Multibody Simulation

Multibody systems are technical systems consisting of different rigid or flexible bodies that are interconnected. The connections may be modeled with classical force laws (massless springs and dampers, actuators, contact) or realized by kinematical constraints, e.g. joints. In the meantime multibody simulation programs are well established and can be found in a variety of industrial sectors, for example in aeronautical engineering or in the automobile industry. In consideration of initial and boundary values, a multibody simulation provides the transient motion of the bodies as well as the forces and moments acting in the connections between bodies. Embedding the Finite Element Method (FEM) into the framework allows to concurrently simulate rigid and flexible bodies and their interactions. Topics:
1. Dynamics of rigid bodies (Newton-Euler equations, Lagrange equations, Hamilton principle, ...)
2. Relative kinematics in space (spatial rotations, ...)
3. Assembly of a multibody system (link forces, constraints, ...)
4. Considering flexible bodies
5. Time integration (Newmark integration scheme, linear/nonlinear systems, constraints, ...)

At the end of the course the students are able to describe a mechanical system as a classical multibody system. The students apply an abstract and modular formalism for the derivation of the respective equations of motion in the planar as well as in the three-dimensional case. Furthermore they are able to integrate flexible bodies modeled by the Finite Element Method into the multibody system. Beside the derivation of the equations describing the dynamics of the system, the students know several numerical time-integration schemes for linear and non-linear constrained systems.

From lecture Engineering Dynamics: sections "Analytical dynamics" and "Dynamics of rigid bodies"

Within the lecture, mathematic relations and derivations are introduced and explained via a presentation (tablet-PC). The slides and the supplementary script help the students to prepare and follow up the lectures. In order to achieve a deep understanding of the fundamentals of constrained, three-dimensional multi-body dynamics, complex relations are derived step-by-step via the tablet-PC and their meaning in the context of multi-body simulation is discussed. By simple example systems presented via the tablet-PC, the practical application of the methods is demonstrated. Matching to the particular topic, physical mock-up models are used for visual explanation of spatial rotations and kinematic relations if possible.

Presentation (tablet), slides, lecture, Matlab examples, animations/visualisations, case studies

Preparation and wrap-up with slides, lecture notes, case studies and Matlab examples. Established further literature can be found in the lecture notes.

After the lecture period, there will be, depending on the number of students, a written (duration 60 min) or oral (one-on-one interview, duration 30 min) exam. The students have to show, that they know how to describe and simulate mechanical multi-body systems. Special attention is paid to the understanding of the fundamental relations and principles. Case studies are used to verify, if the students are able to apply the learned methods.