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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.
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.
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.
Reducing energy consumption is one of the major challenges for present day and will continue for future generations. The emerging EU directives relating to energy (EU EPBD and the EU Directive on Emissions Trading) now place demands on building owners to rate the energy performance of their buildings for efficient energy management. Moreover European Legislation (Directive 2006/32/EC) requires Facility Managers to reduce building energy consumption and operational costs. Currently sophisticated building services systems are available integrating off-the-shelf building management components. However this ad-hoc combination presents many difficulties to building owners in the management and upgrade of these systems. This paper addresses the need for integration concepts, holistic monitoring and analysis methodologies, life-cycle oriented decision support and sophisticated control strategies through the seamless integration of people, ICT-devices and computational resources via introducing the newly developed integrated system architecture. The first concept was applied to a residential building and the results were elaborated to improve current building conditions.
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.
We give a sufficient and a necessary condition for an analytic function "f" on the unit disk "D" with Hadamard gap to belong to a class of weighted logarithmic Bloch space as well as to the corresponding little weighted logarithmic Bloch space under some conditions posed on the defined weight function. Also, we study the relations between the class of weighted logarithmic Bloch functions and some other classes of analytic functions by the help of analytic functions in the Hadamard gap class.
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.
The present article proposes an alternative way to compute the torsional stiffness based on three-dimensional continuum mechanics instead of applying a specific theory of torsion. A thin, representative beam slice is discretized by solid finite elements. Adequate boundary conditions and coupling conditions are integrated into the numerical model to obtain a proper answer on the torsion behaviour, thus on shear center, shear stress and torsional stiffness. This finite element approach only includes general assumptions of beam torsion which are independent of cross-section geometry. These assumptions essentially are: no in-plane deformation, constant torsion and free warping. Thus it is possible to achieve numerical solutions of high accuracy for arbitrary cross-sections. Due to the direct link to three-dimensional continuum mechanics, it is possible to extend the range of torsion analysis to sections which are composed of different materials or even to heterogeneous beams on a high scale of resolution. A brief study follows to validate the implementation and results are compared to analytical solutions.
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.