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We present recent developments of adaptive wavelet solvers for elliptic eigenvalue problems. We describe the underlying abstract iteration scheme of the preconditioned perturbed iteration. We apply the iteration to a simple model problem in order to identify the main ideas which a numerical realization of the abstract scheme is based upon. This indicates how these concepts carry over to wavelet discretizations. Finally we present numerical results for the Poisson eigenvalue problem on an L-shaped domain.

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.

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.

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.

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.

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.

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.

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.

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.

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.

Information technology plays a key role in the everyday operation of buildings and campuses. Many proprietary technologies and methodologies can assist in effective Building Performance Monitoring (BPM) and efficient managing of building resources. The integration of related tools like energy simulator packages, facility, energy and building management systems, and enterprise resource planning systems is of benefit to BPM. However, the complexity to integrating such domain specific systems prevents their common usage. Service Oriented Architecture (SOA) has been deployed successfully in many large multinational companies to create integrated and flexible software systems, but so far this methodology has not been applied broadly to the field of BPM. This paper envisions that SOA provides an effective integration framework for BPM. Service oriented architecture for the ITOBO framework for sustainable and optimised building operation is proposed and an implementation for a building performance monitoring system is introduced.

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.

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.

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.

In order to model and simulate collapses of large scale complex structures, a user-friendly and high performance software system is essential. Because a large number of simulation experiments have to be performed, therefore, next to an appropriate simulation model and high performance computing, efficient interactive control and visualization capabilities of model parameters and simulation results are crucial. To this respect, this contribution is concerned with advancements of the software system CADCE (Computer Aided Demolition using Controlled Explosives) that is extended under particular consideration of computational steering concepts. Thereby, focus is placed on problems and solutions for the collapse simulation of real world large scale complex structures. The simulation model applied is based on a multilevel approach embedding finite element models on a local as well as a near field length scale, and multibody models on a global scale. Within the global level simulation, relevant effects of the local and the near field scale, such as fracture and failure processes of the reinforced concrete parts, are approximated by means of tailor-made multibody subsystems. These subsystems employ force elements representing nonlinear material characteristics in terms of force/displacement relationships that, in advance, are determined by finite element analysis. In particular, enhancements concerning the efficiency of the multibody model and improvements of the user interaction are presented that are crucial for the capability of the computational steering. Some scenarios of collapse simulations of real world large scale structures demonstrate the implementation of the above mentioned approaches within the computational steering.

CRITICAL STRESS ASSESSMENT IN ANGLE TO GUSSET PLATE BOLTED CONNECTION BY SIMPLIFIED FEM MODELLING
(2010)

Simplified modelling of friction grip bolted connections of steel member – to – gusset plate is often applied in engineering practise. The paper deals with the simplification of pre-tensioned bolt model and simplification of load transfer within connection. Influence on normal strain (and thus stress) distribution at critical cross-section is investigated. Laboratory testing of single-angle or double-angle members – to – gusset plates bolted connections were taken as basis for numerical analysis. FE models were created using 1D and 2D elements. Angles and gusset plates were modelled with shell elements. Two methods of modelling of friction grip bolting were considered: bolt-regarding approach with 1D element systems modelling bolts and two variants of bolt-disregarding approach with special constraints over some part of member and gusset plate surfaces in contact: a) constraints over whole area of contact, b) constraints over the area around each bolt shank (“partially tied”). Modelling of friction grip bolted connections using simplified bolt modelling may be effective, especially in the case of analysis concerning elastic range only. In such a case disregarding bolts and replacing them with “partially tied” modelling seems to be more attractive. It is less time-consuming and provides results of similar accuracy in comparison to analysis utilizing simplified bolt modelling.

The uncertainty existing in the construction industry is bigger than in other industries. Consequently, most construction projects do not go totally as planned. The project management plan needs therefore to be adapted repeatedly within the project lifecycle to suit the actual project conditions. Generally, the risks of change in the project management plan are difficult to be identified in advance, especially if these risks are caused by unexpected events such as human errors or changes in the client preferences. The knowledge acquired from different resources is essential to identify the probable deviations as well as to find proper solutions to the faced change risks. Hence, it is necessary to have a knowledge base that contains known solutions for the common exceptional cases that may cause changes in each construction domain. The ongoing research work presented in this paper uses the process modeling technique of Event-driven Process Chains to describe different patterns of structure changes in the schedule networks. This results in several so called “change templates”. Under each template different types of change risk/ response pairs can be categorized and stored in a knowledge base. This knowledge base is described as an ontology model populated with reference construction process data. The implementation of the developed approach can be seen as an iterative scheduling cycle that will be repeated within the project lifecycle as new change risks surface. This can help to check the availability of ready solutions in the knowledge base for the situation at hand. Moreover, if the solution is adopted, CPSP, “Change Project Schedule Plan „a prototype developed for the purpose of this research work, will be used to make the needed structure changes of the schedule network automatically based on the change template. What-If scenarios can be implemented using the CPSP prototype in the planning phase to study the effect of specific situations without endangering the success of the project objectives. Hence, better designed and more maintainable project schedules can be achieved.

