TY - CHAP
A1 - Häfner, Stefan
A1 - Eckardt, Stefan
A1 - Könke, Carsten
T1 - A geometrical inclusion-matrix model for the finite element analysis of concrete at multiple scales
N2 - This paper introduces a method to generate adequate inclusion-matrix geometries of concrete in two and three dimensions, which are independent of any specific numerical discretization. The article starts with an analysis on shapes of natural aggregates and discusses corresponding mathematical realizations. As a first prototype a two-dimensional generation of a mesoscale model is introduced. Particle size distribution functions are analysed and prepared for simulating an adequate three-dimensional representation of the aggregates within a concrete structure. A sample geometry of a three-dimensional test cube is generated and the finite element analysis of its heterogeneous geometry by a uniform mesh is presented. Concluding, aspects of a multiscale analysis are discussed and possible enhancements are proposed.
KW - Beton
KW - Dreidimensionales Modell
KW - Finite-Elemente-Methode
Y1 - 2003
U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:gbv:wim2-20111215-3018
ER -
TY - JOUR
A1 - Schrader, Kai
A1 - Könke, Carsten
T1 - Hybrid computing models for large-scale heterogeneous 3d microstructures
JF - International Journal for Multiscale Computational Engineering
N2 - Hybrid computing models for large-scale heterogeneous 3d microstructures
KW - Angewandte Mathematik
KW - Strukturmechanik
Y1 - 2011
SP - 365
EP - 377
ER -
TY - JOUR
A1 - Luu, M.
A1 - Martinez-Rodrigo, M.D.
A1 - Zabel, Volkmar
A1 - Könke, Carsten
T1 - H∞ optimization of fluid viscous dampers for reducing vibrations of high-speed railway bridges
JF - Journal of Sound and Vibration
N2 - H∞ optimization of fluid viscous dampers for reducing vibrations of high-speed railway bridges
KW - Angewandte Mathematik
KW - Strukturmechanik
Y1 - 2014
SP - 2421
EP - 2442
ER -
TY - JOUR
A1 - Schrader, Kai
A1 - Könke, Carsten
T1 - Distributed computing for the nonlinear analysis of multiphase composites
JF - Advances in Engineering Software
N2 - Distributed computing for the nonlinear analysis of multiphase composites
KW - Angewandte Mathematik
KW - Strukturmechanik
Y1 - 2013
SP - 20
EP - 32
ER -
TY - JOUR
A1 - Luther, Torsten
A1 - Könke, Carsten
T1 - Coupled cohesive zone representations from 3D quasicontinuum simulation on aluminum grain boundaries
JF - International Journal for Multiscale Computational Engineering
N2 - Coupled cohesive zone representations from 3D quasicontinuum simulation on aluminum grain boundaries
KW - Angewandte Mathematik
KW - Strukturmechanik
Y1 - 2010
ER -
TY - JOUR
A1 - Könke, Carsten
A1 - Eckardt, Stefan
A1 - Häfner, Stefan
A1 - Luther, Torsten
A1 - Unger, Jörg F.
T1 - Multiscale simulation methods in damage prediction of brittle and ductile materials
JF - International Journal for Multiscale Computational Engineering
N2 - Multiscale simulation methods in damage prediction of brittle and ductile materials
KW - Angewandte Mathematik
KW - Strukturmechanik
Y1 - 2010
SP - 17
EP - 36
ER -
TY - JOUR
A1 - Nasser, Mourad
A1 - Schwedler, Michael
A1 - Wuttke, Frank
A1 - Könke, Carsten
T1 - Seismic analysis of structural response using simplified soil-structure interaction models
JF - Bauingenieur, D-A-CH-Mitteilungsblatt
N2 - Seismic analysis of structural response using simplified soil-structure interaction models
KW - Angewandte Mathematik
KW - Strukturmechanik
Y1 - 2010
ER -
TY - JOUR
A1 - Luther, Torsten
A1 - Könke, Carsten
T1 - Polycrystal models for the analysis of intergranular crack growth in metallic materials
JF - Engineering Fracture Mechanics
N2 - Polycrystal models for the analysis of intergranular crack growth in metallic materials
KW - Angewandte Mathematik
KW - Strukturmechanik
Y1 - 2009
SP - 2332
EP - 2343
ER -
TY - JOUR
A1 - Eckardt, Stefan
A1 - Könke, Carsten
T1 - Adaptive damage simulation of concrete using heterogeneous multiscale models
JF - Journal of Algorithms & Computational Technology
N2 - Adaptive damage simulation of concrete using heterogeneous multiscale models
KW - Angewandte Mathematik
KW - Strukturmechanik
Y1 - 2008
SP - 275
EP - 297
ER -
TY - CHAP
A1 - Nasser, Mourad
A1 - Schwedler, Michael
A1 - Wuttke, Frank
A1 - Könke, Carsten
A1 - Schanz, Tom
T1 - Dynamic Soil-Structure Interaction Models: Theory and Application
N2 - Dynamic Soil-Structure Interaction Models: Theory and Application
KW - Angewandte Mathematik
KW - Strukturmechanik
Y1 - 2009
ER -
TY - CHAP
A1 - Luther, Torsten
A1 - Könke, Carsten
T1 - Micro and Meso Scale Analysis of Brittle Grain Boundary Damage in Polycrystalline Materials
N2 - Micro and Meso Scale Analysis of Brittle Grain Boundary Damage in Polycrystalline Materials
KW - Angewandte Mathematik
KW - Strukturmechanik
Y1 - 2009
ER -
TY - JOUR
A1 - Unger, Jörg F.
