| 1. |
- Arnold, Martin, et al.
(författare)
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Efficient corrector iteration for DAE time integration in multibody dynamics
- 2006
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Ingår i: Computer Methods in Applied Mechanics and Engineering. - : Elsevier BV. - 0045-7825. ; 195:50-51, s. 6958-6973
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Tidskriftsartikel (refereegranskat)abstract
- Efficient time integration is a key issue in computational multibody dynamics. Implicit time integration methods for stiff systems and constrained systems require the solution of a system of nonlinear equations in each time step. The nonlinear equations are solved iteratively by Newton type methods that are tailored to the structure of the equations of motion in multibody dynamics. In the present paper we discuss classical and recent methods for reducing the numerical effort in the application to multibody systems that are modelled in joint coordinates. The methods have been implemented in an industrial multibody system simulation package. Results of numerical tests for two benchmark problems from vehicle dynamics are presented.
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| 2. |
- Führer, Claus, et al.
(författare)
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Integration av numeriska metoder i kemiteknikutbildningen
- 2005
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Ingår i: [Host publication title missing].
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Konferensbidrag (refereegranskat)abstract
- Kemiteknikprogrammet fick en ny utbildningsplan 2001. Enligt den gamla utbildningsplanen fanns det en valfri kurs i numerisk analys under årskurs 4 med ett fåtal studenter. I den nya utbildningsplanen integrerades numeriska metoder med kemiteknik redan under första terminen. Metoder undervisas där problemställningen finns. Vi har valt att kalla undervisningen i numeriska metoder för beräkningsteknik. Den beräkningsmässiga delen av kursen i kemiteknik tillsammans med beräkningsteknik omfattar ca 6 poäng av en 12 poängs kurs. I kemiteknik tränas teknologerna att ställa upp modeller för kemitekniska system. För att lösa dessa krävs i flera fall hjälp av numeriska metoder. I kemiteknik används huvudsakligen färdiga funktioner för att lösa modellerna. Beräkningsteknik lär ut principen bakom de använda metoderna. Vi diskuterar de fördelar vi ser i integrerade och ämnesövergripande upplägg av kursen samt våra erfarenheter av undervisningen efter kursen har gått i fyra år. Vi avslutar med att diskutera hur denna ändring har påverkat programmet i sin helhet.
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| 3. |
- Modin, Klas, et al.
(författare)
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Geometric Integration of Weakly Dissipative Systems
- 2009
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Ingår i: Numerical Analysis and Applied Mathematics, Vols 1 and 2. - 1551-7616 .- 0094-243X. ; 1168, s. 877-877
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Konferensbidrag (refereegranskat)abstract
- Some problems in mechanics, e.g. in bearing simulation, contain subsystems that are conservative as well as weakly dissipative subsystems. Our experience is that geometric integration methods are often superior for such systems, as long as the dissipation is weak. Here we develop adaptive methods for dissipative perturbations of Hamiltonian systems. The methods are "geometric" in the sense that the form of the dissipative perturbation is preserved. The methods are linearly explicit, i.e., they require the solution of a linear subsystem. We sketch an analysis in terms of backward error analysis and numerical comparisons with a conventional RK method of the same order is given.
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| 4. |
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| 5. |
- Modin, Klas, et al.
(författare)
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Time-step adaptivity in variational integrators with application to contact problems
- 2006
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Ingår i: Zeitschrift für Angewandte Mathematik und Mechanik. - : Wiley. - 0044-2267. ; 86:10, s. 785-794
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Tidskriftsartikel (refereegranskat)abstract
- Variable time-step methods, with general step-size control objectives, are developed within the framework of variational integrators. This is accomplished by introducing discrete transformations similar to Poincares time transformation. While gaining from adaptive time-steps, the resulting integrators preserve the structural advantages of variational integrators, i.e., they are symplectic and momentum preserving. As an application, the methods are utilized for dynamic multibody systems governed by contact force laws. A suitable scaling function defining the step-size control objective is derived.
