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Rapid advancements of modern technologies put high demands on mathematical modelling of engineering systems. Typically, systems are no longer “simple” objects, but rather coupled systems involving multiphysics phenomena, the modelling of which involves coupling of models that describe different phenomena. After constructing a mathematical model, it is essential to analyse the correctness of the coupled models and to detect modelling errors compromising the final modelling result. Broadly, there are two classes of modelling errors: (a) errors related to abstract modelling, eg, conceptual errors concerning the coherence of a model as a whole and (b) errors related to concrete modelling or instance modelling, eg, questions of approximation quality and implementation. Instance modelling errors, on the one hand, are relatively well understood. Abstract modelling errors, on the other, are not appropriately addressed by modern modelling methodologies. The aim of this paper is to initiate a discussion on abstract approaches and their usability for mathematical modelling of engineering systems with the goal of making it possible to catch conceptual modelling errors early and automatically by computer assistant tools. To that end, we argue that it is necessary to identify and employ suitable mathematical abstractions to capture an accurate conceptual description of the process of modelling engineering systems.
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.
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 construction engineering, a schedule’s input data, which is usually not exactly known in the planning phase, is considered deterministic when generating the schedule. As a result, construction schedules become unreliable and deadlines are often not met. While the optimization of construction schedules with respect to costs and makespan has been a matter of research in the past decades, the optimization of the robustness of construction schedules has received little attention. In this paper, the effects of uncertainties inherent to the input data of construction schedules are discussed. Possibilities are investigated to improve the reliability of construction schedules by considering alternative processes for certain tasks and by identifying the combination of processes generating the most robust schedule with respect to the makespan of a construction project.
We briefly review and use the recent comprehensive research on the manifolds of square roots of −1 in real Clifford geometric algebras Cl(p,q) in order to construct the Clifford Fourier transform. Basically in the kernel of the complex Fourier transform the complex imaginary unit j is replaced by a square root of −1 in Cl(p,q). The Clifford Fourier transform (CFT) thus obtained generalizes previously known and applied CFTs, which replaced the complex imaginary unit j only by blades (usually pseudoscalars) squaring to −1. A major advantage of real Clifford algebra CFTs is their completely real geometric interpretation. We study (left and right) linearity of the CFT for constant multivector coefficients in Cl(p,q), translation (x-shift) and modulation (w -shift) properties, and signal dilations. We show an inversion theorem. We establish the CFT of vector differentials, partial derivatives, vector derivatives and spatial moments of the signal. We also derive Plancherel and Parseval identities as well as a general convolution theorem.
It is well-known that the solution of the fundamental equations of linear elasticity for a homogeneous isotropic material in plane stress and strain state cases can be equivalently reduced to the solution of a biharmonic equation. The discrete version of the Theorem of Goursat is used to describe the solution of the discrete biharmonic equation by the help of two discrete holomorphic functions. In order to obtain a Taylor expansion of discrete holomorphic functions we introduce a basis of discrete polynomials which fulfill the so-called Appell property with respect to the discrete adjoint Cauchy-Riemann operator. All these steps are very important in the field of fracture mechanics, where stress and displacement fields in the neighborhood of singularities caused by cracks and notches have to be calculated with high accuracy. Using the sum representation of holomorphic functions it seems possible to reproduce the order of singularity and to determine important mechanical characteristics.
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.
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.
Performing parameter identification prior to numerical simulation is an essential task in geotechnical engineering. However, it has to be kept in mind that the accuracy of the obtained parameter is closely related to the chosen experimental setup, such as the number of sensors as well as their location. A well considered position of sensors can increase the quality of the measurement and to reduce the number of monitoring points. This Paper illustrates this concept by means of a loading device that is used to identify the stiffness and permeability of soft clays. With an initial setup of the measurement devices the pore water pressure and the vertical displacements are recorded and used to identify the afore mentioned parameters. Starting from these identified parameters, the optimal measurement setup is investigated with a method based on global sensitivity analysis. This method shows an optimal sensor location assuming three sensors for each measured quantity, and the results are discussed.
One of the most promising and recent advances in computer-based planning is the transition from classical geometric modeling to building information modeling (BIM). Building information models support the representation, storage, and exchange of various information relevant to construction planning. This information can be used for describing, e.g., geometric/physical properties or costs of a building, for creating construction schedules, or for representing other characteristics of construction projects. Based on this information, plans and specifications as well as reports and presentations of a planned building can be created automatically. A fundamental principle of BIM is object parameterization, which allows specifying geometrical, numerical, algebraic and associative dependencies between objects contained in a building information model. In this paper, existing challenges of parametric modeling using the Industry Foundation Classes (IFC) as a federated model for integrated planning are shown, and open research questions are discussed.
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.