A1 - Könke, Carsten
T1 - Coupling of scales in a multiscale simulation using neural networks
JF - Computers & Structures
N2 - Coupling of scales in a multiscale simulation using neural networks
KW - Angewandte Mathematik
KW - Strukturmechanik
Y1 - 2008
ER -
TY - CHAP
A1 - Hatahet, Tareq
A1 - Könke, Carsten
T1 - Rational Framework for Probability of Collapse in Buildings
N2 - Rational Framework for Probability of Collapse in Buildings
KW - Angewandte Mathematik
KW - Strukturmechanik
Y1 - 2014
ER -
TY - CHAP
A1 - Schwedler, Michael
A1 - Könke, Carsten
T1 - Integrierte Tragwerksanalysen mittels Bauwerksinformationsmodellen und isogeometrischer FE-Methoden
N2 - Integrierte Tragwerksanalysen mittels Bauwerksinformationsmodellen und isogeometrischer FE-Methoden
KW - Angewandte Mathematik
KW - Strukturmechanik
Y1 - 2014
SN - 978-3-00-041256-1
ER -
TY - CHAP
A1 - Unger, Jörg F.
A1 - Könke, Carsten
T1 - Simulation of concrete using the extended finite element method
N2 - Simulation of concrete using the extended finite element method
KW - Angewandte Mathematik
KW - Strukturmechanik
Y1 - 2006
ER -
TY - JOUR
A1 - Bruhin, R.
A1 - Stock, U.A.
A1 - Drücker, J.-P.
A1 - Azhari, T.
A1 - Wippermann, J.
A1 - Albes, J.M.
A1 - Hintze, D.
A1 - Eckardt, Stefan
A1 - Könke, Carsten
A1 - Wahlers, T.
T1 - Numerical simulation techniques to study the structural response of the human chest following median sternotomy
JF - The Annals of Thoracic Surgery
N2 - Numerical simulation techniques to study the structural response of the human chest following median sternotomy
KW - Angewandte Mathematik
KW - Strukturmechanik
Y1 - 2005
SP - 623
EP - 630
ER -
TY - JOUR
A1 - Unger, Jörg F.
A1 - Eckardt, Stefan
A1 - Könke, Carsten
T1 - Modelling of cohesive crack growth in concrete structures with the extended finite element method
JF - Computer Methods in Applied Mechanics and Engineering
N2 - Modelling of cohesive crack growth in concrete structures with the extended finite element method
KW - Angewandte Mathematik
KW - Strukturmechanik
Y1 - 2007
SP - 4087
EP - 4100
ER -
TY - CHAP
A1 - Eckardt, Stefan
A1 - Könke, Carsten
T1 - Coupling techniques for heterogeneous multiscale models of concrete
N2 - Coupling techniques for heterogeneous multiscale models of concrete
KW - Angewandte Mathematik
KW - Strukturmechanik
Y1 - 2007
ER -
TY - CHAP
A1 - Luther, Torsten
A1 - Könke, Carsten
T1 - Multi-scale strategies for simulating brittle fracture in metallic materials
N2 - Multi-scale strategies for simulating brittle fracture in metallic materials
KW - Angewandte Mathematik
KW - Strukturmechanik
Y1 - 2007
ER -
TY - CHAP
A1 - Unger, Jörg F.
