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- Elastic BVP (3)
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In this paper we propose a finite volume discretization for the threedimensional Biot poroelasticity system in multilayered domains. For the stability reasons, staggered grids are used. The discretization accounts for discontinuity of the coefficients across the interfaces between layers with different physical properties. Numerical experiments, based on the proposed discretization showed second order convergence in the maximum norm for the primary as well as flux unknowns of the system. A certain application example is presented as well.
Testing a new suspension based on real load data is performed on elaborate multi channel test rigs. Usually wheel forces and moments measured during driving maneuvers are reproduced on the rig. Because of the complicated interaction between rig and suspension each new rig configuration has to prove its efficiency with respect to the requirements and the configuration might be subject to optimization. This paper deals with modeling a new rig concept based on two hexapods. The real physical rig has been designed and meanwhile built by MOOG-FCS for VOLKSWAGEN. The aim of the simulation project reported here was twofold: First the simulation of the rig together with real VOLKSWAGEN suspension models at a time where the design was not yet finalized was used to verify and optimize the desired properties of the rig. Second the simulation environment was set up in a way that it can be used to prepare real tests on the rig. The model contains the geometric configuration as well as the hydraulics and the controller. It is implemented as an ADAMS/Car template and can be combined with different suspension models to get a complete assembly representing the entire test rig. Using this model, all steps required for a real test run such as controller adaptation, drive file iteration and simulation can be performed. Geometric or hydraulic parameters can be modified easily to improve the setup and adapt the system to the suspension and the load data.
In this article, we give some generalisations of existing Lipschitz estimates for the stop and the play operator with respect to an arbitrary convex and closed characteristic a separable Hilbert space. We are especially concerned with the dependency of their outputs with respect to different scalar products.
Reliable methods for the analysis of tolerance-affected analog circuits are of great importance in nowadays microelectronics. It is impossible to produce circuits with exactly those parameter specifications proposed in the design process. Such component tolerances will always lead to small variations of a circuit’s properties, which may result in unexpected behaviour. If lower and upper bounds to parameter variations can be read off the manufacturing process, interval arithmetic naturally enters the circuit analysis area. This paper focuses on the frequency-response analysis of linear analog circuits, typically consisting of current and voltage sources as well as resistors, capacitances, inductances, and several variants of controlled sources. These kind of circuits are still widely used in analog circuit design as equivalent circuit diagrams for representing in certain application tasks Interval methods have been applied to analog circuits before. But yet this was restricted to circuit equations only, with no interdependencies between the matrix elements. But there also exist formulations of analog circuit equations containing dependent terms. Hence, for an efficient application of interval methods, it is crucial to regard possible dependencies in circuit equations. Part and parcel of this strategy is the handling of fill-in patterns for those parameters related to uncertain components. These patterns are used in linear circuit analysis for efficient equation setup. Such systems can efficiently be solved by successive application of the Sherman-Morrison formula. The approach can also be extended to complex-valued systems from frequency domain analysis of more general linear circuits. Complex values result here from a Laplace transform of frequency-dependent components like capacitances and inductances. In order to apply interval techniques, a real representation of the linear system of equations can be used for separate treatment of real and imaginary part of the variables. In this representation each parameter corresponds to the superposition of two fill-in patterns. Crude bounds – obtained by treating both patterns independently – can be improved by consideration of the correlations to tighter enclosures of the solution. The techniques described above have been implemented as an extension to the toolbox Analog Insydes, an add-on package to the computer algebra system Mathematica for modeling, analysis, and design of analog circuits.
In dem Forschungsvorhaben “Schubtragverhalten des Stahlbetongurtes von Verbundträgern im Bereich von großen Stegöffnungen“ wurden umfangreiche experimentelle und rechnerische Untersuchungen zum Querkrafttragverhalten und zur Querkrafttragfähigkeit des Betongurts im Bereich von großen Stegöffnungen durchgeführt. Anhand von 21 großmaßstäblichen Traglastversuchen, die erstmals so konzipiert waren, dass im Öffnungsbereich nahezu die gesamte Querkraft durch den Betongurt übertragen werden musste, konnte die Querkrafttragfähigkeit des Betongurts bestimmt werden. Neue Erkenntnisse über den Lastabtragungs- und Versagensmechanismus im Öffnungsbereich konnten durch die Auswertung der Dehnungen der Kopfbolzendübel im Öffnungsbereich und das nachträgliche Aufsägen des Betongurts der Versuchsträger gewonnen werden. Im rechnerischen Teil wurden ein dreidimensionales FE-Modell erstellt, das die Versuche in ihren wesentlichen Teilen abbildete, und Vergleichsberechnungen durchgeführt. Durch den Vergleich der rechnerischen mit den experimentell ermittelten Werten wurde das Modell überprüft. Auf dieser Grundlage wurden anschließend Parameteruntersuchungen durchgeführt. Schließlich wurde auf der Basis der experimentellen und rechnerischen Untersuchungen ein Ingenieurmodell zur Bestimmung der Querkrafttragfähigkeit im Öffnungsbereich entwickelt, mit dem sich die Querkrafttragfähigkeit des Betongurts im Öffnungsbereich nachweisen lässt. Ferner stellte sich heraus, dass die Querkrafttragfähigkeit des Betongurts im Öffnungsbereich durch Dübelleisten erheblich gesteigert werden kann, was wirtschaftliche Vorteile eröffnet.
With the UML 2.0 standard, the Unified Modeling Language took a big step towards SDL, incorporating many features of the language. SDL is a mature and complete language with formal semantics. The Z.109 standard defines a UML Profile for SDL, mapping UML constructs to corresponding counterparts in SDL, giving them a precise semantics. In this report, we present a case study for the formalisation of the Z.109 standard. The formal definition makes the mapping precise and can be used to derive tool support.
This report discusses two approaches for a posteriori error indication in the linear elasticity solver DDFEM: An indicator based on the Richardson extrapolation and Zienkiewicz-Zhu-type indicator. The solver handles 3D linear elasticity steady-state problems. It uses own input language to describe the mesh and the boundary conditions. Finite element discretization over tetrahedral meshes with first or second order shape functions (hierarchical basis) has been used to resolve the model. The parallelization of the numerical method is based on the domain decomposition approach. DDFEM is highly portable over a set of parallel computer architectures supporting the MPI-standard.
Error estimates for quasistatic global elastic correction and linear kinematic hardening material
(2006)
We consider in this paper the quasistatic boundary value problems of linear elasticity and nonlinear elastoplasticity with linear kinematic hardening material. We derive expressions and estimates for the difference of solutions (i.e. stress, strain and displacement) of both models. Further, we study the error between the elastoplastic solution and the solution of a postprocessing method, that corrects the solution of the linear elastic problem in order to approximate the elastoplastic model.