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Discretized Model (discretized + model)

Distribution by Scientific Domains
Engineering75%

Selected Abstracts

A Numerical Simulation Model for Shield Tunnelling with Compressed Air Support

GEOMECHANICS AND TUNNELLING, Issue 3 2008
Felix Nagel Dipl.-Ing.
This paper is concerned with a numerical simulation model (ekate) specifically designed for shield tunnelling in fully and partially saturated soils based upon the Finite Element Method (FEM). The model considers all relevant components , the soil, the lining, the tail void grouting, the hydraulic jacks and different types of face support , involved in shield tunnelling. The surrounding soft soil is formulated as a three-phase material, consisting of the soil skeleton, pore water and air. This model allows for the simulation of consolidation processes in partially saturated soils as well as of flow of compressed air often used as temporary face support during repair interventions at the cutting wheel. Despite the complexity connected with the relatively high degree of realism of the simulation model, only little effort is required from the user to establish a realistic 3D model for shield tunnelling. To this end an automatic model generator has been developed which allows for a user friendly generation of the discretized model including all components involved and to investigate variants with a minimum effort for the user. The model allows for realistic predictions of settlements and also provides information on deformations and stresses in the ground, the lining and the TBM, respectively. In addition to its use as a prognosis tool in the design process, in particular for tunnelling projects in sensitive urban areas, the model also may be used to assist the driving and steering process in mechanized tunnelling. The paper provides an overview over the main components of the model, the automatic model generator and the tri-phasic representation of the soil. A simulation of a compressed air intervention of a shield tunnel in soft soil demonstrates the applicability of the model. Ein numerisches Simulationsmodell für druckluftgestützte Schildvortriebe In diesem Beitrag wird ein Simulationsmodell basierend auf der Methode der Finiten Elemente (FEM) für die Berechnung schildvorgetriebener Tunnel in un-, voll- und teilgesättigten Böden vorgestellt. In diesem numerischen Modell werden alle beim maschinellen Tunnelbau wesentlichen Komponenten , der Boden, der Ausbau, die Schildschwanzverpressung, die Vortriebspressen sowie unterschiedliche Arten der Ortsbruststützung , wirklichkeitsnah berücksichtigt. Der Baugrund wird im Simulationsmodell als dreiphasiges Material modelliert, bestehend aus dem Korngerüst, dem Porenwasser und der Porenluft. Diese Materialformulierung für den Baugrund ermöglicht die Analyse von Konsolidierungsprozessen in teilgesättigten Böden ebenso wie von Strömungsvorgängen im Boden bei Verwendung von Druckluft als temporärer Ortsbruststützung. Druckluft wird häufig beim Wechsel von Schneidwerkzeugen eingesetzt. Ungeachtet der Komplexität des Modells, die mit der relativ wirklichkeitsnahen Abbildung des Vortriebsgeschehens verbunden ist, ist nur ein sehr geringer Aufwand für die Modellgenerierung erforderlich. Um diesen Eingabeaufwand auf ein Minimum zu reduzieren, wurde ein automatischer Modellgenerator entwickelt, der den Ingenieur bei der Eingabe unterstützt und die Untersuchung von Planungsalternativen deutlich vereinfacht. Das Modell ermöglicht wirklichkeitsnahe Prognosen von Bodenbewegungen und Beanspruchungen, wie sie für die Planung von Vortrieben insbesondere unter setzungsempfindlichen, innerstädtischen Gebieten erforderlich sind. Darüber hinaus stellt das Modell ein wertvolles Hilfsmittel bei der vortriebsbegleitenden Steuerung von Vortriebsmaschinen in Lockergestein dar. Neben den wesentlichen Komponenten des numerischen Modells, des Modellgenerators und der Dreiphasen-Formulierung für den Boden enthält der Beitrag als prototypisches Anwendungsbeispiel die Simulation einer Druckluftintervention in Lockergestein. [source]

A G space theory and a weakened weak (W2) form for a unified formulation of compatible and incompatible methods: Part II applications to solid mechanics problems

INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 9 2010
G. R. Liu
Abstract In part I of this paper, we have established the G space theory and fundamentals for W2 formulation. Part II focuses on the applications of the G space theory to formulate W2 models for solid mechanics problems. We first define a bilinear form, prove some of the important properties, and prove that the W2 formulation will be spatially stable, and convergent to exact solutions. We then present examples of some of the possible W2 models including the SFEM, NS-FEM, ES-FEM, NS-PIM, ES-PIM, and CS-PIM. We show the major properties of these models: (1) they are variationally consistent in a conventional sense, if the solution is sought in a proper H space (compatible cases); (2) They pass the standard patch test when the solution is sought in a proper G space with discontinuous functions (incompatible cases); (3) the stiffness of the discretized model is reduced compared with the finite element method (FEM) model and possibly to the exact model, allowing us to obtain upper bound solutions with respect to both the FEM and the exact solutions and (4) the W2 models are less sensitive to the quality of the mesh, and triangular meshes can be used without any accuracy problems. These properties and theories have been confirmed numerically via examples solved using a number of W2 models including compatible and incompatible cases. We shall see that the G space theory and the W2 forms can formulate a variety of stable and convergent numerical methods with the FEM as one special case. Copyright © 2009 John Wiley & Sons, Ltd. [source]

Rotational motion of a discretized buckled beam

PROCEEDINGS IN APPLIED MATHEMATICS & MECHANICS, Issue 1 2006
H. Troger
We study a simple discretized model of a vertical cylindrical beam with circular cross-section which is clamped at its lower end and free at its upper end. If the beam is longer than a critical length the initially straight configuration will loose its stability and the beam will buckle due to its own weight. Now the base of the buckled beam is rotated about its vertical axis. Several different families of steady state motions are detected for the undamped system. Their stability is investigated. Moreover it is shown that there is a big difference in the behavior of the discretized model of the beam whether internal damping is included in the model or not. (© 2006 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim) [source]

Moment based regression algorithms for drift and volatility estimation in continuous-time Markov switching models

THE ECONOMETRICS JOURNAL, Issue 2 2008
Robert J. Elliott
Summary, We consider a continuous time Markov switching model (MSM) which is widely used in mathematical finance. The aim is to estimate the parameters given observations in discrete time. Since there is no finite dimensional filter for estimating the underlying state of the MSM, it is not possible to compute numerically the maximum likelihood parameter estimate via the well known expectation maximization (EM) algorithm. Therefore in this paper, we propose a method of moments based parameter estimator. The moments of the observed process are computed explicitly as a function of the time discretization interval of the discrete time observation process. We then propose two algorithms for parameter estimation of the MSM. The first algorithm is based on a least-squares fit to the exact moments over different time lags, while the second algorithm is based on estimating the coefficients of the expansion (with respect to time) of the moments. Extensive numerical results comparing the algorithm with the EM algorithm for the discretized model are presented. [source]