A1 - Könke, Carsten
T1 - Neural networks as material models within a multiscale approach
N2 - Neural networks as material models within a multiscale approach
KW - Angewandte Mathematik
KW - Strukturmechanik
Y1 - 2007
ER -
TY - JOUR
A1 - Häfner, Stefan
A1 - Eckardt, Stefan
A1 - Luther, Torsten
A1 - Könke, Carsten
T1 - Mesoscale modeling of concrete: Geometry and numerics
JF - Computers and Structures
N2 - Mesoscale modeling of concrete: Geometry and numerics
KW - Angewandte Mathematik
KW - Strukturmechanik
Y1 - 2006
SP - 450
EP - 461
ER -
TY - CHAP
A1 - Luther, Torsten
A1 - Könke, Carsten
T1 - Application of an Atom Continuum Model in Process of Damage Simulation on Multiple Length Scales
N2 - Application of an Atom Continuum Model in Process of Damage Simulation on Multiple Length Scales
KW - Angewandte Mathematik
KW - Strukturmechanik
Y1 - 2008
ER -
TY - CHAP
A1 - Eckardt, Stefan
A1 - Könke, Carsten
T1 - Damage simulation of concrete on the mesoscale
N2 - Damage simulation of concrete on the mesoscale
KW - Angewandte Mathematik
KW - Strukturmechanik
Y1 - 2005
ER -
TY - CHAP
A1 - Könke, Carsten
A1 - Petryna, Y.
A1 - Singh, Ripudaman
T1 - Risk assessment for damage tolerant structures
N2 - Risk assessment for damage tolerant structures
KW - Angewandte Mathematik
KW - Strukturmechanik
Y1 - 2005
ER -
TY - CHAP
A1 - Könke, Carsten
A1 - Eckardt, Stefan
A1 - Häfner, Stefan
A1 - Luther, Torsten
A1 - Unger, Jörg F.
T1 - Schädigungs- und Verbundmodellierung für Stahlbetontragwerke
N2 - Schädigungs- und Verbundmodellierung für Stahlbetontragwerke
KW - Angewandte Mathematik
KW - Strukturmechanik
Y1 - 2005
ER -
TY - CHAP
A1 - Luther, Torsten
A1 - Könke, Carsten
T1 - Micro-Mesoscale Analysis of Crack Initiation and Propagation in Metallic Polycrystals
N2 - Micro-Mesoscale Analysis of Crack Initiation and Propagation in Metallic Polycrystals
KW - Angewandte Mathematik
KW - Strukturmechanik
Y1 - 2005
ER -
TY - CHAP
A1 - Häfner, Stefan
A1 - Kessel, Marco
A1 - Könke, Carsten
T1 - Multiphase B-spline finite elements of variable order in the mechanical analysis of heterogeneous solids
N2 - Multiphase B-spline finite elements of variable order in the mechanical analysis of heterogeneous solids
KW - Angewandte Mathematik
KW - Strukturmechanik
Y1 - 2006
ER -
TY - CHAP
A1 - Häfner, Stefan
A1 - Könke, Carsten
T1 - Multigrid preconditioned conjugate gradient method in the mechanical analysis of heterogeneous solids
N2 - Multigrid preconditioned conjugate gradient method in the mechanical analysis of heterogeneous solids
KW - Angewandte Mathematik
KW - Strukturmechanik
Y1 - 2006
ER -
TY - CHAP
A1 - Könke, Carsten
T1 - Damage tolerant design
N2 - Damage tolerant design
KW - Angewandte Mathematik
KW - Strukturmechanik
Y1 - 2006
ER -
TY - CHAP
A1 - Könke, Carsten
A1 - Eckardt, Stefan
A1 - Häfner, Stefan
T1 - Spatial and temporal multiscale simulations of damage processes for concrete
N2 - Spatial and temporal multiscale simulations of damage processes for concrete
KW - Angewandte Mathematik
KW - Strukturmechanik
Y1 - 2006
ER -
TY - CHAP
A1 - Luther, Torsten
A1 - Könke, Carsten
T1 - Investigation of crack growth in polycrystalline mesostructures
N2 - Investigation of crack growth in polycrystalline mesostructures
KW - Angewandte Mathematik
KW - Strukturmechanik
Y1 - 2006
ER -
TY - CHAP
A1 - Luther, Torsten
A1 - Könke, Carsten
T1 - Analysis of crack initiation and propagation in polyctystalline meso- and microstructures of metal materials
N2 - Analysis of crack initiation and propagation in polyctystalline meso- and microstructures of metal materials
KW - Angewandte Mathematik
KW - Strukturmechanik
Y1 - 2006
ER -
TY - JOUR
A1 - Nguyen-Tuan, Long
A1 - Könke, Carsten
A1 - Bettzieche, Volker
A1 - Lahmer, Tom
T1 - Numerical modeling and validation for 3D coupled-nonlinear thermo-hydro-mechanical problems in masonry dams
JF - Computers & Structures
N2 - Numerical modeling and validation for 3D coupled-nonlinear thermo-hydro-mechanical problems in masonry dams
KW - Angewandte Mathematik
KW - Stochastik
KW - Strukturmechanik
Y1 - 2017
SP - 143
EP - 154
ER -
TY - JOUR
A1 - Lahmer, Tom
A1 - Nguyen-Tuan, Long
A1 - Könke, Carsten
A1 - Bettzieche, Volker
T1 - Thermo-hydro-mechanische 3-D-Simulation von Staumauern‐Modellierung und Validierung
JF - WASSERWIRTSCHAFT
N2 - Thermo-hydro-mechanische 3-D-Simulation von Staumauern‐Modellierung und Validierung
KW - Angewandte Mathematik
KW - Stochastik
KW - Strukturmechanik
Y1 - 2016
SP - 27
EP - 30
ER -
TY - JOUR
A1 - Lahmer, Tom
A1 - Könke, Carsten
A1 - Bettzieche, Volker
