Hendrik Geisler, M. Sc.

Time-separated stochastic mechanics

• TSM for damage processes

  In industrial applications the reliability of components with high cycle load is of interest. In addition to the TSM a damage model needs to be used. The combination of TSM with a damage model enables to predict the evolution of the reaction forces, which are influenced by the stochastic nature of the materials and the damage processes. The advantages of the Time-Separated Stochastic Mechanics remain. The stochastic properties can be computed in advance of any concrete finite element simulation. This results in a low computational effort in comparison to Monte Carlo Simulations and enables to simulate industrially relevant problems with moderate computational resources.

  Leitung: P. Junker, J. Nagel

  Team: H. Geisler

  Jahr: 2021
• TSM for dynamic processes

  Modeling and simulation of materials with stochastic properties is typically computationally expensive especially for nonlinear materials or dynamic simulations. The Time-separated stochastic mechanics (TSM) can be extended for the dynamic analysis of stochastic visco-elasic materials by incorporation of the transient terms. In transient time-domain simulations a good approximation of the expectation and variance of the reaction force and the stresses for the dynamic response can be observed. A numerical extra cost of 10% compared with one deterministic finite element simulation is reported. However, the Monte Carlo simulation needs a minimum number of 400 finite element computations to arrive at results, that can be considered converged. Therefore, the TSM provides a fast yet accurate procedure for the dynamic simulation of visco-elastic structures witch stochastic properties.

  Leitung: P. Junker, J. Nagel

  Team: H. Geisler

  Jahr: 2022