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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.

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.

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.

In order to make control decisions, Smart Buildings need to collect data from multiple sources and bring it to a central location, such as the Building Management System (BMS). This needs to be done in a timely and automated fashion. Besides data being gathered from different energy using elements, information of occupant behaviour is also important for a building’s requirement analysis. In this paper, the parameter of Occupant Density was considered to help find behaviour of occupants towards a building space. Through this parameter, support for building energy consumption and requirements based on occupant need and demands was provided. The demonstrator presented provides information on the number of people present in a particular building space at any time, giving the space density. Such collections of density data made over a certain period of time represents occupant behaviour towards the building space, giving its usage patterns. Similarly, inventory items were tracked and monitored for moving out or being brought into a particular read zone. For both, people and inventory items, this was achieved using small, low-cost, passive Ultra-High Frequency (UHF) Radio Frequency Identification (RFID) tags. Occupants were given the tags in a form factor of a credit card to be possessed at all times. A central database was built where occupant and inventory information for a particular building space was maintained for monitoring and providing a central data access.

In this paper we present rudiments of a higher dimensional analogue of the Szegö kernel method to compute 3D mappings from elementary domains onto the unit sphere. This is a formal construction which provides us with a good substitution of the classical conformal Riemann mapping. We give explicit numerical examples and discuss a comparison of the results with those obtained alternatively by the Bergman kernel method.

In this note, we describe quite explicitly the Howe duality for Hodge systems and connect it with the well-known facts of harmonic analysis and Clifford analysis. In Section 2, we recall briefly the Fisher decomposition and the Howe duality for harmonic analysis. In Section 3, the well-known fact that Clifford analysis is a real refinement of harmonic analysis is illustrated by the Fisher decomposition and the Howe duality for the space of spinor-valued polynomials in the Euclidean space under the so-called L-action. On the other hand, for Clifford algebra valued polynomials, we can consider another action, called in Clifford analysis the H-action. In the last section, we recall the Fisher decomposition for the H-action obtained recently. As in Clifford analysis the prominent role plays the Dirac equation in this case the basic set of equations is formed by the Hodge system. Moreover, analysis of Hodge systems can be viewed even as a refinement of Clifford analysis. In this note, we describe the Howe duality for the H-action. In particular, in Proposition 1, we recognize the Howe dual partner of the orthogonal group O(m) in this case as the Lie superalgebra sl(2 1). Furthermore, Theorem 2 gives the corresponding multiplicity free decomposition with an explicit description of irreducible pieces.

THE FOURIER-BESSEL TRANSFORM
(2010)

In this paper we devise a new multi-dimensional integral transform within the Clifford analysis setting, the so-called Fourier-Bessel transform. It appears that in the two-dimensional case, it coincides with the Clifford-Fourier and cylindrical Fourier transforms introduced earlier. We show that this new integral transform satisfies operational formulae which are similar to those of the classical tensorial Fourier transform. Moreover the L2-basis elements consisting of generalized Clifford-Hermite functions appear to be eigenfunctions of the Fourier-Bessel transform.

This paper describes the application of interval calculus to calculation of plate deflection, taking in account inevitable and acceptable tolerance of input data (input parameters). The simply supported reinforced concrete plate was taken as an example. The plate was loaded by uniformly distributed loads. Several parameters that influence the plate deflection are given as certain closed intervals. Accordingly, the results are obtained as intervals so it was possible to follow the direct influence of a change of one or more input parameters on output (in our example, deflection) values by using one model and one computing procedure. The described procedure could be applied to any FEM calculation in order to keep calculation tolerances, ISO-tolerances, and production tolerances in close limits (admissible limits). The Wolfram Mathematica has been used as tool for interval calculation.

This paper deals with the modelling and the analysis of masonry vaults. Numerical FEM analyses are performed using LUSAS code. Two vault typologies are analysed (barrel and cross-ribbed vaults) parametrically varying geometrical proportions and constraints. The proposed model and the developed numerical procedure are implemented in a computer analysis. Numerical applications are developed to assess the model effectiveness and the efficiency of the numerical procedure. The main object of the present paper is the development of a computational procedure which allows to define 3D structural behaviour of masonry vaults. For each investigated example, the homogenized limit analysis approach has been employed to predict ultimate load and failure mechanisms. Finally, both a mesh dependence study and a sensitivity analysis are reported. Sensitivity analysis is conducted varying in a wide range mortar tensile strength and mortar friction angle with the aim of investigating the influence of the mechanical properties of joints on collapse load and failure mechanisms. The proposed computer model is validated by a comparison with experimental results available in the literature.

