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Using Multi-time Stepping in Finite Element Models to Meet Real Time Constraints

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In the field of Real-Time Hybrid Simulation (RTHS) several studies have investigated various unique physical setups, while the numerical models have remained relatively simple. In the area of RTHS, finite element models are coupled with physical experiments to help solve large, nonlinear structural engineering problems. The goal of this research is to enable the use of more complex numerical models into real-time hybrid simulations to simulate global system level behavior of the structures and components.
Traditionally, dynamic finite element models are evaluated at a single time step. Multi-timestepping is the process of breaking the domain of a model into several sub-domains, which can then be evaluated at different timesteps depending on the required accuracy of the model. In this project, multi-timestepping allows the numerical model to be solved with high frequencies at areas of interest and near the physical-numerical model interaction, while allowing for lower sampling frequency and reduced calculation time in other areas of the structure.
One goal of this paper is to assess the limits on size of numerical models that can be run in real-time, and determine ways in which model complexity can be increased while meeting real time constraints. We use Matlab’s Simulink and xPC system for real-time implementation of our multi-timestepping method. This system allows us to execute Simulink models on a target computer, while also enabling the host computer to be located at a physically remote location. The advantage of the xPC target setup is that it is a very light-weight operating system which allows the entire processing power of the target computer to be devoted to running the RTHS simulation.
Developing appropriate performance criteria and conducting system-level error analyses are also goals of this research. The upper limits of how complex the numerical model can be, changes with different timesteps, the system itself, and of course the capabilities of the host and target computers. Investigating the errors involved with different numerical models, solution methods, control and compensation methods gives us not only a better picture of the accuracy of the model but also allows us a way to ensure models will work well within the time constraints inherent in real-time hybrid testing. Additional goals of this research are to investigate the effects of using implicit vs. explicit methods of solution, to vary numerical complexity by considering both larger and more complex systems and varying time steps, and to be able to adapt to computational issues by developing the ability to switch between models and integration methods in real time.
Initial steps of this research are pure numerical simulations, with the physical component still in
development. Preliminary results indicate that the concept of multi-time-stepping can be effectively used
to run bigger computational models in real-time for a more realistic hybrid simulation.


Cite this work

Researchers should cite this work as follows:

  • Gregory Brendan Bunting; Payton Lindsay; Amin Maghareh; Arun Prakash; Shirley Dyke (2013), "Using Multi-time Stepping in Finite Element Models to Meet Real Time Constraints,"

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