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 - 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 - 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 - 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 - 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 - 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 - 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 - 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 - 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 - 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 -