T1 - Optimale Positionierung von Messeinrichtungen an Staumauern zur Bauwerksüberwachung
JF - WASSERWIRTSCHAFT
N2 - Optimale Positionierung von Messeinrichtungen an Staumauern zur Bauwerksüberwachung
KW - Angewandte Mathematik
KW - Stochastik
KW - Strukturmechanik
Y1 - 2010
SP - 16
EP - 16
ER -
TY - JOUR
A1 - Lahmer, Tom
A1 - Könke, Carsten
A1 - Bettzieche, Volker
T1 - Optimal positioning of sensors for the monitoring of water dams
JF - WASSERWIRTSCHAFT
N2 - Optimal positioning of sensors for the monitoring of water dams
KW - Angewandte Mathematik
KW - Stochastik
KW - Strukturmechanik
Y1 - 2010
SP - 16
EP - 19
ER -
TY - CHAP
A1 - Unger, Jörg F.
A1 - Most, Thomas
A1 - Bucher, Christian
A1 - Könke, Carsten
T1 - Adaptation of the natural element method for crack growth simulations
N2 - Adaptation of the natural element method for crack growth simulations
KW - Angewandte Mathematik
KW - Strukturmechanik
Y1 - 2004
ER -
TY - CHAP
A1 - Unger, Jörg F.
A1 - Eckardt, Stefan
A1 - Könke, Carsten
T1 - Numerical Models for the simulation of concrete on the mesoscale
N2 - Numerical Models for the simulation of concrete on the mesoscale
KW - Angewandte Mathematik
KW - Strukturmechanik
Y1 - 2005
ER -
TY - CHAP
A1 - Eckardt, Stefan
A1 - Häfner, Stefan
A1 - Könke, Carsten
T1 - Simulation of the fracture behaviour of concrete using continuum damage models at the mesoscale
N2 - Simulation of the fracture behaviour of concrete using continuum damage models at the mesoscale
KW - Angewandte Mathematik
KW - Strukturmechanik
Y1 - 2004
ER -
TY - CHAP
A1 - Häfner, Stefan
A1 - Könke, Carsten
T1 - A multigrid finite element method for the mesoscale analysis of concrete
N2 - A multigrid finite element method for the mesoscale analysis of concrete
KW - Angewandte Mathematik
KW - Strukturmechanik
Y1 - 2004
ER -
TY - INPR
A1 - Radmard Rahmani, Hamid
A1 - Könke, Carsten
T1 - Passive Control of Tall Buildings Using Distributed Multiple Tuned Mass Dampers
N2 - The vibration control of the tall building during earthquake excitations is a challenging task due to their complex seismic behavior. This paper investigates the optimum placement and properties of the Tuned Mass Dampers (TMDs) in tall buildings, which are employed to control the vibrations during earthquakes. An algorithm was developed to spend a limited mass either in a single TMD or in multiple TMDs and distribute them optimally over the height of the building. The Non-dominated Sorting Genetic Algorithm (NSGA – II) method was improved by adding multi-variant genetic operators and utilized to simultaneously study the optimum design parameters of the TMDs and the optimum placement. The results showed that under earthquake excitations with noticeable amplitude in higher modes, distributing TMDs over the height of the building is more effective in mitigating the vibrations compared to the use of a single TMD system. From the optimization, it was observed that the locations of the TMDs were related to the stories corresponding to the maximum modal displacements in the lower modes and the stories corresponding to the maximum modal displacements in the modes which were highly activated by the earthquake excitations. It was also noted that the frequency content of the earthquake has significant influence on the optimum location of the TMDs.
KW - Schwingungsdämpfer
KW - Hochbau
KW - tall buildings
KW - passive control
KW - genetic algorithm
KW - tuned mass dampers
Y1 - 2019
U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:gbv:wim2-20190311-38597
ER -
TY - CHAP
A1 - Ahmad, Sofyan
A1 - Zabel, Volkmar
A1 - Könke, Carsten
T1 - WAVELET-BASED INDICATORS FOR RESPONSE SURFACE MODELS IN DAMAGE IDENTIFICATION OF STRUCTURES
T2 - Digital Proceedings, International Conference on the Applications of Computer Science and Mathematics in Architecture and Civil Engineering : July 04 - 06 2012, Bauhaus-University Weimar
N2 - In this paper, wavelet energy damage indicator is used in response surface methodology to identify the damage in simulated filler beam railway bridge. The approximate model is addressed to include the operational and surrounding condition in the assessment. The procedure is split into two stages, the training and detecting phase. During training phase, a so-called response surface is built from training data using polynomial regression and radial basis function approximation approaches. The response surface is used to detect the damage in structure during detection phase. The results show that the response surface model is able to detect moderate damage in one of bridge supports while the temperatures and train velocities are varied.
