TY - CHAP A1 - Karaki, Ghada ED - Gürlebeck, Klaus ED - Lahmer, Tom T1 - SELECTION AND SCALING OF GROUND MOTION RECORDS FOR SEISMIC ANALYSIS USING AN OPTIMIZATION ALGORITHM 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 - The nonlinear time history analysis and seismic performance based methods require a set of scaled ground motions. The conventional procedure of ground motion selection is based on matching the motion properties, e.g. magnitude, amplitude, fault distance, and fault mechanism. The seismic target spectrum is only used in the scaling process following the random selection process. Therefore, the aim of the paper is to present a procedure to select a sets of ground motions from a built database of ground motions. The selection procedure is based on running an optimization problem using Dijkstra’s algorithm to match the selected set of ground motions to a target response spectrum. The selection and scaling procedure of optimized sets of ground motions is presented by examining the analyses of nonlinear single degree of freedom systems. 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:wim2-20170314-28058 SN - 1611-4086 ER - TY - CHAP A1 - Hommel, Angela A1 - Gürlebeck, Klaus ED - Gürlebeck, Klaus ED - Lahmer, Tom T1 - THE RELATIONSHIP BETWEEN LINEAR ELASTICITY THEORY AND COMPLEX FUNCTION THEORY STUDIED ON THE BASIS OF FINITE DIFFERENCES 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 - It is well-known that the solution of the fundamental equations of linear elasticity for a homogeneous isotropic material in plane stress and strain state cases can be equivalently reduced to the solution of a biharmonic equation. The discrete version of the Theorem of Goursat is used to describe the solution of the discrete biharmonic equation by the help of two discrete holomorphic functions. In order to obtain a Taylor expansion of discrete holomorphic functions we introduce a basis of discrete polynomials which fulfill the so-called Appell property with respect to the discrete adjoint Cauchy-Riemann operator. All these steps are very important in the field of fracture mechanics, where stress and displacement fields in the neighborhood of singularities caused by cracks and notches have to be calculated with high accuracy. Using the sum representation of holomorphic functions it seems possible to reproduce the order of singularity and to determine important mechanical characteristics. 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:wim2-20170314-28010 SN - 1611-4086 ER - TY - CHAP A1 - Hölter, Raoul A1 - Mahmoudi, Elham A1 - Schanz, Tom ED - Gürlebeck, Klaus ED - Lahmer, Tom T1 - OPTIMAL SENSOR LOCATION FOR PARAMETER IDENTIFICATION IN SOFT CLAY 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 - Performing parameter identification prior to numerical simulation is an essential task in geotechnical engineering. However, it has to be kept in mind that the accuracy of the obtained parameter is closely related to the chosen experimental setup, such as the number of sensors as well as their location. A well considered position of sensors can increase the quality of the measurement and to reduce the number of monitoring points. This Paper illustrates this concept by means of a loading device that is used to identify the stiffness and permeability of soft clays. With an initial setup of the measurement devices the pore water pressure and the vertical displacements are recorded and used to identify the afore mentioned parameters. Starting from these identified parameters, the optimal measurement setup is investigated with a method based on global sensitivity analysis. This method shows an optimal sensor location assuming three sensors for each measured quantity, and the results are discussed. 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:wim2-20170314-28008 SN - 1611-4086 ER - TY - CHAP A1 - Grigor'ev, Yuri ED - Gürlebeck, Klaus ED - Lahmer, Tom T1 - REGULAR QUATERNIONIC FUNCTIONS AND THEIR APPLICATIONS 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 - The theory of regular quaternionic functions of a reduced quaternionic variable is a 3-dimensional generalization of complex analysis. The Moisil-Theodorescu system (MTS) is a regularity condition for such functions depending on the radius vector r = ix+jy+kz seen as a reduced quaternionic variable. The analogues of the main theorems of complex analysis for the MTS in quaternion forms are established: Cauchy, Cauchy integral formula, Taylor and Laurent series, approximation theorems and Cauchy type integral properties. The analogues of positive powers (inner spherical monogenics) are investigated: the set of recurrence formulas between the inner spherical monogenics and the explicit formulas are established. Some applications of the regular function in the elasticity theory and hydrodynamics are given. 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:wim2-20170314-27988 SN - 1611-4086 ER - TY - CHAP A1 - Ferreira, Milton dos Santos A1 - Vieira, Nelson ED - Gürlebeck, Klaus ED - Lahmer, Tom T1 - EIGENFUNCTIONS AND FUNDAMENTAL SOLUTIONS FOR THE FRACTIONAL LAPLACIAN IN 3 DIMENSIONS 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 - Recently there has been a surge of interest in PDEs involving fractional derivatives in different fields of engineering. In this extended abstract we present some of the results developedin [3]. We compute the fundamental solution for the three-parameter fractional Laplace operator Δ by transforming the eigenfunction equation into an integral equation and applying the method of separation of variables. The obtained solutions are expressed in terms of Mittag-Leffer functions. For more details we refer the interested reader to [3] where it is also presented an operational approach based on the two Laplace transform. 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:wim2-20170314-27968 SN - 1611-4086 ER - TY - CHAP A1 - Al-Yasiri, Zainab A1 - Gürlebeck, Klaus ED - Gürlebeck, Klaus ED - Lahmer, Tom T1 - ON BOUNDARY VALUE PROBLEMS FOR P-LAPLACE AND P-DIRAC EQUATIONS 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 - The p-Laplace equation is a nonlinear generalization of the Laplace equation. This generalization is often used as a model problem for special types of nonlinearities. The p-Laplace equation can be seen as a bridge between very general nonlinear equations and the linear Laplace equation. The aim of this paper is to solve the p-Laplace equation for 2 < p < 3 and to find strong solutions. The idea is to apply a hypercomplex integral operator and spatial function theoretic methods to transform the p-Laplace equation into the p-Dirac equation. This equation will be solved iteratively by using a fixed point theorem. 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:wim2-20170314-27928 SN - 1611-4086 ER -