In recent years special hypercomplex Appell polynomials have been introduced by several authors and their main properties have been studied by different methods and with different objectives. Like in the classical theory of Appell polynomials, their generating function is a hypercomplex exponential function. The observation that this generalized exponential function has, for example, a close relationship with Bessel functions confirmed the practical significance of such an approach to special classes of hypercomplex differentiable functions. Its usefulness for combinatorial studies has also been investigated. Moreover, an extension of those ideas led to the construction of complete sets of hypercomplex Appell polynomial sequences. Here we show how this opens the way for a more systematic study of the relation between some classes of Special Functions and Elementary Functions in Hypercomplex Function Theory.

The numerical simulation of microstructure models in 3D requires, due to enormous d.o.f., significant resources of memory as well as parallel computational power. Compared to homogeneous materials, the material hetrogeneity on microscale induced by different material phases demand for adequate computational methods for discretization and solution process of the resulting highly nonlinear problem. To enable an efficient/scalable solution process of the linearized equation systems the heterogeneous FE problem will be described by a FETI-DP (Finite Element Tearing and Interconnecting - Dual Primal) discretization. The fundamental FETI-DP equation can be solved by a number of different approaches. In our approach the FETI-DP problem will be reformulated as Saddle Point system, by eliminating the primal and Lagrangian variables. For the reduced Saddle Point system, only defined by interior and dual variables, special Uzawa algorithms can be adapted for iteratively solving the FETI-DP saddle-point equation system (FETI-DP SPE). A conjugate gradient version of the Uzawa algorithm will be shown as well as some numerical tests regarding to FETI-DP discretization of small examples using the presented solution technique. Furthermore the inversion of the interior-dual Schur complement operator can be approximated using different techniques building an adequate preconditioning matrix and therewith leading to substantial gains in computing time efficiency.

Within the scheduling of construction projects, different, partly conflicting objectives have to be considered. The specification of an efficient construction schedule is a challenging task, which leads to a NP-hard multi-criteria optimization problem. In the past decades, so-called metaheuristics have been developed for scheduling problems to find near-optimal solutions in reasonable time. This paper presents a Simulated Annealing concept to determine near-optimal construction schedules. Simulated Annealing is a well-known metaheuristic optimization approach for solving complex combinatorial problems. To enable dealing with several optimization objectives the Pareto optimization concept is applied. Thus, the optimization result is a set of Pareto-optimal schedules, which can be analyzed for selecting exactly one practicable and reasonable schedule. A flexible constraint-based simulation approach is used to generate possible neighboring solutions very quickly during the optimization process. The essential aspects of the developed Pareto Simulated Annealing concept are presented in detail.

A practical framework for generating cross correlated fields with a specified marginal distribution function, an autocorrelation function and cross correlation coefficients is presented in the paper. The contribution promotes a recent journal paper [1]. The approach relies on well known series expansion methods for simulation of a Gaussian random field. The proposed method requires all cross correlated fields over the domain to share an identical autocorrelation function and the cross correlation structure between each pair of simulated fields to be simply defined by a cross correlation coefficient. Such relations result in specific properties of eigenvectors of covariance matrices of discretized field over the domain. These properties are used to decompose the eigenproblem which must normally be solved in computing the series expansion into two smaller eigenproblems. Such decomposition represents a significant reduction of computational effort. Non-Gaussian components of a multivariate random field are proposed to be simulated via memoryless transformation of underlying Gaussian random fields for which the Nataf model is employed to modify the correlation structure. In this method, the autocorrelation structure of each field is fulfilled exactly while the cross correlation is only approximated. The associated errors can be computed before performing simulations and it is shown that the errors happen especially in the cross correlation between distant points and that they are negligibly small in practical situations.

