Colloquia

Samenvatting

Linear finite element methods are a robust approach for modeling transient behavior in dynamic systems with fixed loads and constant boundary conditions, the so called time-invariant problems. However, many dynamic systems are not invariant in time. When these systems start to move, the location of the contact points and loads change, as seen in a translational joint. Here the continuous sliding contact has to be modeled using a discrete mesh. This causes the problem that the point of contact is ill-defined at each time step. In this thesis, three different methods are considered to solve this problem.

The first method is to use length-varying elements utilizing the Arbitrary Lagrangian-Eulerian (ALE) method. Using these elements the node on which the external force or constraint is acting can be positioned on an arbitrary point on the beam. In the second method an interpolation scheme is used to convert a force at an arbitrary point to equivalent forces and moments on the adjacent node. This makes the system well-defined at each time step, allowing the system to be solved using standard finite element techniques using a state-space model. Thirdly, as the models can be time consuming to solve the system, a data-driven method is proposed. Here only a partial model is generated using one of the previous models and used as input for the Dynamic Mode Decomposition (DMD). By using the DMD the most relevant modes are extracted and used to generate future states of the model.

Both the interpolation and ALE method can model this problem accurately. The interpolation method is able to solve the system in significantly less time compared to the ALE method. However, the interpolation method cannot be applied to every case. Especially looking further to more complex systems like highly flexible beams, the ALE method can be a promising approach due to its flexibility. The proposed DMD methods are able to replicate but not able to approximate future time steps, hence it cannot be used to reduce computational time.