TY  - CHAP
A1  - Raue, Erich
ED  - Gürlebeck, Klaus
ED  - Könke, Carsten
T1  - NONLINEAR ANALYSIS OF COMPOSITE CROSS-SECTIONS WITH PRE-DEFORMATIONS
N2  - An energy method based on the LAGRANGE Principle of the minimum of total potential en-ergy is presented to calculate the stresses and strains of composite cross-sections. The stress-strain relation of each partition of the cross-section can be an arbitrary piecewise continuous function. The strain energy is transformed into a line integral by GAUSS’s integral theorem. The total strain of each partition of the cross-section is split into load-dependent strain and pre-strain. Pre-strains have to be taken into account when the cross-section is pre-stressed, retrofit-ted or influenced by shrinkage, temperature etc. The unconstrained minimum problem can be solved for each load combination using standard software. The application of the method presented in the paper is demonstrated by means of examples.
KW  - Angewandte Informatik
KW  - Angewandte Mathematik
KW  - Architektur <Informatik>
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:wim2-20170314-28804
UR  - http://euklid.bauing.uni-weimar.de/ikm2009/paper.html
SN  - 1611-4086
ER  - 
TY  - JOUR
A1  - Zhang, Yongzheng
T1  - Nonlocal dynamic Kirchhoff plate formulation based on nonlocal operator method
JF  - Engineering with Computers
N2  - In this study, we propose a nonlocal operator method (NOM) for the dynamic analysis of (thin) Kirchhoff plates. The nonlocal Hessian operator is derived based on a second-order Taylor series expansion. The NOM does not require any shape functions and associated derivatives as ’classical’ approaches such as FEM, drastically facilitating the implementation. Furthermore, NOM is higher order continuous, which is exploited for thin plate analysis that requires C1 continuity. The nonlocal dynamic governing formulation and operator energy functional for Kirchhoff plates are derived from a variational principle. The Verlet-velocity algorithm is used for the time discretization. After confirming the accuracy of the nonlocal Hessian operator, several numerical examples are simulated by the nonlocal dynamic Kirchhoff plate formulation.
KW  - Angewandte Mathematik
KW  - nonlocal operator method
KW  - nonlocal Hessian operator
KW  - operator energy functional
KW  - dual-support
KW  - variational principle
Y1  - 2022
U6  - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:gbv:wim2-20220209-45849
UR  - https://link.springer.com/article/10.1007/s00366-021-01587-1
VL  - 2022
SP  - 1
EP  - 35
PB  - Springer
CY  - London
ER  - 
TY  - CHAP
A1  - Ebert, Svend
A1  - Bernstein, Swanhild
A1  - Cerejeiras, Paula
A1  - Kähler, Uwe
ED  - Gürlebeck, Klaus
ED  - Könke, Carsten
T1  - NONZONAL WAVELETS ON S^N
N2  - In the present article we will construct wavelets on an arbitrary dimensional sphere S^n due the approach of approximate Identities. There are two equivalently approaches to wavelets. The group theoretical approach formulates a square integrability condition for a group acting via unitary, irreducible representation on the sphere. The connection to the group theoretical approach will be sketched. The concept of approximate identities uses the same constructions in the background, here we select an appropriate section of dilations and translations in the group acting on the sphere in two steps. At First we will formulate dilations in terms of approximate identities and than we call in translations on the sphere as rotations. This leads to the construction of an orthogonal polynomial system in L²(SO(n+1)). That approach is convenient to construct concrete wavelets, since the appropriate kernels can be constructed form the heat kernel leading to the approximate Identity of Gauss-Weierstra\ss. We will work out conditions to functions forming a family of wavelets, subsequently we formulate how we can construct zonal wavelets from a approximate Identity and the relation to admissibility of nonzonal wavelets. Eventually we will give an example of a nonzonal Wavelet on $S^n$, which we obtain from the approximate identity of Gauss-Weierstraß.
