Course

Multibody Dynamics: Flexibility

Use of finite element models for simulating flexible system dynamics

To ensure the structural integrity of many contemporary mechanical systems, machines and mechanisms, it is important to accurately predict the internal stresses and deformations of critical parts using simulation models. In the course Multibody Dynamics: Flexibility it is discussed which methods are suitable for determining stresses and deformations of components that undergo arbitrarily large movements.

Mechanical analysis of structures whose deformations remain small, can be performed excellently with linear finite element models. However, linear models are not sufficient for large movements. Within the field of Flexible Multibody Dynamics, the so-called Floating Frame Formulation offers an opportunity to combine linear finite element models of individual components in a dynamic analysis of the entire system. In this way unnecessarily inefficient non-linear finite element models can be avoided.

A successful implementation of the Floating Frame Formulation allows one to determine internal stresses and deformations of components during movement. An advantage of this is that arbitrary assumptions about the boundary conditions and quasi-static loads are not necessary. In addition, this method also offers many possibilities for the implementation of further reduction techniques to further limit the calculation time.

Including flexible bodies in system dynamics

The course consists of 2 days on which theoretical aspects will be discussed. In addition, participants themselves get to work setting up flexible multibody dynamics simulations. You can use Matlab (if you have a license yourself) and / or Python (open source) for this.

Day 1: Kinematics & Model Reduction
• Establishing a kinematic model of a system consisting of several flexible bodies in terms of generalized coordinates.
• The reduction of finite element models to the relevant degrees of freedom to enable coupling with the multibody model.

Day 2: Kinetics & model coupling
• Creating a dynamic model of a system consisting of different flexible bodies using the mass and stiffness properties of individual components.
• Carrying out a numerical simulation of the dynamic system behavior in which the equations of motion of the system are solved and the reaction forces are determined.

Intended for
The course Multibody Dynamics: Flexibility is intended for mechanics who are active in machine dynamics, have some experience with multibody dynamics of rigid systems and want to know more about how flexible bodies can be included in system dynamics. If you have no practical experience or are not yet familiar with the theoretical background of multibody dynamics, it is recommended that you first follow the Introduction to Multibody Dynamics course.

Interested in related courses? Also have a look at the course Machine dynamics.

Photo: Von Mises stress during motion by Jurjen Blaauw