Elastic multibody systems arise in the simulation of vehicles, robots, air- and spacecrafts. They feature a mixed structure
with differential-algebraic equations (DAEs) governing the gross motion and partial differential equations (PDEs) describing
the elastic deformation of particular bodies. We introduce a general modelling framework for this new application field and
discuss numerical simulation techniques from several points of view. Due to different time scales, singular perturbation theory
and model reduction play an important role. A slider crank mechanism with a 2D FE grid for the elastic connecting rod illustrates
the techniques.
This revised version was published online in June 2006 with corrections to the Cover Date. 相似文献
In this article, linear regular index 2 DAEs A(t)[D(t)x(t)]′+B(t)x(t)=q(t) are considered. Using a decoupling technique, initial condition and boundary condition are properly formulated. Regular index 1 DAEs are obtained by a regularization method. We study the behavior of the solution of the regularization system via asymptotic expansions. The error analysis between the solutions of the DAEs and its regularization system is given. 相似文献
We introduce a model order reduction (MOR) procedure for differential-algebraic equations, which is based on the intrinsic differential equation contained in the starting system and on the remaining algebraic constraints. The decoupling procedure in differential and algebraic part is based on the projector and matrix chain which leads to the definition of tractability index. The differential part can be reduced by using any MOR method, we use Krylov-based projection methods to illustrate our approach. The reduction on the differential part induces a reduction on the algebraic part. In this paper, we present the method for index-1 differential-algebraic equations. We implement numerically this procedure and show numerical evidence of its validity. 相似文献
The authors have developed a Taylor series method for solving numerically an initial-value problem differential-algebraic
equation (DAE) that can be of high index, high order, nonlinear, and fully implicit, BIT, 45 (2005), pp. 561–592. Numerical
results have shown that this method is efficient and very accurate. Moreover, it is particularly suitable for problems that
are of too high an index for present DAE solvers.
This paper develops an effective method for computing a DAE’s System Jacobian, which is needed in the structural analysis
of the DAE and computation of Taylor coefficients. Our method involves preprocessing of the DAE and code generation employing
automatic differentiation. Theory and algorithms for preprocessing and code generation are presented.
An operator-overloading approach to computing the System Jacobian is also discussed.
AMS subject classification (2000) 34A09, 65L80, 65L05, 41A58 相似文献
This paper reports efforts towards establishing a parallel numerical algorithm known as Waveform Relaxation (WR) for simulating large systems of differential/algebraic equations. The WR algorithm was established as a relaxation based iterative method for the numerical integration of systems of ODEs over a finite time interval. In the WR approach, the system is broken into subsystems which are solved independently, with each subsystem using the previous iterate waveform as “guesses” about the behavior of the state variables in other subsystems. Waveforms are then exchanged between subsystems, and the subsystems are then resolved repeatedly with this improved information about the other subsystems until convergence is achieved.
In this paper, a WR algorithm is introduced for the simulation of generalized high-index DAE systems. As with ODEs, DAE systems often exhibit a multirate behavior in which the states vary as differing speeds. This can be exploited by partitioning the system into subsystems as in the WR for ODEs. One additional benefit of partitioning the DAE system into subsystems is that some of the resulting subsystems may be of lower index and, therefore, do not suffer from the numerical complications that high-index systems do. These lower index subsystems may therefore be solved by less specialized simulations. This increases the efficiency of the simulation since only a portion of the problem must be solved with specially tailored code. In addition, this paper established solvability requirements and convergence theorems for varying index DAE systems for WR simulation. 相似文献