@article{KirichukMostBucher, author = {Kirichuk, A. and Most, Thomas and Bucher, Christian}, title = {Numerical nonlinear analysis of kinematically excited shells}, series = {International Journal for Computational Civil and Structural Engineering}, journal = {International Journal for Computational Civil and Structural Engineering}, pages = {61 -- 74}, abstract = {Numerical nonlinear analysis of kinematically excited shells}, subject = {Angewandte Mathematik}, language = {en} } @article{MostBucherSchorling, author = {Most, Thomas and Bucher, Christian and Schorling, York}, title = {Dynamic stability analysis of non-linear structures with geometrical imperfections under random loading}, series = {Journal of Sound and Vibration}, journal = {Journal of Sound and Vibration}, pages = {381 -- 400}, abstract = {Dynamic stability analysis of non-linear structures with geometrical imperfections under random loading}, subject = {Angewandte Mathematik}, language = {en} } @article{MostBucher, author = {Most, Thomas and Bucher, Christian}, title = {A moving least squares weighting function for the element-free Galerkin method which almost fulfills essential boundary conditions}, series = {Structural Engineering and Mechanics}, journal = {Structural Engineering and Mechanics}, pages = {315 -- 332}, abstract = {A moving least squares weighting function for the element-free Galerkin method which almost fulfills essential boundary conditions}, subject = {Angewandte Mathematik}, language = {en} } @article{MostBucher, author = {Most, Thomas and Bucher, Christian}, title = {Stochastic simulation of cracking in concrete structures using multi-parameter random fields}, series = {International Journal of Reliability and Safety}, journal = {International Journal of Reliability and Safety}, pages = {168 -- 187}, abstract = {Stochastic simulation of cracking in concrete structures using multi-parameter random fields}, subject = {Angewandte Mathematik}, language = {en} } @inproceedings{MostEckardtSchraderetal., author = {Most, Thomas and Eckardt, Stefan and Schrader, Kai and Deckner, T.}, title = {AN IMPROVED COHESIVE CRACK MODEL FOR COMBINED CRACK OPENING AND SLIDING UNDER CYCLIC LOADING}, editor = {G{\"u}rlebeck, Klaus and K{\"o}nke, Carsten}, organization = {Bauhaus-Universit{\"a}t Weimar}, doi = {10.25643/bauhaus-universitaet.2993}, url = {http://nbn-resolving.de/urn:nbn:de:gbv:wim2-20170327-29933}, pages = {20}, abstract = {The modeling of crack propagation in plain and reinforced concrete structures is still a field for many researchers. If a macroscopic description of the cohesive cracking process of concrete is applied, generally the Fictitious Crack Model is utilized, where a force transmission over micro cracks is assumed. In the most applications of this concept the cohesive model represents the relation between the normal crack opening and the normal stress, which is mostly defined as an exponential softening function, independently from the shear stresses in tangential direction. The cohesive forces are then calculated only from the normal stresses. By Carol et al. 1997 an improved model was developed using a coupled relation between the normal and shear damage based on an elasto-plastic constitutive formulation. This model is based on a hyperbolic yield surface depending on the normal and the shear stresses and on the tensile and shear strength. This model also represents the effect of shear traction induced crack opening. Due to the elasto-plastic formulation, where the inelastic crack opening is represented by plastic strains, this model is limited for applications with monotonic loading. In order to enable the application for cases with un- and reloading the existing model is extended in this study using a combined plastic-damage formulation, which enables the modeling of crack opening and crack closure. Furthermore the corresponding algorithmic implementation using a return mapping approach is presented and the model is verified by means of several numerical examples. Finally an investigation concerning the identification of the model parameters by means of neural networks is presented. In this analysis an inverse approximation of the model parameters is performed by using a given set of points of the load displacement curves as input values and the model parameters as output terms. It will be shown, that the elasto-plastic model parameters could be identified well with this approach, but require a huge number of simulations.