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Civil engineers take advantage of models to design reliable structures. In order to fulfill the design goal with a certain amount of confidence, the utilized models should be able to predict the probable structural behavior under the expected loading schemes. Therefore, a major challenge is to find models which provide less uncertain and more robust responses. The problem gets even twofold when the model to be studied is a global model comprised of different interacting partial models. This study aims at model quality evaluation of global models with a focus on frame-wall systems as the case study. The paper, presents the results of the first step taken toward accomplishing this goal. To start the model quality evaluation of the global frame-wall system, the main element (i.e. the wall) was studied through nonlinear static and dynamic analysis using two different modeling approaches. The two selected models included the fiber section model and the Multiple-Vertical-Line-Element-Model (MVLEM). The influence of the wall aspect ratio (H=L) and the axial load on the response of the models was studied. The results from nonlinear static and dynamic analysis of both models are presented and compared. The models resulted in quite different responses in the range of low aspect ratio walls under large axial loads due to different contribution of the shear deformations to the top displacement. In the studied cases, the results implied that careful attention should be paid to the model quality evaluation of the wall models specifically when they are supposed to be coupled to other partial models such as a moment frame or a soil-footing substructure which their response is sensitive to shear deformations. In this case, even a high quality wall model would not result in a high quality coupled system since it fails to interact properly with the rest of the system.
The aim of our contribution is to clarify the relation between totally regular variables and Appell sequences of hypercomplex holomorphic polynomials (sometimes simply called monogenic power-like functions) in Hypercomplex Function Theory. After their introduction in 2006 by two of the authors of this note on the occasion of the 17th IKM, the latter have been subject of investigations by different authors with different methods and in various contexts. The former concept, introduced by R. Delanghe in 1970 and later also studied by K. Gürlebeck in 1982 for the case of quaternions, has some obvious relationship with the latter, since it describes a set of linear hypercomplex holomorphic functions all power of which are also hypercomplex holomorphic. Due to the non-commutative nature of the underlying Clifford algebra, being totally regular variables or Appell sequences are not trivial properties as it is for the integer powers of the complex variable z=x+ iy. Simple examples show also, that not every totally regular variable and its powers form an Appell sequence and vice versa. Under some very natural normalization condition the set of all para-vector valued totally regular variables which are also Appell sequences will completely be characterized. In some sense the result can also be considered as an answer to a remark of K. Habetha in chapter 16: Function theory in algebras of the collection Complex analysis. Methods, trends, and applications, Akademie-Verlag Berlin, (Eds. E. Lanckau and W. Tutschke) 225-237 (1983) on the use of exact copies of several complex variables for the power series representation of any hypercomplex holomorphic function.
This paper presents a robust model updating strategy for system identification of wind turbines. To control the updating parameters and to avoid ill-conditioning, the global sensitivity analysis using the elementary effects method is conducted. The formulation of the objective function is based on M¨uller-Slany’s strategy for multi-criteria functions. As a simulationbased optimization, a simulation adapter is developed to interface the simulation software ANSYS and the locally developed optimization software MOPACK. Model updating is firstly tested on the beam model of the rotor blade. The defect between the numerical model and the reference has been markedly reduced by the process of model updating. The effect of model updating becomes more pronounced in the comparison of the measured and the numerical properties of the wind turbine model. The deviations of the frequencies of the updated model are rather small. The complete comparison including the free vibration modes by the modal assurance criteria shows the excellent coincidence of the modal parameters of the updated model with the ones from the measurements. By successful implementation of the model validation via model updating, the applicability and effectiveness of the solution concept has been demonstrated.
This paper is focused on the first numerical tests for coupling between analytical solution and finite element method on the example of one problem of fracture mechanics. The calculations were done according to ideas proposed in [1]. The analytical solutions are constructed by using an orthogonal basis of holomorphic and anti-holomorphic functions. For coupling with finite element method the special elements are constructed by using the trigonometric interpolation theorem.
It is well known that complex quaternion analysis plays an important role in the study of higher order boundary value problems of mathematical physics. Following the ideas given for real quaternion analysis, the paper deals with certain orthogonal decompositions of the complex quaternion Hilbert space into its subspaces of null solutions of Dirac type operator with an arbitrary complex potential. We then apply them to consider related boundary value problems, and to prove the existence and uniqueness as well as the explicit representation formulae of the underlying solutions.
