtechnischen Umsetzungen f{\"u}r erweiterte Analysenmethoden wie Nachbeulanalysen, Pfadwechsel und Approximationen imperfekter Pfade erm{\"o}glicht eine Erweiterung des Methodenvorrates. Die innerhalb der Arbeit untersuchten Beispiele zeigen, dass durch die Anwendung der behandelten Verfahren das Tragverhalten einer stabilit{\"a}tsgef{\"a}hrdeten Struktur wesentlich besser eingesch{\"a}tzt werden kann als bei Beschr{\"a}nkung auf die herk{\"o}mmlichen Analysemethoden.}, subject = {Nichtlineare Stabilit{\"a}tstheorie}, language = {de} }