### Introduction and Motivation

Nowadays simulation models are commonly used for the computer-aided analysis and optimization in many technical development processes. For the analysis of dynamic systems, in which the components undergo large rigid body motions, the method of multibody systems is an efficient and widely used modeling approach. The areas of application are very diverse and range from vehicle dynamics to robotics and biomechanics.

With the increasing demands on the real systems, the demands on the simulation models increase too. For instance, in the past the deformations of the bodies were often neglected. However, undesired vibrations or deformations might have an undesired influence on the machine precision. Thus, efficient methods have been developed, which considers the deformation of the bodies, in order to increase the model quality. These flexible multibody systems do not only provide to a more precise description of the kinematics, but allow also an improved contact simulation between bodies or the direct application of computer-aided structural optimizations. They are also applied in model-based control, which is not an easy task, because flexible multibody systems are typical examples of under-actuated systems. In summary flexible multibody systems are the basis for numerous research projects at the Institute of Mechanics and Ocean Engineering and, thus, their efficient modeling and analysis is of great importance.

*Modeling elements of flexible multibody systems*

DynManto (formerly denoted as SimFMBS) is a Matlab toolbox for the modeling, analysis and optimization of rigid and flexible multibody systems developed at the Institute of Mechanics and Ocean Engineering. The basic idea of this academic software project is to provide a simulation tool that allows students and scientists to easily and quickly create and simulate models for the analysis of multibody systems. The system equations are formulated in differential-algebraic form and are numerically solved with the help of stabilization or projection methods. The kinematics of both rigid and flexible bodies is described using the floating frame of reference approach.

*DynManto: Flexible slider-crank mechanism*

The description of flexible bodies in multibody systems is usually much more complex than the description of rigid bodies. Rigid bodies can be completely described by a very small set of standard data, which includes the mass, the position of the center of mass, the mass moment of inertia and the position and orientation of markers. In contrast, the description of flexible bodies depends on a separate model that describes its deformation behavior. The finite element method is often used as separate because it allows the description of arbitrarily shaped bodies. Examples of commercial finite element programs, which are used at the Institute of Mechanics and Ocean Engineering, are ABAQUS or ANSYS. The Matlab toolbox RED, which is developed at the Institute of Mechanics and Ocean Engineering, is used to import finite element models of flexible bodies from ABAQUS or ANSYS to Matlab. However, the finite element models usually possess too many degrees of freedom. Before incorporating the finite element model into the multibody system its size must be reduced and a set of standard data must be calculated.

# References

- Schwertassek, R., Wallrapp, O. (2017).
*Dynamik flexibler Mehrkörpersysteme: Methoden der Mechanik zum rechnergestützten Entwurf und zur Analyse mechatronischer Systeme*. Springer-Verlag. - Shabana, A. A. (2013).
*Dynamics of multibody systems*. Cambridge university press. - Bauchau, O. A. (2010).
*Flexible multibody dynamics*(Vol. 176). Springer Science & Business Media.