KW - Angewandte Mathematik
KW - Computerunterstütztes Verfahren
KW - Angewandte Informatik
Y1 - 2012
U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:gbv:wim2-20170306-27588
SN - 1611-4086
ER -
TY - CHAP
A1 - Theiler, Michael
A1 - Könke, Carsten
ED - Maia, Nuno
T1 - Damping in Bolted Joints
T2 - Proceedings of International Conference on Structural Engineering Dynamics (ICEDyn) 2013
N2 - With the help of modern CAE-based simulation processes, it is possible to predict the dynamic behavior of fatigue strength problems in order to improve products of many industries, e.g. the building, the machine construction or the automotive industry. Amongst others, it can be used to improve the acoustic design of automobiles in an early development stage.
Nowadays, the acoustics of automobiles plays a crucial role in the process of vehicle development. Because of the advanced demand of comfort and due to statutory rules the manufacturers are faced with the challenge of optimizing their car’s sound emissions. The optimization includes not only the reduction of noises. Lately with the trend to hybrid and electric cars, it has been shown that vehicles can become too quiet. Thus, the prediction of structural and acoustic properties based on FE-simulations is becoming increasingly important before any experimental prototype is examined. With the state of the art, qualitative comparisons between different implementations are possible. However, an accurate and reliable quantitative prediction is still a challenge.
One aspect in the context of increasing the prediction quality of acoustic (or general oscillating) problems - especially in power-trains of automobiles - is the more accurate implementation of damping in joint structures. While material damping occurs globally and homogenous in a structural system, the damping due to joints is a very local problem, since energy is especially dissipated in the vicinity of joints.
This paper focusses on experimental and numerical studies performed on a single (extracted) screw connection. Starting with experimental studies that are used to identify the underlying physical model of the energy loss, the locally influencing parameters (e.g. the damping factor) should be identified. In contrast to similar research projects, the approach tends to a more local consideration within the joint interface. Tangential stiffness and energy loss within the interface are spatially distributed and interactions between the influencing parameters are regarded. As a result, the damping matrix is no longer proportional to mass or stiffness matrix, since it is composed of the global material damping and the local joint damping. With this new approach, the prediction quality can be increased, since the local distribution of the physical parameters within the joint interface corresponds much closer to the reality.
KW - Damping
Y1 - 2013
U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:gbv:wim2-20130701-19709
SN - 978-989-96276-4-2
ER -
TY - CHAP
A1 - Unger, Jörg F.
A1 - Könke, Carsten
ED - Gürlebeck, Klaus
ED - Könke, Carsten
T1 - DISCRETE CRACK SIMULATION OF CONCRETE USING THE EXTENDED FINITE ELEMENTMETHOD
N2 - The extended finite element method (XFEM) offers an elegant tool to model material discontinuities and cracks within a regular mesh, so that the element edges do not necessarily coincide with the discontinuities. This allows the modeling of propagating cracks without the requirement to adapt the mesh incrementally. Using a regular mesh offers the advantage, that simple refinement strategies based on the quadtree data structure can be used to refine the mesh in regions, that require a high mesh density. An additional benefit of the XFEM is, that the transmission of cohesive forces through a crack can be modeled in a straightforward way without introducing additional interface elements. Finally different criteria for the determination of the crack propagation angle are investigated and applied to numerical tests of cracked concrete specimens, which are compared with experimental results.
