TY - CHAP A1 - Lahmer, Tom A1 - Ghorashi, Seyed Shahram ED - Gürlebeck, Klaus ED - Lahmer, Tom ED - Werner, Frank T1 - XFEM-BASED CRACK IDENTIFICATION APPLYING REGULARIZING METHODS IN A MULTILEVEL APPROACH 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 - Many structures in different engineering applications suffer from cracking. In order to make reliable prognosis about the serviceability of those structures it is of utmost importance to identify cracks as precisely as possible by non-destructive testing. A novel approach (XIGA), which combines the Isogeometric Analysis (IGA) and the Extended Finite Element Method (XFEM) is used for the forward problem, namely the analysis of a cracked material, see [1]. Applying the NURBS (Non-Uniform Rational B-Spline) based approach from IGA together with the XFEM allows to describe effectively arbitrarily shaped cracks and avoids the necessity of remeshing during the crack identification problem. We want to exploit these advantages for the inverse problem of detecting existing cracks by non-destructive testing, see e.g. [2]. The quality of the reconstructed cracks however depends on two major issues, namely the quality of the measured data (measurement error) and the discretization of the crack model. The first one will be taken into account by applying regularizing methods with a posteriori stopping criteria. The second one is critical in the sense that too few degrees of freedom, i.e. the number of control points of the NURBS, do not allow for a precise description of the crack. An increased number of control points, however, increases the number of unknowns in the inverse analysis and intensifies the ill-posedness. The trade-off between accuracy and stability is aimed to be found by applying an inverse multilevel algorithm [3, 4] where the identification is started with short knot vectors which successively will be enlarged during the identification process. KW - Angewandte Informatik KW - Angewandte Mathematik KW - Computerunterstütztes Verfahren Y1 - 2012 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:gbv:wim2-20170314-27717 UR - http://euklid.bauing.uni-weimar.de/ikm2012 SN - 1611-4086 ER - TY - JOUR A1 - Jiang, Jin-Wu A1 - Wang, Bing-Shen A1 - Rabczuk, Timon T1 - Why twisting angles are diverse in graphene Moir’e patterns? JF - Journal of Applied Physics N2 - Why twisting angles are diverse in graphene Moir’e patterns? KW - Angewandte Mathematik KW - Strukturmechanik Y1 - 2013 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 - Smith, Andrew Paul A1 - Garloff, Jürgen A1 - Werkle, Horst ED - Gürlebeck, Klaus ED - Könke, Carsten T1 - VERIFIED SOLUTION OF FINITE ELEMENT MODELS WITH UNCERTAIN NODE LOCATIONS N2 - We consider a structural truss problem where all of the physical model parameters are uncertain: not just the material values and applied loads, but also the positions of the nodes are assumed to be inexact but bounded and are represented by intervals. Such uncertainty may typically arise from imprecision during the process of manufacturing or construction, or round-off errors. In this case the application of the finite element method results in a system of linear equations with numerous interval parameters which cannot be solved conventionally. Applying a suitable variable substitution, an iteration method for the solution of a parametric system of linear equations is firstly employed to obtain initial bounds on the node displacements. Thereafter, an interval tightening (pruning) technique is applied, firstly on the element forces and secondly on the node displacements, in order to obtain tight guaranteed enclosures for the interval solutions for the forces and displacements. 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:wim2-20170314-29010 UR - http://euklid.bauing.uni-weimar.de/ikm2009/paper.html SN - 1611-4086 ER - TY - JOUR A1 - Döring, R. A1 - Hoffmeyer, J. A1 - Seeger, T. A1 - Vormwald, Michael T1 - Verformungsverhalten und rechnerische Abschätzung der Ermüdungslebensdauer metallischer Werkstoffe unter mehrachsig nichtproportionaler Beanspruchung JF - Materialwissenschaft und Werkstofftechnik N2 - Verformungsverhalten und rechnerische Abschätzung der Ermüdungslebensdauer metallischer Werkstoffe unter mehrachsig nichtproportionaler Beanspruchung KW - Angewandte Mathematik KW - Strukturmechanik Y1 - 2002 SP - 280 EP - 288 ER - TY - CHAP A1 - De Bie, Hendrik A1 - Sommen, Frank ED - Gürlebeck, Klaus ED - Könke, Carsten T1 - VECTOR AND BIVECTOR FOURIER TRANSFORMS IN CLIFFORD ANALYSIS N2 - In the past, several types of Fourier transforms in Clifford analysis have been studied. In this paper, first an overview of these different transforms is given. Next, a new equation in a Clifford algebra is proposed, the solutions of which will act as kernels of a new class of generalized Fourier transforms. Two solutions of this equation are studied in more detail, namely a vector-valued solution and a bivector-valued solution, as well as the associated integral transforms. 