From passenger’s perspective, punctuality is one of the most important features of tram route operation. We present a stochastic simulation model with special focus on determining important factors of influence. The statistical analysis bases on large samples (sample size is nearly 2000) accumulated from comprehensive measurements on eight tram routes in Cracow. For the simulation, we are not only interested in average values but also in stochastic characteristics like the variance and other properties of the distribution. A realization of trams operations is assumed to be a sequence of running times between successive stops and times spent by tram at the stops divided in passengers alighting and boarding times and times waiting for possibility of departure . The running time depends on the kind of track separation including the priorities in traffic lights, the length of the section and the number of intersections. For every type of section, a linear mixed regression model describes the average running time and its variance as functions of the length of the section and the number of intersections. The regression coefficients are estimated by the iterative re-weighted least square method. Alighting and boarding time mainly depends on type of vehicle, number of passengers alighting and boarding and occupancy of vehicle. For the distribution of the time waiting for possibility of departure suitable distributions like Gamma distribution and Lognormal distribution are fitted.

SIMULATION AND MATHEMATICAL OPTIMIZATION OF THE HYDRATION OF CONCRETE FOR AVOIDING THERMAL CRACKS
(2010)

After mixing of concrete, the hardening starts by an exothermic chemical reaction known as hydration. As the reaction rate depends on the temperature the time in the description of the hydration is replaced by the maturity which is defined as an integral over a certain function depending on the temperature. The temperature distribution is governed by the heat equation with a right hand side depending on the maturity and the temperature itself. We compare of the performance of different time integration schemes of higher order with an automatic time step control. The simulation of the heat distribution is of importance as the development of mechanical properties is driven by the hydration. During this process it is possible that the tensile stresses exceed the tensile strength and cracks occur. The goal is to produce cheap concrete without cracks. Simple crack-criterions use only temperature differences, more involved ones are based on thermal stresses. If the criterion predicts cracks some changes in the input data are needed. This can be interpreted as optimization. The final goal will be to adopt model based optimization (in contrast to simulation based optimization) to the problem of the hydration of young concrete and the avoidance of cracks. The first step is the simulation of the hydration, which we focus in this paper.

In this paper three different formulations of a Bernoulli type free boundary problem are discussed. By analyzing the shape Hessian in case of matching data it is distinguished between well-posed and ill-posed formulations. A nonlinear Ritz-Galerkin method is applied for discretizing the shape optimization problem. In case of well-posedness existence and convergence of the approximate shapes is proven. In combination with a fast boundary element method efficient first and second order shape optimization algorithms are obtained.

In spite of the extensive research in dynamic soil-structure interaction (SSI), there still exist miscon-ceptions concerning the role of SSI in the seismic performance of structures, especially the ones founded on soft soil. This is due to the fact that current analytical SSI models that are used to evaluate the influence of soil on the overall structural behavior are approximate models and may involve creeds and practices that are not always precise. This is especially true in the codified approaches which in-clude substantial approximations to provide simple frameworks for the design. As the direct numerical analysis requires a high computational effort, performing an analysis considering SSI is computationally uneconomical for regular design applications. This paper outlines the set up some milestones for evaluating SSI models. This will be achieved by investigating the different assumptions and involved factors, as well as varying the configurations of R/C moment-resisting frame structures supported by single footings which are subject to seismic excita-tions. It is noted that the scope of this paper is to highlight, rather than fully resolve, the above subject. A rough draft of the proposed approach is presented in this paper, whereas a thorough illustration will be carried out throughout the presentation in the course of the conference.

We investigate aspects of tram-network section reliability, which operates as a part of the model of whole city tram-network reliability. Here, one of the main points of interest is the character of the chronological development of the disturbances (namely the differences between time of departure provided in schedule and real time of departure) on subsequent sections during tram line operation. These developments were observed in comprehensive measurements done in Krakow, during one of the main transportation nodes (Rondo Mogilskie) rebuilding. All taken building activities cause big disturbances in tram lines operation with effects extended to neighboring sections. In a second part, the stochastic character of section running time will be analyzed more detailed. There will be taken into consideration sections with only one beginning stop and also with two or three beginning stops located at different streets at an intersection. Possibility of adding results from sections with two beginning stops to one set will be checked with suitable statistical tests which are used to compare the means of the two samples. Section running time may depend on the value of gap between two following trams and from the value of deviation from schedule. This dependence will be described by a multi regression formula. The main measurements were done in the city center of Krakow in two stages: before and after big changes in tramway infrastructure.