Sensor faults can affect the dependability and the accuracy of structural health monitoring (SHM) systems. Recent studies demonstrate that artificial neural networks can be used to detect sensor faults. In this paper, decentralized artificial neural networks (ANNs) are applied for autonomous sensor fault detection. On each sensor node of a wireless SHM system, an ANN is implemented to measure and to process structural response data. Structural response data is predicted by each sensor node based on correlations between adjacent sensor nodes and on redundancies inherent in the SHM system. Evaluating the deviations (or residuals) between measured and predicted data, sensor faults are autonomously detected by the wireless sensor nodes in a fully decentralized manner. A prototype SHM system implemented in this study, which is capable of decentralized autonomous sensor fault detection, is validated in laboratory experiments through simulated sensor faults. Several topologies and modes of operation of the embedded ANNs are investigated with respect to the dependability and the accuracy of the fault detection approach. In conclusion, the prototype SHM system is able to accurately detect sensor faults, demonstrating that neural networks, processing decentralized structural response data, facilitate autonomous fault detection, thus increasing the dependability and the accuracy of structural health monitoring systems.
A topology optimization method has been developed for structures subjected to multiple load cases (Example of a bridge pier subjected to wind loads, traffic, superstructure...). We formulate the problem as a multi-criterial optimization problem, where the compliance is computed for each load case. Then, the Epsilon constraint method (method proposed by Chankong and Haimes, 1971) is adapted. The strategy of this method is based on the concept of minimizing the maximum compliance resulting from the critical load case while the other remaining compliances are considered in the constraints. In each iteration, the compliances of all load cases are computed and only the maximum one is minimized. The topology optimization process is switching from one load to another according to the variation of the resulting compliance. In this work we will motivate and explain the proposed methodology and provide some numerical examples.
Numerical simulations in the general field of civil engineering are common for the design process of structures and/or the assessment of existing buildings. The behaviour of these structures is analytically unknown and is approximated with numerical simulation methods like the Finite Element Method (FEM). Therefore the real structure is transferred into a global model (GM, e.g. concrete bridge) with a wide range of sub models (partial models PM, e.g. material modelling, creep). These partial models are coupled together to predict the behaviour of the observed structure (GM) under different conditions. The engineer needs to decide which models are suitable for computing realistically and efficiently the physical processes determining the structural behaviour. Theoretical knowledge along with the experience from prior design processes will influence this model selection decision. It is thus often a qualitative selection of different models. The goal of this paper is to present a quantitative evaluation of the global model quality according to the simulation of a bridge subject to direct loading (dead load, traffic) and indirect loading (temperature), which induce restraint effects. The model quality can be separately investigated for each partial model and also for the coupled partial models in a global structural model. Probabilistic simulations are necessary for the evaluation of these model qualities by using Uncertainty and Sensitivity Analysis. The method is applied to the simulation of a semi-integral concrete bridge with a monolithic connection between the superstructure and the piers, and elastomeric bearings at the abutments. The results show that the evaluation of global model quality is strongly dependent on the sensitivity of the considered partial models and their related quantitative prediction quality. This method is not only a relative comparison between different models, but also a quantitative representation of model quality using probabilistic simulation methods, which can support the process of model selection for numerical simulations in research and practice.
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.
SELECTION AND SCALING OF GROUND MOTION RECORDS FOR SEISMIC ANALYSIS USING AN OPTIMIZATION ALGORITHM
(2015)
The nonlinear time history analysis and seismic performance based methods require a set of scaled ground motions. The conventional procedure of ground motion selection is based on matching the motion properties, e.g. magnitude, amplitude, fault distance, and fault mechanism. The seismic target spectrum is only used in the scaling process following the random selection process. Therefore, the aim of the paper is to present a procedure to select a sets of ground motions from a built database of ground motions. The selection procedure is based on running an optimization problem using Dijkstra’s algorithm to match the selected set of ground motions to a target response spectrum. The selection and scaling procedure of optimized sets of ground motions is presented by examining the analyses of nonlinear single degree of freedom systems.
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.
With the advances of the computer technology, structural optimization has become a prominent field in structural engineering. In this study an unconventional approach of structural optimization is presented which utilize the Energy method with Integral Material behaviour (EIM), based on the Lagrange’s principle of minimum potential energy. The equilibrium condition with the EIM, as an alternative method for nonlinear analysis, is secured through minimization of the potential energy as an optimization problem. Imposing this problem as an additional constraint on a higher cost function of a structural property, a bilevel programming problem is formulated. The nested strategy of solution of the bilevel problem is used, treating the energy and the upper objective function as separate optimization problems. Utilizing the convexity of the potential energy, gradient based algorithms are employed for its minimization and the upper cost function is minimized using the gradient free algorithms, due to its unknown properties. Two practical examples are considered in order to prove the efficiency of the method. The first one presents a sizing problem of I steel section within encased composite cross section, utilizing the material nonlinearity. The second one is a discrete shape optimization of a steel truss bridge, which is compared to a previous study based on the Finite Element Method.
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.
Tests on Polymer Modified Cement Concrete (PCC) have shown significant large creep deformation. The reasons for that as well as additional material phenomena are explained in the following paper. Existing creep models developed for standard concrete are studied to determine the time-dependent deformations of PCC. These models are: model B3 by Bažant and Bajewa, the models according to Model Code 90 and ACI 209 as well as model GL2000 by Gardner and Lockman. The calculated creep strains are compared to existing experimental data of PCC and the differences are pointed out. Furthermore, an optimization of the model parameters is performed to fit the models to the experimental data to achieve a better model prognosis.