Many structures in different engineering applications suffer from cracking. In order to make reliable prognosis about the serviceability of those structures it is of utmost importance to identify cracks as precisely as possible by non-destructive testing. A novel approach (XIGA), which combines the Isogeometric Analysis (IGA) and the Extended Finite Element Method (XFEM) is used for the forward problem, namely the analysis of a cracked material, see [1]. Applying the NURBS (Non-Uniform Rational B-Spline) based approach from IGA together with the XFEM allows to describe effectively arbitrarily shaped cracks and avoids the necessity of remeshing during the crack identification problem. We want to exploit these advantages for the inverse problem of detecting existing cracks by non-destructive testing, see e.g. [2]. The quality of the reconstructed cracks however depends on two major issues, namely the quality of the measured data (measurement error) and the discretization of the crack model. The first one will be taken into account by applying regularizing methods with a posteriori stopping criteria. The second one is critical in the sense that too few degrees of freedom, i.e. the number of control points of the NURBS, do not allow for a precise description of the crack. An increased number of control points, however, increases the number of unknowns in the inverse analysis and intensifies the ill-posedness. The trade-off between accuracy and stability is aimed to be found by applying an inverse multilevel algorithm [3, 4] where the identification is started with short knot vectors which successively will be enlarged during the identification process.
THE INFLUENCE OF THE LOCAL CONCAVITY ON THE FUNCTIONING OF BEARING SHELL OF HIGH-RISE CONSTRUCTION
(2012)
Areas with various defects and damages, which reduce carrying capacity, were examined in a study of metal chimneys. In this work, the influence of the local dimples on the function of metal chimneys was considered. Modeling tasks were completed in the software packages LIRA and ANSYS. Parameters were identified, which characterize the local dimples, and a numerical study of the influence of local dimples on the stress-strain state of shells of metal chimneys was conducted. A distribution field of circular and meridional tension was analyzed in a researched area. Zones of influence of dimples on the bearing cover of metal chimneys were investigated. The bearing capacities of high-rise structures with various dimple geometries and various cover parameters were determined with respect to specified areas of the trunk. Dependent relationships are represented graphically for the decrease in bearing capacity of a cover with respect to dimples. Diameter and thickness of covers of metal chimneys were constructed according to the resulting data.
The aim of this paper we discuss explicit series constructions for the fundamental solution of the Helmholtz operator on some important examples non-orientable conformally at manifolds. In the context of this paper we focus on higher dimensional generalizations of the Klein bottle which in turn generalize higher dimensional Möbius strips that we discussed in preceding works. We discuss some basic properties of pinor valued solutions to the Helmholtz equation on these manifolds.
The process of analysis and design in structural engineering requires the consideration of different partial models, for example loading, structural materials, structural elements, and analysis types. The various partial models are combined by coupling several of their components. Due to the large number of available partial models describing similar phenomena, many different model combinations are possible to simulate the same aspects of a structure. The challenging task of an engineer is to select a model combination that ensures a sufficient, reliable prognosis. In order to achieve this reliable prognosis of the overall structural behavior, a high individual quality of the partial models and an adequate coupling of the partial models is required. Several methodologies have been proposed to evaluate the quality of partial models for their intended application, but a detailed study of the coupling quality is still lacking. This paper proposes a new approach to assess the coupling quality of partial models in a quantitative manner. The approach is based on the consistency of the coupled data and applies for uni- and bidirectional coupled partial models. Furthermore, the influence of the coupling quality on the output quantities of the partial models is considered. The functionality of the algorithm and the effect of the coupling quality are demonstrated using an example of coupled partial models in structural engineering.
Bridge vibration due to traffic loading has been subject of extensive research in the last decades. Such studies are concerned with deriving solutions for the bridge-vehicle interaction (BVI) and analyzing the dynamic responses considering randomness of the coupled model’s (BVI) input parameters and randomness of road unevenness. This study goes further to examine the effects of such randomness of input parameters and processes on the variance of dynamic responses in quantitative measures. The input parameters examined in the sensitivity analysis are, stiffness and damping of vehicle’s suspension system, axle spacing, and stiffness and damping of bridge. This study also examines the effects of the initial excitation of a vehicle on the influences of the considered input parameters. Variance based sensitivity analysis is often applied to deterministic models. However, the models for the dynamic problem is a stochastic one due to the simulations of the random processes. Thus, a setting using a joint meta-model; one for the mean response and other for the dispersion of the response is developed. The joint model is developed within the framework of Generalized Linear Models (GLM). An enhancement of the GLM procedure is suggested and tested; this enhancement incorporates Moving Least Squares (MLS) approximation algorithms in the fitting of the mean component of the joint model. The sensitivity analysis is then performed on the joint-model developed for the dynamic responses caused by BVI.