Due to increasing numbers of wind energy converters, the accurate assessment of the lifespan of their structural parts and the entire converter system is becoming more and more paramount. Lifespan-oriented design, inspections and remedial maintenance are challenging because of their complex dynamic behavior. Wind energy converters are subjected to stochastic turbulent wind loading causing corresponding stochastic structural response and vibrations associated with an extreme number of stress cycles (up to 109 according to the rotation of the blades). Currently, wind energy converters are constructed for a service life of about 20 years. However, this estimation is more or less made by rule of thumb and not backed by profound scientific analyses or accurate simulations. By contrast, modern structural health monitoring systems allow an improved identification of deteriorations and, thereupon, to drastically advance the lifespan assessment of wind energy converters. In particular, monitoring systems based on artificial intelligence techniques represent a promising approach towards cost-efficient and reliable real-time monitoring. Therefore, an innovative real-time structural health monitoring concept based on software agents is introduced in this contribution. For a short time, this concept is also turned into a real-world monitoring system developed in a DFG joint research project in the authors’ institute at the Ruhr-University Bochum. In this paper, primarily the agent-based development, implementation and application of the monitoring system is addressed, focusing on the real-time monitoring tasks in the deserved detail.

Quality is one of the most important properties of a product. Providing the optimal quality can reduce costs for rework, scrap, recall or even legal actions while satisfying customers demand for reliability. The aim is to achieve ``built-in'' quality within product development process (PDP). The common approach therefore is the robust design optimization (RDO). It uses stochastic values as constraint and/or objective to obtain a robust and reliable optimal design. In classical approaches the effort required for stochastic analysis multiplies with the complexity of the optimization algorithm. The suggested approach shows that it is possible to reduce this effort enormously by using previously obtained data. Therefore the support point set of an underlying metamodel is filled iteratively during ongoing optimization in regions of interest if this is necessary. In a simple example, it will be shown that this is possible without significant loss of accuracy.

PARAMETER IDENTIFICATION OF MESOSCALE MODELS FROM MACROSCOPIC TESTS USING BAYESIAN NEURAL NETWORKS
(2010)

In this paper, a parameter identification procedure using Bayesian neural networks is proposed. Based on a training set of numerical simulations, where the material parameters are simulated in a predefined range using Latin Hypercube sampling, a Bayesian neural network, which has been extended to describe the noise of multiple outputs using a full covariance matrix, is trained to approximate the inverse relation from the experiment (displacements, forces etc.) to the material parameters. The method offers not only the possibility to determine the parameters itself, but also the accuracy of the estimate and the correlation between these parameters. As a result, a set of experiments can be designed to calibrate a numerical model.

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.

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.

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.

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.

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.

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.

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.

NUMERICAL SIMULATION OF THERMO-HYGRAL ALKALI-SILICA REACTION MODEL IN CONCRETE AT THE MESOSCALE
(2010)

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.

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.

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.

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.

NONZONAL WAVELETS ON S^N
(2010)

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.

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.

In the paper presented, reinforced concrete shells of revolution are analyzed in both meridional and circumferential directions. Taking into account the physical non-linearity of the material, the internal forces and the deflections of the shell as well as the strain distribution at the cross-sections are calculated. The behavior of concrete under compression is described by linear and non-linear stress-strain relations. The description of the behavior of concrete under tension must account for tension stiffening effects. A tri-linear function is used to formulate the material law of reinforcement. The problem cannot be solved analytically due to the physical non-linearity. Thus a numerical solution is formulated by means of the LAGRANGE Principle of the minimum of the total potential energy. The kinematically admissible field of deformation is defined by the displacements u in the meridional and w in the radial direction. These displacements must satisfy the equations of compatibility and the kinematical boundary conditions of the shell. The strains are linearly distributed across the wall thickness. The strain energy depends on the specific of the material behavior. Using integral formulations of the material law [1], the strain energy of each part of the cross-section is defined as a function of the strains at the boundaries of the cross-sections. The shell is discretised in the meridional direction. Various methods of numerical differentiation and numerical integration are applied in order to determine the deformations and the strain energy. The unknown displacements u and w are calculated by a non-restricted extremum problem based on the minimum of the total potential energy. From mathematical point of view, the objective function is a convex function, thus the minimum can be determined without difficulty. The advantage of this formulation is that unlike non-linear methods with path-following algorithms the calculation does not have to account for changing stiffness and load increments. All iterations necessary to find the solution are integrated into the “Solver”. The model presented provides many ways of investigating the influence of various material parameters on the stresses and deformations of the entire shell structure.

