TY - JOUR A1 - Bucher, Christian A1 - Most, Thomas T1 - A comparison of approximate response functions in structural reliability analysis JF - Probabilistic Engineering Mechanics N2 - A comparison of approximate response functions in structural reliability analysis KW - Angewandte Mathematik KW - Strukturmechanik Y1 - 2008 SP - 154 EP - 163 ER - TY - JOUR A1 - Most, Thomas A1 - Bucher, Christian T1 - A moving least squares weighting function for the element-free Galerkin method which almost fulfills essential boundary conditions JF - Structural Engineering and Mechanics N2 - A moving least squares weighting function for the element-free Galerkin method which almost fulfills essential boundary conditions KW - Angewandte Mathematik KW - Strukturmechanik Y1 - 2005 SP - 315 EP - 332 ER - TY - CHAP A1 - Most, Thomas A1 - Bucher, Christian A1 - Macke, M. ED - Gürlebeck, Klaus ED - Könke, Carsten T1 - A NATURAL NEIGHBOR BASED MOVING LEAST SQUARES APPROACH WITH INTERPOLATING WEIGHTING FUNCTION N2 - The Element-free Galerkin Method has become a very popular tool for the simulation of mechanical problems with moving boundaries. The internally applied Moving Least Squares approximation uses in general Gaussian or cubic weighting functions and has compact support. Due to the approximative character of this method the obtained shape functions do not fulfill the interpolation condition, which causes additional numerical effort for the imposition of the essential boundary conditions. The application of a singular weighting function, which leads to singular coefficient matrices at the nodes, can solve this problem, but requires a very careful placement of the integration points. Special procedures for the handling of such singular matrices were proposed in literature, which require additional numerical effort. In this paper a non-singular weighting function is presented, which leads to an exact fulfillment of the interpolation condition. This weighting function leads to regular values of the weights and the coefficient matrices in the whole interpolation domain even at the nodes. Furthermore this function gives much more stable results for varying size of the influence radius and for strongly distorted nodal arrangements than classical weighting function types. Nevertheless, for practical applications the results are similar as these obtained with the regularized weighting type presented by the authors in previous publications. Finally a new concept will be presented, which enables an efficient analysis of systems with strongly varying node density. In this concept the nodal influence domains are adapted depending on the nodal configuration by interpolating the influence radius for each direction from the distances to the natural neighbor nodes. This approach requires a Voronoi diagram of the domain, which is available in this study since Delaunay triangles are used as integration background cells. In the numerical examples it will be shown, that this method leads to a more uniform and reduced number of influencing nodes for systems with varying node density than the classical circular influence domains, which means that the small additional numerical effort for interpolating the influence radius leads to remarkable reduction of the total numerical cost in a linear analysis while obtaining similar results. For nonlinear calculations this advantage would be even more significant. KW - Architektur KW - CAD KW - Computerunterstütztes Verfahren Y1 - 2006 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:gbv:wim2-20170327-29943 UR - http://euklid.bauing.uni-weimar.de/ikm2006/index.php_lang=de&what=papers.html ER - TY - CHAP A1 - Most, Thomas A1 - Bucher, Christian ED - Gürlebeck, Klaus ED - Könke, Carsten T1 - ADAPTIVE RESPONSE SURFACE APPROACH USING ARTIFICIAL NEURAL NETWORKS AND MOVING LEAST SQUARES N2 - In engineering science the modeling and numerical analysis of complex systems and relations plays an important role. In order to realize such an investigation, for example a stochastic analysis, in a reasonable computational time, approximation procedure have been developed. A very famous approach is the response surface method, where the relation between input and output quantities is represented for example by global polynomials or local interpolation schemes as Moving Least Squares (MLS). In recent years artificial neural networks (ANN) have been applied as well for such purposes. Recently an adaptive response surface approach for reliability analyses was proposed, which is very efficient concerning the number of expensive limit state function evaluations. Due to the applied simplex interpolation the procedure is limited to small dimensions. In this paper this approach is extended for larger dimensions using combined ANN and MLS response surfaces for evaluating the adaptation criterion with only one set of joined limit state points. As adaptation criterion a combination by using the maximum difference in the conditional probabilities of failure and the maximum difference in the approximated radii is applied. Compared to response surfaces on directional samples or to plain directional sampling the failure probability can be estimated with a much smaller number of limit state points. KW - Architektur KW - CAD KW - Computerunterstütztes Verfahren Y1 - 2006 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:gbv:wim2-20170327-29922 UR - http://euklid.bauing.uni-weimar.de/ikm2006/index.php_lang=de&what=papers.html ER - TY - JOUR A1 - Brehm, Maik A1 - Zabel, Volkmar A1 - Bucher, Christian T1 - An automatic mode pairing strategy using an enhanced modal assurance citerion based on modal strain energies JF - Journal of Sound and Vibration N2 - In the context of finite element model updating using output-only vibration test data, natural frequencies and mode shapes are used as validation criteria. Consequently, the correct pairing of experimentally obtained and numerically derived natural frequencies and mode shapes is important. In many cases, only limited spatial information is available and noise is present in the measurements. Therefore, the automatic selection of the most likely numerical mode shape corresponding