KW  - Angewandte Informatik
KW  - Angewandte Mathematik
KW  - Architektur <Informatik>
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:wim2-20170314-28406
UR  - http://euklid.bauing.uni-weimar.de/ikm2009/paper.html
SN  - 1611-4086
ER  - 
TY  - CHAP
A1  - Ubysz, Andrzej
A1  - Maj, Marek
A1  - Stachon, T.
A1  - Rogoza, Agnieszka
ED  - Gürlebeck, Klaus
ED  - Könke, Carsten
T1  - NUMERICAL ANALYSIS OF STRESS DISTRIBUTION IN THE REINFORCED CONCRETE SUPPORT BEAM BRACKET EXPOSED TO DAMAGE
N2  - The article presents analysis of stress distribution in the reinforced concrete support beam bracket which is a component of prefabricated reinforced concrete building. The building structure is spatial frame where dilatations were applied. The proper stiffness of its structure is provided by frames with stiff joints, monolithic lift shifts and staircases. The prefabricated slab floors are supported by beam shelves which are shaped as inverted letter ‘T’. Beams are supported by the column brackets. In order to lower the storey height and fulfill the architectural demands at the same time, the designer lowered the height of beam at the support zone. The analyzed case refers to the bracket zone where the slant crack. on the support beam bracket was observed. It could appear as a result of overcrossing of allowable tension stresses in reinforced concrete, in the bracket zone. It should be noted that the construction solution applied, i.e. concurrent support of the “undercut” beam on the column bracket causes local concentration of stresses in the undercut zone where the strongest transverse forces and tangent stresses occur concurrently. Some additional rectangular stresses being a result of placing the slab floors on the lower part of beam shelves sum up with those described above.
KW  - Angewandte Informatik
KW  - Angewandte Mathematik
KW  - Architektur <Informatik>
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:wim2-20170314-28693
UR  - http://euklid.bauing.uni-weimar.de/ikm2009/paper.html
SN  - 1611-4086
ER  - 
TY  - CHAP
A1  - Rogoza, Agnieszka
A1  - Ubysz, Andrzej
ED  - Gürlebeck, Klaus
ED  - Könke, Carsten
T1  - NUMERICAL ANALYSIS OF THE CRACKED REINFORCED CONCRETE BEAMS
N2  - We present the way of calculation of displacement in the bent reinforced concrete bar elements where rearrangement of internal forces and plastic hinge occurred. The described solution is based on prof. Borcz’s mathematical model. It directly takes into consideration the effects connected with the occurrence of plastic hinge, such as for example a crack, by means of a differential equation of axis of the bent reinforced concrete beam. The EN Eurocode 2 makes it possible to consider the influence of plastic hinge on the values of the reinforced concrete structures. This influence can also be assumed using other analytical methods. However, the results obtained by the application of Eurocode 2 are higher from those received in testing. Just comparably big error level occurs when calculations are made by means of Borcz’s method, but in the latter case, the results depend on the assumptions made beforehand. This method makes it possible to apply the experimental results using parameters r1 i r0. When the experimental results are taken into account, one could observe the compatibility between the calculations and actual deflections of the structure.
KW  - Angewandte Informatik
KW  - Angewandte Mathematik
KW  - Architektur <Informatik>
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:wim2-20170314-28835
UR  - http://euklid.bauing.uni-weimar.de/ikm2009/paper.html
SN  - 1611-4086
ER  - 
TY  - CHAP
A1  - Nguyen-Tuan, Long
A1  - Datcheva, Maria
A1  - Schanz, Tom
ED  - Gürlebeck, Klaus
ED  - Könke, Carsten
T1  - NUMERICAL SIMULATION AND INVERSE ANALYSIS OF THERMO-HYDRO-MECHANICAL BEHAVIOR OF SAND-BENTONITE MIXTURE
N2  - Sand-bentonite mixtures are well recognized as buffer and sealing material in nuclear waste repository constructions. The behaviour of compacted sand-bentonite mixture needs to be well understood in order to guarantee the safety and the efficiency of the barrier construction. This paper presents numerical simulations of swelling test and coupled thermo-hydro-mechanical (THM) test on compacted sand-bentonite mixture in order to reveal the influence of the temperature and hydraulic gradients on the distribution of temperature, mechanical stress and water content in such materials. Sensitivity analysis is carried out to identify the parameters which influence the most the response of the numerical model. Results of back analysis of the model parameters are reported and critically assessed.