Nodal integration of finite elements has been investigated recently. Compared with full integration it shows better convergence when applied to incompressible media, allows easier remeshing and highly reduces the number of material evaluation points thus improving efficiency. Furthermore, understanding it may help to create new integration schemes in meshless methods as well. The new integration technique requires a nodally averaged deformation gradient. For the tetrahedral element it is possible to formulate a nodal strain which passes the patch test. On the downside, it introduces non-physical low energy modes. Most of these "spurious modes" are local deformation maps of neighbouring elements. Present stabilization schemes rely on adding a stabilizing potential to the strain energy. The stabilization is discussed within this article. Its drawbacks are easily identified within numerical experiments: Nonlinear material laws are not well represented. Plastic strains may often be underestimated. Geometrically nonlinear stabilization greatly reduces computational efficiency. The article reinterpretes nodal integration in terms of imposing a nonconforming C0-continuous strain field on the structure. By doing so, the origins of the spurious modes are discussed and two methods are presented that solve this problem. First, a geometric constraint is formulated and solved using a mixed formulation of Hu-Washizu type. This assumption leads to a consistent representation of the strain energy while eliminating spurious modes. The solution is exact, but only of theoretical interest since it produces global support. Second, an integration scheme is presented that approximates the stabilization criterion. The latter leads to a highly efficient scheme. It can even be extended to other finite element types such as hexahedrals. Numerical efficiency, convergence behaviour and stability of the new method is validated using linear tetrahedral and hexahedral elements.

A stress based remodeling approach is used to investigate the sensitivity of the collagen architecture in humane eye tissues on the biomechanical response of the lamina cribrosa with a particular focus on the stress environment of the nerve fibers. This approach is based on a multi-level biomechanical framework, where the biomechanical properties of eye tissues are derived from a single crimped fibril at the micro-scale via the collagen network of distributed fibrils at the meso-scale to the incompressible and anisotropic soft tissue at the macro-scale. Biomechanically induced remodeling of the collagen network is captured on the meso-scale by allowing for a continuous reorientation of collagen fibrils. To investigate the multi-scale phenomena related to glaucomatous neuropathy a generalized computational homogenization scheme is applied to a coupled two-scale analysis of the human eye considering a numerical macro- and meso-scale model of the lamina cribrosa.

For many applications, nonuniformly distributed functional data is given which lead to large–scale scattered data problems. We wish to represent the data in terms of a sparse representation with a minimal amount of degrees of freedom. For this, an adaptive scheme which operates in a coarse-to-fine fashion using a multiscale basis is proposed. Specifically, we investigate hierarchical bases using B-splines and spline-(pre)wavelets. At each stage a leastsquares approximation of the data is computed. We take into account different requests arising in large-scale scattered data fitting: we discuss the fast iterative solution of the least square systems, regularization of the data, and the treatment of outliers. A particular application concerns the approximate continuation of harmonic functions, an issue arising in geodesy.

MULTI-SITE CONSTRUCTION PROJECT SCHEDULING CONSIDERING RESOURCE MOVING TIME IN DEVELOPING COUNTRIES
(2010)

Under the booming construction demands in developing countries, particularly in Vietnam situation, construction contractors often perform multiple concurrent projects in different places. In construction project scheduling processes, the existing scheduling methods often assume the resource moving time between activities/projects to be negligible. When multiple projects are deployed in different places and far from each other, this assumption has many shortcomings for properly modelling the real-world constraints. Especially, with respect to developing countries such as the Vietnam which contains transportation systems that are still in backward and low technical standards. This paper proposes a new algorithm named Multi-Site Construction Project Scheduling - MCOPS. The objective of this algorithm is to solve the problem of minimising multi-site construction project duration under limited available conditions of renewable resources (labour, machines and equipment) combining with the moving time of required resource among activities/projects. Additionally, in order to mitigate the impact of resource moving time into the multi-site project duration, this paper proposed a new priority rule: Minimum Resource Moving Time (MinRMT). The MinRMT is applied to rank the finished activities according to a priority order, to support the released resources to the scheduling activities. In order to investigate the impact of the resource moving time among activities during the scheduling process, computational experimentation was implemented. The results of the MCOPS-based computational experiments showed that, the resource moving time among projects has significantly impacted the multi-site project durations and this amount of time can not be ignored in the multi-site project scheduling process. Besides, the efficient application of the MinRMT is also demonstrated through the achieved results of the computational experiment in this paper. Though the efforts in this paper are based on the Vietnamese construction conditions, the proposed method can be usefully applied in other developing countries which have similar construction conditions.