}, subject = {Architektur }, language = {en} } @inproceedings{MostBucherMacke, author = {Most, Thomas and Bucher, Christian and Macke, M.}, title = {A NATURAL NEIGHBOR BASED MOVING LEAST SQUARES APPROACH WITH INTERPOLATING WEIGHTING FUNCTION}, editor = {G{\"u}rlebeck, Klaus and K{\"o}nke, Carsten}, organization = {Bauhaus-Universit{\"a}t Weimar}, doi = {10.25643/bauhaus-universitaet.2994}, url = {http://nbn-resolving.de/urn:nbn:de:gbv:wim2-20170327-29943}, pages = {17}, abstract = {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.}, subject = {Architektur }, language = {en} } @inproceedings{MostBucher, author = {Most, Thomas and Bucher, Christian}, title = {ADAPTIVE RESPONSE SURFACE APPROACH USING ARTIFICIAL NEURAL NETWORKS AND MOVING LEAST SQUARES}, editor = {G{\"u}rlebeck, Klaus and K{\"o}nke, Carsten}, organization = {Bauhaus-Universit{\"a}t Weimar}, doi = {10.25643/bauhaus-universitaet.2992}, url = {http://nbn-resolving.de/urn:nbn:de:gbv:wim2-20170327-29922}, pages = {13}, abstract = {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.}, subject = {Architektur }, language = {en} } @article{MostBucher, author = {Most, Thomas and Bucher, Christian}, title = {Energy-based simulation of concrete cracking using an improved mixed-mode cohesive crack model within a meshless discretization}, series = {International Journal for Numerical and Analytical Methods in Geomechanics}, journal = {International Journal for Numerical and Analytical Methods in Geomechanics}, pages = {285 -- 305}, abstract = {Energy-based simulation of concrete cracking using an improved mixed-mode cohesive crack model within a meshless discretization}, subject = {Angewandte Mathematik}, language = {en} } @article{Most, author = {Most, Thomas}, title = {A natural neighbour-based moving least-squares approach for the element-free Galerkin method}, series = {International Journal for Numerical Methods in Engineering}, journal = {International Journal for Numerical Methods in Engineering}, pages = {224 -- 252}, abstract = {A natural neighbour-based moving least-squares approach for the element-free Galerkin method}, subject = {Angewandte Mathematik}, language = {en} } @article{MostBucher, author = {Most, Thomas and Bucher, Christian}, title = {Probabilistic analysis of concrete cracking using neural networks and random fields}, series = {Probabilistic Engineering Mechanics}, journal = {Probabilistic Engineering Mechanics}, pages = {219 -- 229}, abstract = {Probabilistic analysis of concrete cracking using neural networks and random fields}, subject = {Angewandte Mathematik}, language = {en} } @article{MostIshiiGengetal., author = {Most, Thomas and Ishii, H. and Geng, X. and Bolzern, P. and Colaneri, P. and De Nicolao, G.}, title = {Discussion on Almost sure stability of stochastic linear systems with ergodic parameters}, series = {European Journal of Control}, journal = {European Journal of Control}, pages = {124 -- 130}, abstract = {Discussion on Almost sure stability of stochastic linear systems with ergodic parameters}, subject = {Angewandte Mathematik}, language = {en} } @article{MostBucher, author = {Most, Thomas and Bucher, Christian}, title = {New concepts for moving least squares: An interpolating non-singular weighting function and weighted nodal least squares}, series = {Engineering Analysis with Boundary Elements}, journal = {Engineering Analysis with Boundary Elements}, pages = {461 -- 470}, abstract = {New concepts for moving least squares: An interpolating non-singular weighting function and weighted nodal least squares}, subject = {Angewandte Mathematik}, language = {en} } @article{BucherMost, author = {Bucher, Christian and Most, Thomas}, title = {A comparison of approximate response functions in structural reliability analysis}, series = {Probabilistic Engineering Mechanics}, journal = {Probabilistic Engineering Mechanics}, pages = {154 -- 163}, abstract = {A comparison of approximate response functions in structural reliability analysis}, subject = {Angewandte Mathematik}, language = {en} }