KW - Architektur
KW - CAD
KW - Computerunterstütztes Verfahren
Y1 - 2006
U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:gbv:wim2-20170327-30303
UR - http://euklid.bauing.uni-weimar.de/ikm2006/index.php_lang=de&what=papers.html
ER -
TY - CHAP
A1 - Eckardt, Stefan
A1 - Könke, Carsten
ED - Gürlebeck, Klaus
ED - Könke, Carsten
T1 - ADAPTIVE SIMULATION OF THE DAMAGE BEHAVIOR OF CONCRETE USING HETEROGENEOUS MULTISCALE MODELS
N2 - In this paper an adaptive heterogeneous multiscale model, which couples two substructures with different length scales into one numerical model is introduced for the simulation of damage in concrete. In the presented approach the initiation, propagation and coalescence of microcracks is simulated using a mesoscale model, which explicitly represents the heterogeneous material structure of concrete. The mesoscale model is restricted to the damaged parts of the structure, whereas the undamaged regions are simulated on the macroscale. As a result an adaptive enlargement of the mesoscale model during the simulation is necessary. In the first part of the paper the generation of the heterogeneous mesoscopic structure of concrete, the finite element discretization of the mesoscale model, the applied isotropic damage model and the cohesive zone model are briefly introduced. Furthermore the mesoscale simulation of a uniaxial tension test of a concrete prism is presented and own obtained numerical results are compared to experimental results. The second part is focused on the adaptive heterogeneous multiscale approach. Indicators for the model adaptation and for the coupling between the different numerical models will be introduced. The transfer from the macroscale to the mesoscale and the adaptive enlargement of the mesoscale substructure will be presented in detail. A nonlinear simulation of a realistic structure using an adaptive heterogeneous multiscale model is presented at the end of the paper to show the applicability of the proposed approach to large-scale structures.
KW - Architektur
KW - CAD
KW - Computerunterstütztes Verfahren
Y1 - 2006
U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:gbv:wim2-20170327-29478
UR - http://euklid.bauing.uni-weimar.de/ikm2006/index.php_lang=de&what=papers.html
ER -
TY - CHAP
A1 - Häfner, Stefan
A1 - Könke, Carsten
ED - Gürlebeck, Klaus
ED - Könke, Carsten
T1 - MULTIGRID PRECONDITIONED CONJUGATE GRADIENT METHOD IN THE MECHANICAL ANALYSIS OF HETEROGENEOUS SOLIDS
N2 - A fast solver method called the multigrid preconditioned conjugate gradient method is proposed for the mechanical analysis of heterogeneous materials on the mesoscale. Even small samples of a heterogeneous material such as concrete show a complex geometry of different phases. These materials can be modelled by projection onto a uniform, orthogonal grid of elements. As one major problem the possible resolution of the concrete specimen is generally restricted due to (a) computation times and even more critical (b) memory demand. Iterative solvers can be based on a local element-based formulation while orthogonal grids consist of geometrical identical elements. The element-based formulation is short and transparent, and therefore efficient in implementation. A variation of the material properties in elements or integration points is possible. The multigrid method is a fast iterative solver method, where ideally the computational effort only increases linear with problem size. This is an optimal property which is almost reached in the implementation presented here. In fact no other method is known which scales better than linear. Therefore the multigrid method gains in importance the larger the problem becomes. But for heterogeneous models with very large ratios of Young's moduli the multigrid method considerably slows down by a constant factor. Such large ratios occur in certain heterogeneous solids, as well as in the damage analysis of solids. As solution to this problem the multigrid preconditioned conjugate gradient method is proposed. A benchmark highlights the multigrid preconditioned conjugate gradient method as the method of choice for very large ratio's of Young's modulus. A proposed modified multigrid cycle shows good results, in the application as stand-alone solver or as preconditioner.
KW - Architektur
KW - CAD
KW - Computerunterstütztes Verfahren
Y1 - 2006
U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:gbv:wim2-20170327-29626
UR - http://euklid.bauing.uni-weimar.de/ikm2006/index.php_lang=de&what=papers.html
ER -
TY - CHAP
A1 - Häfner, Stefan
A1 - Könke, Carsten
ED - Gürlebeck, Klaus
ED - Könke, Carsten
T1 - DAMAGE SIMULATION OF HETEROGENEOUS SOLIDS BY NONLOCAL FORMULATIONS ON ORTHOGONAL GRIDS
N2 - The present paper is part of a comprehensive approach of grid-based modelling. This approach includes geometrical modelling by pixel or voxel models, advanced multiphase B-spline finite elements of variable order and fast iterative solver methods based on the multigrid method. So far, we have only presented these grid-based methods in connection with linear elastic analysis of heterogeneous materials. Damage simulation demands further considerations. The direct stress solution of standard bilinear finite elements is severly defective, especially along material interfaces. Besides achieving objective constitutive modelling, various nonlocal formulations are applied to improve the stress solution. Such a corrective data processing can either refer to input data in terms of Young's modulus or to the attained finite element stress solution, as well as to a combination of both. A damage-controlled sequentially linear analysis is applied in connection with an isotropic damage law. Essentially by a high resolution of the heterogeneous solid, local isotropic damage on the material subscale allows to simulate complex damage topologies such as cracks. Therefore anisotropic degradation of a material sample can be simulated. Based on an effectively secantial global stiffness the analysis is numerically stable. The iteration step size is controlled for an adequate simulation of the damage path. This requires many steps, but in the iterative solution process each new step starts with the solution of the prior step. Therefore this method is quite effective. The present paper provides an introduction of the proposed concept for a stable simulation of damage in heterogeneous solids.