Planning and construction processes are characterized by the peculiarity that they need to be designed individually for each project. It is necessary to set up an individual schedule for each project. As a basis for a new project, schedules from already finished projects are used, but adaptions are always necessary. In practice, scheduling tools only document a process. Schedules cover a set of activities, their duration and a set of interdependencies between activities. The design of a process is up to the user. It is not necessary to specify each interdependency, and completeness and correctness need to be checked manually. No methodologies are available to guarantee properties such as correctness or completeness. The considerations presented in the paper are based on an approach where a planning and a construction process including the interdependencies between planning and construction activities are regarded as a result. Selected information need to be specified by a user, and a proposal for an order of planning and construction activities is computed. As a consequence, process properties such as correctness and completeness can be guaranteed with respect to user input. Especially in Germany, clients are allowed to modify their requirements at any time. This leads to modifications in the planning and construction processes. This paper covers a mathematical formulation for this problem based on set theory. A complex structure is set up covering objects and relations; and operations are defined that guarantee consistency in the underlying and versioned process description. The presented considerations are based on previous work. This paper can be regarded as the next step in a series of previous work describing how a suitable concept for handling, planning and construction processes in civil engineering can be formed.

Several results concerning the distribution of the headway of busses in the flow behind a traffic signal are presented. In the main focus of interest is the description of analytical models, which are verified by the results of Monte-Carlo-Methods. The advantage of analytical models (verified, but not derived by simulation methods) is their flexibility with respect to possible generalizations. For instance, several random distributions of the flow incoming to the traffic signal can be compared. The attention will be directed at the question, how the primary headway H (analyzed in front of the traffic signal) is mapped to the headway H’ analyzed behind of the traffic signal and how the random distribution of H is mapped to that of H’. For the traffic flow in front of the traffic signal several models will be discussed. The first case considers the situation, that busses operate on a common lane with the individual motor car traffic and the traffic flow is saturated. In the second situation, busses operate on a separated bus lane. Moreover, a mixed situation is discussed to model as close to reality as possible.

The application of partly decoupled approach by means of continuum mechanics facilitates the calculation of structural responses due to welding. The numerical results demonstrate the ability of a qualitative prediction of welded connections. As it is intended to integrate the local effects of a joint in structural analysis of steel constructions, it is necessary to meet higher approaches towards quality. The wide array of material parameters are presented, which are affecting the thermal, metallurgical and mechanical behavior, and which have to be identified. For that purpose further investigations are necessary to analyze the sensitivity of the models towards different material properties. The experimental determination of every material parameter is not possible due to the extraordinary laborious efforts needed. Besides that, experimentally identified parameters can be applied only for the tested steel quality for measured temperature-time regimes. For that reason alternative approaches for identification of material parameters, such as optimization strategies, have to be applied. After a definition of material parameters a quantitative prediction of welded connections will also be possible. Numerical results show the effect of phase transformation, activated by welding process, on residual stress state. As these phenomena occur in local areas in the range of crystal and grain sizes, the description of microscopic phenomena and their propagation on a macroscopic level due to approaches of homogenization might be expedient. Nevertheless, one should bear in mind, the increasing number of material parameters as well as the complexity of their experimental determination. Thus the microscopic approach should always be investigated under the scope of ability and efficiency of a required prediction. Under certain circumstances a step backwards, adopting a phenomenological approach, also can be beneficial.

There are many different approaches to simulate the mechanical behavior of RC−Frames with masonry infills. In this paper, selected modeling techniques for masonry infills and reinforced concrete frame members will be discussed − stressing the attention on the damaging effects of the individual members and the entire system under quasi−static horizontal loading. The effect of the infill walls on the surrounding frame members is studied using equivalent strut elements. The implemented model consider in−plane failure modes for the infills, such as bed joint sliding and corner crushing. These frame member models differ with respect to their stress state. Finally, examples are provided and compared with experimental data from a real size test executed on a three story RC−Frame with and without infills. The quality of the model is evaluated on the basis of load−displacement relationships as well as damage progression.

