### Abstract

Real-time hybrid testing combines testing of physical components with numerical simulations. The concept of the method requires that the numerical simulations should be executed in real time. However, for large numerical models including nonlinear behavior a combination of computationally costly assembling of the internal forces element by element at each equilibrium point and a strict requirement for small time steps to maintain accuracy and stability often prevents real time execution. Thus, enhanced numerical capacity is required. In the present study a basis reduction method is used to reformulate kinematic nonlinear equations of motion into a sum of constant matrices each multiplied by a reduced coordinate decreasing the assembling time. Furthermore the method allows for cutting off some of the higher frequency content not representing real physics decreasing the stability requirement for the time step. However, it is important that the chosen basis can represent the nonlinearities of the system. If not locking of the system can be a consequence ruining the accuracy of the results. To demonstrate the potential of the method in a real time simulation perspective and the importance of choosing a sufficient basis a composite beam and a cantilever beam including kinematic nonlinearities and exposed to harmonic loadings are analyzed. To reduce locking modes with higher order terms are included. From the analysis it is concluded that the method exhibits encouraging potential with respect to real time execution if a sufficient basis is chosen.

Original language | English |
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Title of host publication | Proceedings of EURODYN 2014 |

Publication date | 2014 |

Pages | 1867-1874 |

Publication status | Published - 2014 |

Event | IX International Conference on Structural Dynamics (EURODYN 2014) - University of Porto, Porto, Portugal Duration: 30 Jun 2014 → 2 Jul 2014 Conference number: 9 http://paginas.fe.up.pt/~eurodyn2014/ |

### Conference

Conference | IX International Conference on Structural Dynamics (EURODYN 2014) |
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Number | 9 |

Location | University of Porto |

Country | Portugal |

City | Porto |

Period | 30/06/2014 → 02/07/2014 |

Internet address |

### Keywords

- Kinematic Nonlinearities
- Basis reduction
- Real-time simulation
- Finite Element Analysis

## Cite this

Andersen, S., & Poulsen, P. N. (2014). Reduction Method for Real-Time Simulations in Hybrid Testing. In

*Proceedings of EURODYN 2014*(pp. 1867-1874)