KW - Architektur
KW - CAD
KW - Computerunterstütztes Verfahren
Y1 - 2006
U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:gbv:wim2-20170327-29638
UR - http://euklid.bauing.uni-weimar.de/ikm2006/index.php_lang=de&what=papers.html
ER -
TY - CHAP
A1 - Häfner, Stefan
A1 - Kessel, Marco
A1 - Könke, Carsten
ED - Gürlebeck, Klaus
ED - Könke, Carsten
T1 - MULTIPHASE B-SPLINE FINITE ELEMENTS OF VARIABLE ORDER IN THE MECHANICAL ANALYSIS OF HETEROGENEOUS SOLIDS
N2 - Advanced finite elements are proposed for the mechanical analysis of heterogeneous materials. The approximation quality of these finite elements can be controlled by a variable order of B-spline shape functions. An element-based formulation is developed such that the finite element problem can iteratively be solved without storing a global stiffness matrix. This memory saving allows for an essential increase of problem size. The heterogeneous material is modelled by projection onto a uniform, orthogonal grid of elements. Conventional, strictly grid-based finite element models show severe oscillating defects in the stress solutions at material interfaces. This problem is cured by the extension to multiphase finite elements. This concept enables to define a heterogeneous material distribution within the finite element. This is possible by a variable number of integration points to each of which individual material properties can be assigned. Based on an interpolation of material properties at nodes and further smooth interpolation within the finite elements, a continuous material function is established. With both, continuous B-spline shape function and continuous material function, also the stress solution will be continuous in the domain. The inaccuracy implied by the continuous material field is by far less defective than the prior oscillating behaviour of stresses. One- and two-dimensional numerical examples are presented.
KW - Architektur
KW - CAD
KW - Computerunterstütztes Verfahren
Y1 - 2006
U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:gbv:wim2-20170327-29643
UR - http://euklid.bauing.uni-weimar.de/ikm2006/index.php_lang=de&what=papers.html
ER -
TY - CHAP
A1 - Luther, Torsten
A1 - Könke, Carsten
ED - Gürlebeck, Klaus
ED - Könke, Carsten
T1 - INVESTIGATION OF CRACK GROWTH IN POLYCRYSTALLINE MESOSTRUCTURES
N2 - The design and application of high performance materials demands extensive knowledge of the materials damage behavior, which significantly depends on the meso- and microstructural complexity. Numerical simulations of crack growth on multiple length scales are promising tools to understand the damage phenomena in complex materials. In polycrystalline materials it has been observed that the grain boundary decohesion is one important mechanism that leads to micro crack initiation. Following this observation the paper presents a polycrystal mesoscale model consisting of grains with orthotropic material behavior and cohesive interfaces along grain boundaries, which is able to reproduce the crack initiation and propagation along grain boundaries in polycrystalline materials. With respect to the importance of modeling the geometry of the grain structure an advanced Voronoi algorithm is proposed to generate realistic polycrystalline material structures based on measured grain size distribution. The polycrystal model is applied to investigate the crack initiation and propagation in statically loaded representative volume elements of aluminum on the mesoscale without the necessity of initial damage definition. Future research work is planned to include the mesoscale model into a multiscale model for the damage analysis in polycrystalline materials.
KW - Architektur
KW - CAD
KW - Computerunterstütztes Verfahren
Y1 - 2006
U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:gbv:wim2-20170327-29886
UR - http://euklid.bauing.uni-weimar.de/ikm2006/index.php_lang=de&what=papers.html
ER -
TY - CHAP
A1 - Unger, Jörg F.
A1 - Könke, Carsten
ED - Gürlebeck, Klaus
ED - Könke, Carsten
T1 - PARAMETER IDENTIFICATION OF MESOSCALE MODELS FROM MACROSCOPIC TESTS USING BAYESIAN NEURAL NETWORKS
N2 - In this paper, a parameter identification procedure using Bayesian neural networks is proposed. Based on a training set of numerical simulations, where the material parameters are simulated in a predefined range using Latin Hypercube sampling, a Bayesian neural network, which has been extended to describe the noise of multiple outputs using a full covariance matrix, is trained to approximate the inverse relation from the experiment (displacements, forces etc.) to the material parameters. The method offers not only the possibility to determine the parameters itself, but also the accuracy of the estimate and the correlation between these parameters. As a result, a set of experiments can be designed to calibrate a numerical model.