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.

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.

The main aim of the research project in progress is to develop virtual models as tools to support decision-making in the planning of construction maintenance. The virtual models gives the capacity to allow them to transmit, visually and interactively, information related to the physical behaviour of materials, components of given infrastructures, defined as a function of the time variable. The interactive application allows decisions to be made on conception options in the definition of plans for maintenance, conservation or rehabilitation. The first virtual prototype that is now in progress concerns just lamps. It allows the examination of the physical model, visualizing, for each element modelled in 3D and linked to a database, the corresponding technical information concerned with the wear and tear aspects of the material, calculated for that period of time. In addition, the analysis of solutions for repair work or substitution and inherent cost are predicted, the results being obtained interactively and visualized in the virtual environment itself. The aim is that the virtual model should be able to be applied directly over the 3D models of new constructions, in situations of rehabilitation. The practical usage of these models is directed, then, towards supporting decision-making in the conception phase and the planning of maintenance. In further work other components will be analysed and incorporated into the virtual system.

The changed global security situation in the last eight years has shown the importance of emergency management plans in public buildings. Therefore, the use of computer simulators for surveying fire safety design and evacuation process is increasing. The aim of these simulators is to have more realistic evacuation simulations. The challenge is, firstly, to realize the virtual simulation environment based on geometrical and material boundary conditions, secondly, to considerate the mutual interaction effects between different parameters and, finally, to have a realistic visualization of the simulated results. In order to carry out this task, an especial new software method on a BIM-platform has to be developed which can integrate all required simulations and will be able to have an immersive output BIM ISEE (Immersive Safety Engineering Environment). The new BIM-ISEE will integrate the Fire Dynamics Simulator (FDS) for fire and evacuation simulation in the Autodesk Revit which is a BIM-platform and will represent the simulation results in the immersive virtual environment at the institute (CES-Lab). With BIM-ISEE the fire safety engineer will be able to obtain more realistic visualizations in the immersive environment, to modify his concept more effectively, to evaluate the simulation results more accurately and to visualize the various simulation results. It can also give the rescue staff the opportunity to perform and evaluate emergency evacuation trainings.

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.

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.

By the use of numerical methods and the rapid development of computer technology in the recent years, a large variety, complexity, refinement and capability of partial models have been achieved. This can be noticed in the evaluation of the reliability of structures, e.g. the increased use of spatial structural systems. For the different fields of civil engineering, well developed partial models already exist. Because these partial models are most often used separately, the general view is not entirely illustrated. Until now, there has been no common methodology for evaluating the efficiency of models; the trust in the prediction of a special engineering model has generally relied on the engineer’s experience. In this paper the basics of evaluation of simple models and coupled partial models of frame structures will be discussed using sustainable numerical methods. Furthermore, quality classes (levels) of design tasks will be defined based on their practical relevance. In addition, analysis methods will be systemized. After analysis of different published assessment methods, it may be noted, that the Efficiency Indicator Method (EWM) is most suitable for the observed evaluation problem. Therefore, the EWM was modified to the Model Efficiency Analysis (MEA) for the purpose of a holistic evaluation. The criteria are characterized by two groups, benefit and expenditure, and it is possible by calculating the quotient (benefit/expenditure) to make a statement about the efficiency of the observed models. Presently, the expenditure value is not a subject of investigation, and so the model efficiency is calculated only by the benefit value. This paper also contains the associated criteria catalog, different normalization methods, as well as weighting possibilities.

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.

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.

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.

Nonlinear analyses are characterised by approximations of the fundamental equations in different quality. Starting with a general description of nonlinear finite element formulation the fundamental equations are derived for plane truss elements. Special emphasis is placed on the determination of internal and external system energy as well as influence of different quality approaches for the displacement-strain relationship on solution quality. To simplify the solution procedure the nonlinear function describing the kinematics is expanded into a Taylor series and truncated after the n-th series term. The different kinematics influence speed of convergence as well as exactness of solution. On a simple truss structure this influence is shown. To assess the quality of different formulations concerning the nonlinear kinematic equation three approaches are discussed. First the overall internal and external energy is compared for different kinematical models. In a second step the energy content related to single terms describing displacement-strain relationship is investigated and used for quality control following two different paths. Based on single ε-terms an adaptive scheme is used to change the kinematical model depending on increasing nonlinearity of the structure. The solution quality has turned out satisfactory compared to the exact result. More detailed investigations are necessary to find criteria for the threshold values for the iterative process as well as for decision on number and step size of incremental load steps.