KW  - Angewandte Informatik
KW  - Angewandte Mathematik
KW  - Architektur <Informatik>
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:wim2-20170314-28767
UR  - http://euklid.bauing.uni-weimar.de/ikm2009/paper.html
SN  - 1611-4086
ER  - 
TY  - CHAP
A1  - Itam, Zarina
ED  - Gürlebeck, Klaus
ED  - Könke, Carsten
T1  - NUMERICAL SIMULATION OF THERMO-HYGRAL ALKALI-SILICA REACTION MODEL IN CONCRETE AT THE MESOSCALE
N2  - This research aims to model Alkali-Silica Reaction gel expansion in concrete under the influence of hygral and thermal loading, based on experimental results. ASR provokes a heterogeneous expansion in concrete leading to dimensional changes and eventually the premature failure of the concrete structure. This can result in map cracking on the concrete surface which will decrease the concrete stiffness. Factors that influence ASR are parameters such as the cement alkalinity, the number of deleterious silica from the aggregate used, concrete porosity, and external factors like temperature, humidity and external source of alkali from ingression of deicing salts. Uncertainties of the influential factors make ASR a difficult phenomenon to solve; hence my approach to this matter is to solve the problem using stochastic modelling, where a numerical simulation of concrete cross-section with integration of experimental results from Finger-Institute for Building Materials Science at the Bauhaus-Universität Weimar. The problem is formulated as a multi-field problem, combining heat transfer, fluid transfer and the reaction rate model with the mechanical stress field. Simulation is performed as a mesoscale model considering aggregates and mortar matrix. The reaction rate model will be conducted using experimental results from concrete expansions due to ASR gained from concrete prism tests. Expansive strains values for transient environmental conditions due to the reaction rate will be determined from calculation based on the reaction rate model. Results from these models will be able to predict the rate of ASR expansion and the cracking propagation that may arise.
KW  - Angewandte Informatik
KW  - Angewandte Mathematik
KW  - Architektur <Informatik>
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:wim2-20170314-28536
UR  - http://euklid.bauing.uni-weimar.de/ikm2009/paper.html
SN  - 1611-4086
ER  - 
TY  - CHAP
A1  - Stein, Peter
ED  - Gürlebeck, Klaus
ED  - Könke, Carsten
T1  - NURBS-BASED ELEMENTS AS A BASIS FOR INTEGRATING ENGINEERING APPLICATIONS
N2  - Building information modeling offers a huge potential for increasing the productivity and quality of construction planning processes. Despite its promising concept, this approach has not found widespread use. One of the reasons is the insufficient coupling of the structural models with the general building model. Instead, structural engineers usually set up a structural model that is independent from the building model and consists of mechanical models of reduced dimension. An automatic model generation, which would be valuable in case of model revisions is therefore not possible. This can be overcome by a volumetric formulation of the problem. A recent approach employed the p-version of the finite element method to this problem. This method, in conjunction with a volumetric formulation is suited to simulate the structural behaviour of both „thick“ solid bodies and thin-walled structures. However, there remains a notable discretization error in the numerical models. This paper therefore proposes a new approach for overcoming this situation. It sugggests the combination of the Isogeometric analysis together with the volumetric models in order to integrate the structural design into the digital, building model-centered planning process and reduce the discretization error. The concept of the isogeometric analysis consists, roughly, in the application of NURBS functions to represent the geometry and the shape functions of the elements. These functions possess some beneficial properties regarding numerical simulation. Their use, however, leads to some intricacies related to the setup of the stiffness matrix. This paper describes some of these properties.