KW - Angewandte Informatik
KW - Angewandte Mathematik
KW - Architektur
KW - Computerunterstütztes Verfahren
KW - Computer Science Models in Engineering; Multiscale and Multiphysical Models; Scientific Computing
Y1 - 2010
U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:gbv:wim2-20170314-28984
UR - http://euklid.bauing.uni-weimar.de/ikm2009/paper.html
SN - 1611-4086
ER -
TY - CHAP
A1 - Eckardt, Stefan
A1 - Könke, Carsten
ED - Gürlebeck, Klaus
ED - Könke, Carsten
T1 - ENERGY RELEASE CONTROL FOR NONLINEAR MESOSCALE SIMULATIONS
N2 - In nonlinear simulations the loading is, in general, applied in an incremental way. Path-following algorithms are used to trace the equilibrium path during the failure process. Standard displacement controlled solution strategies fail if snap-back phenomena occur. In this contribution, a path-following algorithm based on the dissipation of the inelastic energy is presented which allows for the simulation of snap-backs. Since the constraint is defined in terms of the internal energy, the algorithm is not restricted to continuum damage models. Furthermore, no a priori knowledge about the final damage distribution is required. The performance of the proposed algorithm is illustrated using nonlinear mesoscale simulations.
KW - Angewandte Informatik
KW - Angewandte Mathematik
KW - Architektur
KW - Computerunterstütztes Verfahren
KW - Computer Science Models in Engineering; Multiscale and Multiphysical Models; Scientific Computing
Y1 - 2010
U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:gbv:wim2-20170314-28414
UR - http://euklid.bauing.uni-weimar.de/ikm2009/paper.html
SN - 1611-4086
ER -
TY - CHAP
A1 - Häfner, Stefan
A1 - Vogel, Frank
A1 - Könke, Carsten
ED - Gürlebeck, Klaus
ED - Könke, Carsten
T1 - FINITE ELEMENT ANALYSIS OF TORSION FOR ARBITRARY CROSS-SECTIONS
N2 - The present article proposes an alternative way to compute the torsional stiffness based on three-dimensional continuum mechanics instead of applying a specific theory of torsion. A thin, representative beam slice is discretized by solid finite elements. Adequate boundary conditions and coupling conditions are integrated into the numerical model to obtain a proper answer on the torsion behaviour, thus on shear center, shear stress and torsional stiffness. This finite element approach only includes general assumptions of beam torsion which are independent of cross-section geometry. These assumptions essentially are: no in-plane deformation, constant torsion and free warping. Thus it is possible to achieve numerical solutions of high accuracy for arbitrary cross-sections. Due to the direct link to three-dimensional continuum mechanics, it is possible to extend the range of torsion analysis to sections which are composed of different materials or even to heterogeneous beams on a high scale of resolution. A brief study follows to validate the implementation and results are compared to analytical solutions.
KW - Angewandte Informatik
KW - Angewandte Mathematik
KW - Architektur
KW - Computerunterstütztes Verfahren
KW - Computer Science Models in Engineering; Multiscale and Multiphysical Models; Scientific Computing
Y1 - 2010
U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:gbv:wim2-20170314-28483
UR - http://euklid.bauing.uni-weimar.de/ikm2009/paper.html
SN - 1611-4086
ER -
TY - CHAP
A1 - Schrader, Kai
A1 - Könke, Carsten
ED - Gürlebeck, Klaus
ED - Könke, Carsten
T1 - SPARSE APPROXIMATE COMPUTATION OF SADDLE POINT PROBLEMS ARISING FROM FETI-DP DISCRETIZATION
N2 - The numerical simulation of microstructure models in 3D requires, due to enormous d.o.f., significant resources of memory as well as parallel computational power. Compared to homogeneous materials, the material hetrogeneity on microscale induced by different material phases demand for adequate computational methods for discretization and solution process of the resulting highly nonlinear problem. To enable an efficient/scalable solution process of the linearized equation systems the heterogeneous FE problem will be described by a FETI-DP (Finite Element Tearing and Interconnecting - Dual Primal) discretization. The fundamental FETI-DP equation can be solved by a number of different approaches. In our approach the FETI-DP problem will be reformulated as Saddle Point system, by eliminating the primal and Lagrangian variables. For the reduced Saddle Point system, only defined by interior and dual variables, special Uzawa algorithms can be adapted for iteratively solving the FETI-DP saddle-point equation system (FETI-DP SPE). A conjugate gradient version of the Uzawa algorithm will be shown as well as some numerical tests regarding to FETI-DP discretization of small examples using the presented solution technique. Furthermore the inversion of the interior-dual Schur complement operator can be approximated using different techniques building an adequate preconditioning matrix and therewith leading to substantial gains in computing time efficiency.
KW - Angewandte Informatik
KW - Angewandte Mathematik
KW - Architektur
KW - Computerunterstütztes Verfahren
KW - Computer Science Models in Engineering; Multiscale and Multiphysical Models; Scientific Computing
Y1 - 2010
U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:gbv:wim2-20170314-28874
UR - http://euklid.bauing.uni-weimar.de/ikm2009/paper.html
SN - 1611-4086
ER -