A four-node quadrilateral shell element with smoothed membrane-bending based on Mindlin-Reissner theory is proposed. The element is a combination of a plate bending and membrane element. It is based on mixed interpolation where the bending and membrane stiffness matrices are calculated on the boundaries of the smoothing cells while the shear terms are approximated by independent interpolation functions in natural coordinates. The proposed element is robust, computationally inexpensive and free of locking. Since the integration is done on the element boundaries for the bending and membrane terms, the element is more accurate than the MITC4 element for distorted meshes. This will be demonstrated for several numerical examples.

Isogeometric finite element analysis has become a powerful alternative to standard finite elements due to their flexibility in handling complex geometries. One major drawback of NURBS based isogeometric finite elements is their less effectiveness of local refinement. In this study, we present an alternative to NURBS based isogeometric finite elements that allow for local refinement. The idea is based on polynomial splines and exploits the flexibility of T-meshes for local refinement. The shape functions satisfy important properties such as non-negativity, local support and partition of unity. We will demonstrate the efficiency of the proposed method by two numerical examples.

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.

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.

FREE VIBRATION FREQUENCIES OF THE CRACKED REINFORCED CONCRETE BEAMS - METHODS OF CALCULATIONS
(2010)

The paper presents method of calculation of natural frequencies of the cracked reinforced concrete beams including discreet model of crack. The described method is based on the stiff finite elements method. It was modified in such a way as to take into account local discontinuities (ie. cracks). In addition, some theoretical studies as well as experimental tests of concrete mechanics based on discrete crack model were taken into consideration. The calculations were performed using the author’s own numerical algorithm. Moreover, other calculation methods of dynamic reinforced concrete beams presented in standards and guidelines are discussed. Calculations performed by using different methods are compared with the results obtained in experimental tests.

ESTIMATING UNCERTAINTIES FROM INACCURATE MEASUREMENT DATA USING MAXIMUM ENTROPY DISTRIBUTIONS
(2010)

Modern engineering design often considers uncertainties in geometrical and material parameters and in the loading conditions. Based on initial assumptions on the stochastic properties as mean values, standard deviations and the distribution functions of these uncertain parameters a probabilistic analysis is carried out. In many application fields probabilities of the exceedance of failure criteria are computed. The out-coming failure probability is strongly dependent on the initial assumptions on the random variable properties. Measurements are always more or less inaccurate data due to varying environmental conditions during the measurement procedure. Furthermore the estimation of stochastic properties from a limited number of realisation also causes uncertainties in these quantities. Thus the assumption of exactly known stochastic properties by neglecting these uncertainties may not lead to very useful probabilistic measures in a design process. In this paper we assume the stochastic properties of a random variable as uncertain quantities caused by so-called epistemic uncertainties. Instead of predefined distribution types we use the maximum entropy distribution which enables the description of a wide range of distribution functions based on the first four stochastic moments. These moments are taken again as random variables to model the epistemic scatter in the stochastic assumptions. The main point of this paper is the discussion on the estimation of these uncertain stochastic properties based on inaccurate measurements. We investigate the bootstrap algorithm for its applicability to quantify the uncertainties in the stochastic properties considering imprecise measurement data. Based on the obtained estimates we apply standard stochastic analysis on a simple example to demonstrate the difference and the necessity of the proposed approach.

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.

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.

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.

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.

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.

In this paper we present an inverse method which is capable of identifying system components in a hydro-mechanically coupled system, i.e. for fluid flow in porous media. As an example we regard water dams that were constructed more than hundred years ago but which are still in use. Over the time ageing processes have changed the condition of these dams. Within the dams fissures might have grown. The proposed method is designed to locate these fissures out of combined mechanical and hydraulic measurements. In a numerical example the fissures or damaged zones are described by a smeared crack model. The task is now to identify simultaneously the spatial distribution of Young’s modulus and the hydraulic permeability due to the fact, that in regions where damages are present, the mechanical stiffness of the system is reduced and the permeability increased. The inversion is shown to be an ill-posed problem. As a consequence regularizing methods have to be applied, where the nonlinear Landweber method (a gradient type method combined with a discrepancy principle) has proven to be an efficient choice.