to a particular experimentally identified mode shape can be a difficult task. The most common criterion for indicating corresponding mode shapes is the modal assurance criterion. Unfortunately, this criterion fails in certain cases and is not reliable for automatic approaches. In this paper, the purely mathematical modal assurance criterion will be enhanced by additional physical information from the numerical model in terms of modal strain energies. A numerical example and a benchmark study with experimental data are presented to show the advantages of the proposed energy-based criterion in comparison to the traditional modal assurance criterion. KW - Angewandte Mathematik KW - Strukturmechanik Y1 - 2010 U6 - http://dx.doi.org/10.1016/j.jsv.2010.07.006 SP - 5375 EP - 5392 ER - TY - CHAP A1 - Brehm, Maik A1 - Zabel, Volkmar A1 - Bucher, Christian A1 - Ribeiro, D. ED - Gürlebeck, Klaus ED - Könke, Carsten T1 - AN AUTOMATIC MODE SELECTION STRATEGY FOR MODEL UPDATING USING THE MODAL ASSURANCE CRITERION AND MODAL STRAIN ENERGIES N2 - In the context of finite element model updating using vibration test data, natural frequencies and mode shapes are used as validation criteria. Consequently, the order of natural frequencies and mode shapes is important. As only limited spatial information is available and noise is present in the measurements, the automatic selection of the most likely numerical mode shape corresponding to a measured mode shape is a difficult task. The most common criterion to indicate corresponding mode shapes is the modal assurance criterion. Unfortunately, this criterion fails in certain cases. In this paper, the pure mathematical modal assurance criterion will be enhanced by additional physical information of the numerical model in terms of modal strain energies. A numerical example and a benchmark study with real measured data are presented to show the advantages of the enhanced energy based criterion in comparison to the traditional modal assurance criterion. 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:wim2-20170314-28330 UR - http://euklid.bauing.uni-weimar.de/ikm2009/paper.html SN - 1611-4086 ER - TY - CHAP A1 - Most, Thomas A1 - Bucher, Christian T1 - Application of the "fictious crack model" to meshless crack growth simulations N2 - In this paper a meshless component is presented, which internally uses the common meshless interpolation technique >Moving Least Squares<. In contrast to usual meshless integration schemes like the cell quadrature and the nodal integration in this study integration zones with triangular geometry spanned by three nodes are used for 2D analysis. The boundary of the structure is defined by boundary nodes, which are similar to finite element nodes. By using the neighborhood relations of the integration zones an efficient search algorithm to detected the nodes in the influence of the integration points was developed. The components are directly coupled with finite elements by using a penalty method. An widely accepted model to describe the fracture behavior of concrete is the >Fictitious Crack Model< which is applied in this study, which differentiates between micro cracks and macro cracks, with and without force transmission over the crack surface, respectively. In this study the crack surface is discretized by node pairs in form of a polygon, which is part of the boundary. To apply the >Fictitious Crack Model< finite interface elements are included between the crack surface nodes. The determination of the maximum principal strain at the crack tip is done by introducing an influence area around the singularity. On a practical example it is shown that the included elements improve the model by the transmission of the surface forces during monotonic loading and by the representation of the contact forces of closed cracks during reverse loading. KW - Bruchmechanik KW - Rissbildung KW - Modellierung Y1 - 2003 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:gbv:wim2-20111215-3359 ER - TY - JOUR A1 - Most, Thomas A1 - Bucher, Christian A1 - Schorling, York T1 - Dynamic stability analysis of non-linear structures with geometrical imperfections under random loading JF - Journal of Sound and Vibration N2 - Dynamic stability analysis of non-linear structures with geometrical imperfections under random loading KW - Angewandte Mathematik KW - Strukturmechanik Y1 - 2004 SP - 381 EP - 400 ER - TY - JOUR A1 - Most, Thomas A1 - Bucher, Christian T1 - Energy-based simulation of concrete cracking using an improved mixed-mode cohesive crack model within a meshless discretization JF - International Journal for Numerical and Analytical Methods in Geomechanics N2 - Energy-based simulation of concrete cracking using an improved mixed-mode cohesive crack model within a meshless discretization KW - Angewandte Mathematik KW - Strukturmechanik Y1 - 2007 SP - 285 EP - 305 ER - TY - CHAP A1 - Bombasaro, Emanuel A1 - Bucher, Christian ED - Gürlebeck, Klaus ED - Könke, Carsten T1 - INVESTIGATION OF MODELING ERRORS OF DIFFERENT RANDOM FIELD BASED WIND LOAD FORMULATIONS N2 - In this paper the influence of changes in the mean wind velocity, the wind profile power-law coefficient, the drag coefficient of the terrain and the structural stiffness are investigated on different complex structural models. This paper gives a short introduction to wind profile models and to the approach by Davenport A. G. to compute the structural reaction of wind induced vibrations. Firstly with help of a simple example (a skyscraper) this approach is shown. Using this simple example gives the reader the possibility to study the variance differences when changing one of the above mentioned parameters on this very easy example and see the influence of different complex structural models on the result. Furthermore an approach for estimation of the needed discretization level is given. With the help of this knowledge the structural model design methodology can be base on deeper understanding of the different behavior of the single models. 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:wim2-20170314-28318 UR - http://euklid.bauing.uni-weimar.de/ikm2009/paper.html SN - 1611-4086 ER -