KW  - Angewandte Informatik
KW  - Angewandte Mathematik
KW  - Architektur <Informatik>
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:wim2-20170314-28944
UR  - http://euklid.bauing.uni-weimar.de/ikm2009/paper.html
SN  - 1611-4086
ER  - 
TY  - CHAP
A1  - Tomaz, Graça Maria
ED  - Gürlebeck, Klaus
ED  - Könke, Carsten
T1  - ON BLOCK MATRICES OF PASCAL TYPE IN CLIFFORD ANALYSIS
N2  - Since the 90-ties the Pascal matrix, its generalizations and applications have been in the focus of a great amount of publications. As it is well known, the Pascal matrix, the symmetric Pascal matrix and other special matrices of Pascal type play an important role in many scientific areas, among them Numerical Analysis, Combinatorics, Number Theory, Probability, Image processing, Sinal processing, Electrical engineering, etc. We present a unified approach to matrix representations of special polynomials in several hypercomplex variables (new Bernoulli, Euler etc. polynomials), extending results of H. Malonek, G.Tomaz: Bernoulli polynomials and Pascal matrices in the context of Clifford Analysis, Discrete Appl. Math. 157(4)(2009) 838-847. The hypercomplex version of a new Pascal matrix with block structure, which resembles the ordinary one for polynomials of one variable will be discussed in detail.
KW  - Angewandte Informatik
KW  - Angewandte Mathematik
KW  - Architektur <Informatik>
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:wim2-20170314-28979
UR  - http://euklid.bauing.uni-weimar.de/ikm2009/paper.html
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  - 
TY  - CHAP
A1  - Simsek, Yilmaz
ED  - Gürlebeck, Klaus
ED  - Lahmer, Tom
ED  - Werner, Frank
T1  - ON INTERPOLATION FUNCTION OF THE BERNSTEIN POLYNOMIALS
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  - The Bernstein polynomials are used for important applications in many branches of Mathematics and the other sciences, for instance, approximation theory, probability theory, statistic theory, num- ber theory, the solution of the di¤erential equations, numerical analysis, constructing Bezier curves, q-calculus, operator theory and applications in computer graphics. The Bernstein polynomials are used to construct Bezier curves. Bezier was an engineer with the Renault car company and set out in the early 1960’s to develop a curve formulation which would lend itself to shape design. Engineers may …nd it most understandable to think of Bezier curves in terms of the center of mass of a set of point masses. Therefore, in this paper, we study on generating functions and functional equations for these polynomials. By applying these functions, we investigate interpolation function and many properties of these polynomials.
KW  - Angewandte Informatik
KW  - Angewandte Mathematik
KW  - Computerunterstütztes Verfahren
Y1  - 2012
U6  - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:gbv:wim2-20170314-27867
UR  - http://euklid.bauing.uni-weimar.de/ikm2012
SN  - 1611-4086
ER  - 
TY  - CHAP
A1  - Nguyen, Manh Hung
A1  - Gürlebeck, Klaus
ED  - Gürlebeck, Klaus
ED  - Lahmer, Tom
ED  - Werner, Frank
T1  - ON M-CONFORMAL MAPPINGS AND GEOMETRIC PROPERTIES
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  - Monogenic functions play a role in quaternion analysis similarly to that of holomorphic functions in complex analysis. A holomorphic function with nonvanishing complex derivative is a conformal mapping. It is well-known that in Rn+1, n ≥ 2 the set of conformal mappings is restricted to the set of Möbius transformations only and that the Möbius transformations are not monogenic. The paper deals with a locally geometric mapping property of a subset of monogenic functions with nonvanishing hypercomplex derivatives (named M-conformal mappings). It is proved that M-conformal mappings orthogonal to all monogenic constants admit a certain change of solid angles and vice versa, that change can characterize such mappings. In addition, we determine planes in which those mappings behave like conformal mappings in the complex plane.