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:wim2-20170314-28371 UR - http://euklid.bauing.uni-weimar.de/ikm2009/paper.html SN - 1611-4086 ER - TY - CHAP A1 - Khristich, Dmitrii A1 - Astapov, Yuri ED - Gürlebeck, Klaus ED - Lahmer, Tom T1 - VARIATIONAL POSITING AND SOLUTION OF COUPLED THERMOMECHANICAL PROBLEMS IN A REFERENCE CONFIGURATION T2 - Digital Proceedings, International Conference on the Applications of Computer Science and Mathematics in Architecture and Civil Engineering : July 20 - 22 2015, Bauhaus-University Weimar N2 - Variational formulation of a coupled thermomechanical problem of anisotropic solids for the case of non-isothermal finite deformations in a reference configuration is shown. The formulation of the problem includes: a condition of equilibrium flow of a deformation process in the reference configuration; an equation of a coupled heat conductivity in a variational form, in which an influence of deformation characteristics of a process on the temperature field is taken into account; tensor-linear constitutive relations for a hypoelastic material; kinematic and evolutional relations; initial and boundary conditions. Based on this formulation several axisymmetric isothermal and coupled problems of finite deformations of isotropic and anisotropic bodies are solved. The solution of coupled thermomechanical problems for a hollow cylinder in case of finite deformation showed an essential influence of coupling on distribution of temperature, stresses and strains. The obtained solutions show the development of stressstrain state and temperature changing in axisymmetric bodies in the case of finite deformations. KW - Angewandte Informatik KW - Angewandte Mathematik KW - Building Information Modeling KW - Computerunterstütztes Verfahren KW - Data, information and knowledge modeling in civil engineering; Function theoretic methods and PDE in engineering sciences; Mathematical methods for (robotics and) computer vision; Numerical modeling in engineering; Optimization in engineering applications Y1 - 2015 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:gbv:wim2-20170314-28091 SN - 1611-4086 ER - TY - JOUR A1 - Lahmer, Tom A1 - Ilg, J. A1 - Lerch, Reinhard T1 - Variance-based sensitivity analyses of piezoelectric models JF - Computer Modeling in Engineering & Sciences N2 - Variance-based sensitivity analyses of piezoelectric models KW - Angewandte Mathematik KW - Stochastik KW - Strukturmechanik Y1 - 2015 SP - 105 EP - 126 ER - TY - CHAP A1 - Macedo, Joaquim Miguel A1 - Benta, Agostinho A1 - Picado-Santos, Luis ED - Gürlebeck, Klaus ED - Lahmer, Tom T1 - USE OF MICROSIMULATION IN THE ADAPTATION TO PORTUGAL OF THE HCM 2000 METHODOLOGY FOR BASIC FREEWAY SEGMENTS T2 - Digital Proceedings, International Conference on the Applications of Computer Science and Mathematics in Architecture and Civil Engineering : July 20 - 22 2015, Bauhaus-University Weimar N2 - Portugal is one of the European countries with higher spatial and population freeway network coverage. The sharp growth of this network in the last years instigates the use of methods of analysis and the evaluation of their quality of service in terms of the traffic performance, typically performed through internationally accepted methodologies, namely that presented in the Highway Capacity Manual (HCM). Lately, the use of microscopic traffic simulation models has been increasingly widespread. These models simulate the individual movement of the vehicles, allowing to perform traffic analysis. The main target of this study was to verify the possibility of using microsimulation as an auxiliary tool in the adaptation of the methodology by HCM 2000 to Portugal. For this purpose, were used the microscopic simulators AIMSUN and VISSIM for the simulation of the traffic circulation in the A5 Portuguese freeway. The results allowed the analysis of the influence of the main geometric and traffic factors involved in the methodology by HCM 2000. In conclusion, the study presents the main advantages and limitations of the microsimulators AIMSUN and VISSIM in modelling the traffic circulation in Portuguese freeways. The main limitation is that these microsimulators are not able to simulate explicitly some of the factors considered in the HCM 2000 methodology, which invalidates their direct use as a tool in the quantification of those effects and, consequently, makes the direct adaptation of this methodology to Portugal impracticable. KW - Angewandte Informatik KW - Angewandte Mathematik KW - Building Information Modeling KW - Computerunterstütztes Verfahren KW - Data, information and knowledge modeling in civil engineering; Function theoretic methods and PDE in engineering sciences; Mathematical methods for (robotics and) computer vision; Numerical modeling in engineering; Optimization in engineering applications Y1 - 2015 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:gbv:wim2-20170314-28122 SN - 1611-4086 ER - TY - CHAP A1 - Abu Abed, Wassim A1 - Milbradt, Peter ED - Gürlebeck, Klaus ED - Könke, Carsten T1 - UNDERSTANDING THE ASPECT OF FUZZINESS IN INTERPOLATION METHODS N2 - Fuzzy functions are suitable to deal with uncertainties and fuzziness in a closed form maintaining the informational content. This paper tries to understand, elaborate, and explain the problem of interpolating crisp and fuzzy data using continuous fuzzy valued functions. Two main issues are addressed here. The first covers how the fuzziness, induced by the reduction and deficit of information i.e. the discontinuity of the interpolated points, can be evaluated considering the used interpolation method and the density of the data. The second issue deals with the need to differentiate between impreciseness and hence fuzziness only in the interpolated quantity, impreciseness only in the location of the interpolated points and impreciseness in both the quantity and the location. In this paper, a brief background of the concept of fuzzy numbers and of fuzzy functions is presented. The numerical side of computing with fuzzy numbers is concisely demonstrated. The problem of fuzzy polynomial interpolation, the interpolation on meshes and mesh free fuzzy interpolation is investigated. The integration of the previously noted uncertainty into a coherent fuzzy valued function is discussed. Several sets of artificial and original measured data are used to examine the mentioned fuzzy interpolations. 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:wim2-20170314-28726 UR - http://euklid.bauing.uni-weimar.de/ikm2009/paper.html SN - 1611-4086 ER -