Bernd Simeon

Pantograph and catenary dynamics: a benchmark problem and its numerical solution

Abstract Coupled systems of partial differential equations (PDEs) and differential–algebraic equations (DAEs) are of actual interest in various practical applications. From this point of view we have recently studied the interaction of pantograph and catenary in high speed trains (Simeon and Arnold, 1998). To stimulate further research on this topic we formulate in the present paper a simplified model problem that reflects basic parts of the nonlinear dynamics in the technical system pantograph/catenary. Following the method of lines the equations of motion are semi-discretized in space using finite differences. For time discretization, typical DAE techniques are applied such as index reduction, projection steps and handling of systems with varying structure.

Swept Volume Parameterization for Isogeometric Analysis

Isogeometric Analysis uses NURBS representations of the domain for performing numerical simulations. The first part of this paper presents a variational framework for generating NURBS parameterizations of swept volumes. The class of these volumes covers a number of interesting free-form shapes, such as blades of turbines and propellers, ship hulls or wings of airplanes. The second part of the paper reports the results of isogeometric analysis which were obtained with the help of the generated NURBS volume parameterizations. In particular we discuss the influence of the chosen parameterization and the incorporation of boundary conditions.

The Drazin inverse in multibody system dynamics

SummaryThe numerical analysis of multibody system dynamics is based on the equations of motion as differential-algebraic systems. A thorough analysis of the linearized equations and their solution theory leads to an equivalent system of ordinary differential equations which gives deeper insight into the derivation of integration schemes and into the stabilization approaches. The main tool is the Drazin inverse, a generalized matrix inverse, which preserves the eigenvalues. The results are illustrated by a realistic truck model. Finally, the approach is extended to the nonlinear index 2 formulation.

A nonlinear truck model and its treatment as a multibody system

Abstract A planar vertical truck model with nonlinear suspension and its multibody system formulation are presented. The equations of motion of the model form a system of differential-algebraic equations (DAEs). All equations are given explicitly, including a complete set of parameter values, consistent initial values, and a sample road excitation. Thus the truck model allows various investigations of the specific DAE effects and represents a test problem for algorithms in control theory, mechanics of multibody systems, and numerical analysis. Several numerical tests show the properties of the model.

ISOGAT: A 2D tutorial MATLAB code for Isogeometric Analysis

A tutorial 2D MATLAB code for solving elliptic diffusion-type problems, including Poissons equation on single patch geometries, is presented. The basic steps of Isogeometric Analysis are explained and two examples are given. The code has a very lean structure and has been kept as simple as possible, such that the analogy but also the differences to traditional finite element analysis become apparent. It is not intended for large-scale problems.

Runge---Kutta methods in elastoplasticity

Runge-Kutta methods for the constitutive equations of elastoplasticity are presented. These equations form a differential-algebraic equation (DAE) of index 2 with unilateral constraints. For the numerical solution, implicit Runge-Kutta methods are combined with the return mapping strategy of computational plasticity. It turns out that the convergence order depends crucially on the switching point detection. Furthermore, it is shown that algebraically stable Runge-Kutta methods preserve the contractivity of the elastoplastic flow.

A higher-order time integration method for viscoplasticity

Time integration in viscoplasticity is discussed from both engineering and mathematical points of view. A second-order integration scheme is presented and combined with an adaptive time stepping algorithm which utilizes local error estimates for the choice of time steps, and a closed-form expression for the consistent tangent operator is derived. The algorithm is applied to the viscoplastic model by Choi and Krempl.

Order reduction of stiff solvers at elastic multibody systems

Elastic multibody systems arise in the simulation of vehicles, robots, air- and spacecrafts. After semidiscretization in space, a partitioned differential-algebraic system of index 3 with large stiffness terms has to be solved. We investigate the behavior of numerical methods for stiff ODEs and DAEs at this problem class and show that strong order reductions may occur. Examples from structural dynamics and multibody systems illustrate the results.

Numerical Analysis of Flexible Multibody Systems

Flexible multibody systems featurea coupled mathematical model with ODEs or DAEs governing the gross motion and PDEs describing the elastic deformation of particular bodies.Frequently, semidiscretization of elastic members leads to a stiff mechanical system with widely different time scales. Thispaper investigates the behavior of numerical time integration methodsat flexible multibody systems and gives some recommendations.Simulation results for a slider crank mechanism and a truck modelillustrate what can go wrong and how implicit methods like RADAU5 can beeffectively applied.

Real-time capable vehicle-trailer coupling by algorithms for differential-algebraic equations

The real-time simulation of vehicle trains requires an accurate and numerically feasible representation of the vehicle–trailer coupling. Although the equations of motion for the chassis instances can be reduced to systems of ordinary differential equations, additional constraints on the relative motion of vehicle and trailer are introduced when considering the hitch. In this article, we present a strategy for the simulation of vehicle–trailer combinations, where the algebraic constraints of the coupling are treated explicitly. Although this approach allows exact modeling of the respective joint geometry and realistic calculation of the coupling forces, a suitable numerical algorithm is required in order to solve the resulting differential-algebraic system of index 3 in real-time. The implementation in a commercial vehicle dynamics program is discussed and real-time simulation results are shown, which prove its feasibility for different coupling joints and demanding driving maneuvers.