KW  - Angewandte Informatik
KW  - Angewandte Mathematik
KW  - Computerunterstütztes Verfahren
Y1  - 2012
U6  - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:gbv:wim2-20170314-27833
UR  - http://euklid.bauing.uni-weimar.de/ikm2012
SN  - 1611-4086
ER  - 
TY  - CHAP
A1  - Soucek, Vladimir
ED  - Gürlebeck, Klaus
ED  - Könke, Carsten
T1  - ON MASSLESS FIELD EQUATION IN HIGHER DIMENSIONS
N2  - The paper is devoted to a study of properties of homogeneous solutions of massless field equation in higher dimensions. We first treat the case of dimension 4. Here we use the two-component spinor language (developed for purposes of general relativity). We describe how are massless field operators related to a higher spin analogues of the de Rham sequence - the so called Bernstein-Gel'fand-Gel'fand (BGG) complexes - and how are they related to the twisted Dirac operators. Then we study similar question in higher (even) dimensions. Here we have to use more tools from representation theory of the orthogonal group. We recall the definition of massless field equations in higher dimensions and relations to higher dimensional conformal BGG complexes. Then we discuss properties of homogeneous solutions of massless field equation. Using some recent techniques for decomposition of tensor products of irreducible $Spin(m)$-modules, we are able to add some new results on a structure of the spaces of homogenous solutions of massless field equations. In particular, we show that the kernel of the massless field equation in a given homogeneity contains at least on specific irreducible submodule.
KW  - Angewandte Informatik
KW  - Angewandte Mathematik
KW  - Architektur <Informatik>
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:wim2-20170314-28925
UR  - http://euklid.bauing.uni-weimar.de/ikm2009/paper.html
SN  - 1611-4086
ER  - 
TY  - CHAP
A1  - Randrianarivony, Maharavo
ED  - Gürlebeck, Klaus
ED  - Könke, Carsten
T1  - ON THE GENERATION OF HIERARCHICAL MESHES FOR MULTILEVEL FEM AND BEM SOLVERS FROM CAD DATA
N2  - As numerical techniques for solving PDE or integral equations become more sophisticated, treatments of the generation of the geometric inputs should also follow that numerical advancement. This document describes the preparation of CAD data so that they can later be applied to hierarchical BEM or FEM solvers. For the BEM case, the geometric data are described by surfaces which we want to decompose into several curved foursided patches. We show the treatment of untrimmed and trimmed surfaces. In particular, we provide prevention of smooth corners which are bad for diffeomorphism. Additionally, we consider the problem of characterizing whether a Coons map is a diffeomorphism from the unit square onto a planar domain delineated by four given curves. We aim primarily at having not only theoretically correct conditions but also practically efficient methods. As for FEM geometric preparation, we need to decompose a 3D solid into a set of curved tetrahedra. First, we describe some method of decomposition without adding too many Steiner points (additional points not belonging to the initial boundary nodes of the boundary surface). Then, we provide a methodology for efficiently checking whether a tetrahedral transfinite interpolation is regular. That is done by a combination of degree reduction technique and subdivision. Along with the method description, we report also on some interesting practical results from real CAD data.
KW  - Angewandte Informatik
KW  - Angewandte Mathematik
KW  - Architektur <Informatik>
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:wim2-20170314-28795
UR  - http://euklid.bauing.uni-weimar.de/ikm2009/paper.html
SN  - 1611-4086
ER  - 
TY  - CHAP
A1  - Constales, Denis
A1  - Kraußhar, Rolf Sören
ED  - Gürlebeck, Klaus
ED  - Könke, Carsten
T1  - ON THE KLEIN-GORDON EQUATION ON THE 3-TORUS
N2  - In this paper we consider the time independent Klein-Gordon equation on some conformally flat 3-tori with given boundary data. We set up an explicit formula for the fundamental solution. We show that we can represent any solution to the homogeneous Klein-Gordon equation on the torus as finite sum over generalized 3-fold periodic elliptic functions that are in the kernel of the Klein-Gordon operator. Furthermore we prove Cauchy and Green type integral formulas and set up a Teodorescu and Cauchy transform for the toroidal Klein-Gordon operator. These in turn are used to set up explicit formulas for the solution to the inhomogeneous version of the Klein-Gordon equation on the 3-torus.
KW  - Angewandte Informatik
KW  - Angewandte Mathematik
KW  - Architektur <Informatik>
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:wim2-20170314-28639
UR  - http://euklid.bauing.uni-weimar.de/ikm2009/paper.html
SN  - 1611-4086
ER  - 
TY  - CHAP
A1  - Gutierrez S, Andrei
A1  - Ramirez, Marco P.