The evident advances of the computational power of the digital computers enable the modeling of the total system of structures. Such modeling demands compatible representations of the couplings of different structural subsystems. Therefore, models of dynamic interaction between the vehicle and the bridge and models of a bridge bearing, a coupling element between the bridge's superstructure and substructure, are of interest and discussed within this paper. The vehicle-bridge interaction may be described as a function connecting two sets of behavior. In this case, the coupling is embodied by mutual parameters that affect both systems, such as the frequency content of the bridge and the vehicle. Whereas the bridge bearings are elements used specifically to couple, in such elements the deformation and the transferred loads are used in characterizing the coupling The nature of these couplings and their influence on the bridge response is different. However, the need to assess the amount of dynamic response transferred by or within these couplings is a common argument.

MICROPLANE MODEL WITH INITIAL AND DAMAGE-INDUCED ANISOTROPY APPLIED TO TEXTILE-REINFORCED CONCRETE
(2010)

The presented material model reproduces the anisotropic characteristics of textile reinforced concrete in a smeared manner. This includes both the initial anisotropy introduced by the textile reinforcement, as well as the anisotropic damage evolution reflecting fine patterns of crack bridges. The model is based on the microplane approach. The direction-dependent representation of the material structure into oriented microplanes provides a flexible way to introduce the initial anisotropy. The microplanes oriented in a yarn direction are associated with modified damage laws that reflect the tension-stiffening effect due to the multiple cracking of the matrix along the yarn.

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.

An introduction is given to Clifford Analysis over pseudo-Euclidean space of arbitrary signature, called for short Ultrahyperbolic Clifford Analysis (UCA). UCA is regarded as a function theory of Clifford-valued functions, satisfying a first order partial differential equation involving a vector-valued differential operator, called a Dirac operator. The formulation of UCA presented here pays special attention to its geometrical setting. This permits to identify tensors which qualify as geometrically invariant Dirac operators and to take a position on the naturalness of contravariant and covariant versions of such a theory. In addition, a formal method is described to construct the general solution to the aforementioned equation in the context of covariant UCA.

From 7 till 9 July 2009, the 18th International Conference on the Applications of Computer Science and Mathematics in Architecture and Civil Engineering is going to take place at the Bauhaus University Weimar. Architects, computer scientists, mathematicians, and engineers from all over the world will meet in Weimar for an interdisciplinary exchange of experiences to report on their results in research, development and practice and to discuss. The conference offers several topics. Plenary lectures and thematic sessions will take place under the chairmanship of the mentioned colleagues.
We invite architects, civil engineers, designers, computer scientists, engineers, mathematicians, planners, project managers, and software developers from business, science and research to participate in the conference.

Euclidean Clifford analysis is a higher dimensional function theory offering a refinement of classical harmonic analysis. The theory is centered around the concept of monogenic functions, i.e. null solutions of a first order vector valued rotation invariant differential operator called the Dirac operator, which factorizes the Laplacian. More recently, Hermitean Clifford analysis has emerged as a new and successful branch of Clifford analysis, offering yet a refinement of the Euclidean case; it focusses on the simultaneous null solutions, called Hermitean (or h-) monogenic functions, of two Hermitean Dirac operators which are invariant under the action of the unitary group. In Euclidean Clifford analysis, the Clifford-Cauchy integral formula has proven to be a corner stone of the function theory, as is the case for the traditional Cauchy formula for holomorphic functions in the complex plane. Previously, a Hermitean Clifford-Cauchy integral formula has been established by means of a matrix approach. This formula reduces to the traditional Martinelli-Bochner formula for holomorphic functions of several complex variables when taking functions with values in an appropriate part of complex spinor space. This means that the theory of Hermitean monogenic functions should encompass also other results of several variable complex analysis as special cases. At present we will elaborate further on the obtained results and refine them, considering fundamental solutions, Borel-Pompeiu representations and the Teoderescu inversion, each of them being developed at different levels, including the global level, handling vector variables, vector differential operators and the Clifford geometric product as well as the blade level were variables and differential operators act by means of the dot and wedge products. A rich world of results reveals itself, indeed including well-known formulae from the theory of several complex variables.