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| 6. |
- Nakhimovski, Iakov, 1976-
(författare)
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Contributions to the Modeling and Simulation of Mechanical Systems with Detailed Contact Analyses
- 2006
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Doktorsavhandling (övrigt vetenskapligt/konstnärligt)abstract
- The motivation for this thesis was the need for further development of multibody dynamics simulation packages focused on detailed contact analysis. The thesis makes contributions in three different areas:Part I summarizes the equations, algorithms and design decisions necessary for dynamics simulation of flexible bodies with moving contacts. The assumed general shape function approach is presented. Additionally, the described technique enables studies of the residual stress release during grinding of flexible bodies. The proposed set of mode shapes was also successfully applied for modeling of heat flow.Part II is motivated by the need to reduce the computation time. The availability of the new cost-efficient multiprocessor computers triggered the development of the presented hybrid parallelization framework. The framework is designed to be easily portable and can be implemented without any system level coding or compiler modifications.Part III is motivated by the need for inter-operation with other simulation tools. A co-simulation framework based on the Transmission Line Modeling (TLM) technology was developed. The framework enables integration of several different simulation components into a single time-domain simulation. The framework has been used for connecting MSC.ADAMS and SKF BEAST simulation models.Throughout the thesis the approach was to present a practitioner roadmap. The detailed description of the theoretical results relevant for a real software implementation is put in focus. The software design decisions are discussed and the results of real industrial simulations are presented.This work has been supported by SKF, SSF/ProViking, ECSEL, KK-stiftelsen.
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| 7. |
- Rantil, Jens, et al.
(författare)
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Multiple-Shooting Optimization using the JModelica.org Platform
- 2009
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Konferensbidrag (refereegranskat)abstract
- Dynamic optimization is the problem of finding the minimum of a cost function subject to a constraint comprised of a system of differential equations. There are many algorithms to numerically solve such optimization problems. One such algorithm is multiple shooting. This paper reports an implementation of a multiple shooting algorithm in Python. The implementation is based on the open source platform JModelica.org, the integrator SUNDIALS and the optimization algorithm scipy_slsqp. The JModelica.org platform supports model descriptions encoded in the Modelica language and optimization specifications expressed in the extension Optimica. The Modelica/Optimica combination provides simple means to express complex optimization problems in a compact and user-oriented manner. The JModelica.org platform, in turn translates the high-level descriptions into efficient C code which can compiled and linked with Python. As a result, the numerical packages available for Python can be used to develop custom applications based on Modelica/Optimica specifications. An example is provided to illustrate the capabilities of the method.
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| 8. |
- Strömgren, Magnus
(författare)
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Some PDAE aspects of the numerical simulation of a CO2 heat pump
- 2006
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Licentiatavhandling (övrigt vetenskapligt/konstnärligt)abstract
- We consider network modelling and numerical simulation of a simple CO2 heat pump consisting of a compressor, a valve and two heat exchangers. In a first step we investigate analytical and numerical properties of the heat exchanger model. The heat exchanger model is derived from the Euler equations under the assumption that the velocity of the refridgerant flow is small compared to the local speed of sound. While the Euler equations form a hyperbolic system, the character of the new system, called The zero Mach number limit of the Euler equations, is unclear. The lack of a time derivative in the momentum equation makes the heat exchanger model by itself a PDAE system. We analyse a frozen-coefficient linearisation of the heat exchanger model by transformation to a canonical form. The canonical form reveales that the system is equivalent to a hyperbolic equation and a parabolic block. The parabolic block is equivalent to a parabolic equation and an algebraic-differential relation, similar to the system that results when the heat equation ut = uxx + f is written as a first order system. We prove a stability estimate suggesting that the solution is more sensitive to perturbations, especially in time-dependent boundary conditions, than is indicated by previous results. Furthermore, we consider semidiscretisation of the linearised heat exchanger model. In a method of lines approach using collocation at the gridpoints, we suggest that it is possible to use a simple first order difference scheme taking into account the direction of the flow and the boundary conditions. We show that using this difference scheme, the solution to the semidiscrete equations satisfies a discrete analogue to the stability estimate in the continuous case. The results of the linear analysis is verified in numerical experiments with the nonlinear heat exchanger model.
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