A1  - Rodriguez, Octavio
A1  - Sanchez N., V.D.
ED  - Gürlebeck, Klaus
ED  - Könke, Carsten
T1  - ON THE SOLUTIONS OF ELECTRICAL IMPEDANCE EQUATION: A PSEUDOANALYTIC APPROACH FOR SEPARABLE-VARIABLES CONDUCTIVITY FUNCTION
N2  - Using a quaternionic reformulation of the electrical impedance equation, we consider a two-dimensional separable-variables conductivity function and, posing two different techniques, we obtain a special class of Vekua equation, whose general solution can be approach by virtue of Taylor series in formal powers, for which is possible to introduce an explicit Bers generating sequence.
KW  - Angewandte Informatik
KW  - Angewandte Mathematik
KW  - Architektur <Informatik>
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:wim2-20170314-28478
UR  - http://euklid.bauing.uni-weimar.de/ikm2009/paper.html
SN  - 1611-4086
ER  - 
TY  - CHAP
A1  - Rodrigues, M. Manuela
ED  - Gürlebeck, Klaus
ED  - Lahmer, Tom
T1  - OPERATIONAL PROPERTIES OF THE LAGUERRE TRANSFORM
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 Laguerre polynomials appear naturally in many branches of pure and applied mathematics and mathematical physics. Debnath introduced the Laguerre transform and derived some of its properties. He also discussed the applications in study of heat conduction and to the oscillations of a very long and heavy chain with variable tension. An explicit boundedness for some class of Laguerre integral transforms will be present.
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:wim2-20170314-28186
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  - Stokmaier, Markus
A1  - Class, A.G.
A1  - Schulenberg, T.
A1  - Lahey Jr., R.T
ED  - Gürlebeck, Klaus
ED  - Lahmer, Tom
T1  - OPTIMISING ACOUSTIC RESONATORS FOR SONOFUSION EXPERIMENTS WITH EVOLUTIONARY ALGORITHMS
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 sizing of simple resonators like guitar strings or laser mirrors is directly connected to the wavelength and represents no complex optimisation problem. This is not the case with liquid-filled acoustic resonators of non-trivial geometries, where several masses and stiffnesses of the structure and the fluid have to fit together. This creates a scenario of many competing and interacting resonances varying in relative strength and frequency when design parameters change. Hence, the resonator design involves a parameter-tuning problem with many local optima. As its solution evolutionary algorithms (EA) coupled to a forced-harmonic FE simulation are presented. A new hybrid EA is proposed and compared to two state-of-theart EAs based on selected test problems. The motivating background is the search for better resonators suitable for sonofusion experiments where extreme states of matter are sought in collapsing cavitation bubbles.
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:wim2-20170314-28202
SN  - 1611-4086
ER  - 
TY  - CHAP
A1  - Vu, Anh Tuan
A1  - Werner, Frank
ED  - Gürlebeck, Klaus
ED  - Könke, Carsten
T1  - OPTIMIZATION OF STEEL STRUCTURES BASED ON DIFFERENTIAL EVOLUTION ALGORITHM
N2  - Steel structural design is an integral part of the building construction process. So far, various methods of design have been applied in practice to satisfy the design requirements. This paper attempts to acquire the Differential Evolution Algorithms in automatization of specific synthesis and rationalization of design process. The capacity of the Differential Evolution Algorithms to deal with continuous and/or discrete optimization of steel structures is also demonstrated. The goal of this study is to propose an optimal design of steel frame structures using built-up I-sections and/or a combination of standard hot-rolled profiles. All optimized steel frame structures in this paper generated optimization solutions better than the original solution designed by the manufacturer. Taking the criteria regarding the quality and efficiency of the practical design into consideration, the produced optimal design with the Differential Evolution Algorithms can completely replace conventional design because of its excellent performance.
KW  - Angewandte Informatik
KW  - Angewandte Mathematik
KW  - Architektur <Informatik>
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:wim2-20170314-29007
UR  - http://euklid.bauing.uni-weimar.de/ikm2009/paper.html
SN  - 1611-4086
ER  -