A Taylor basis for kinematic nonlinear real‐time simulations. Part II: The Taylor basis

Sebastian Andersen*, Peter Noe Poulsen

*Corresponding author for this work

Research output: Contribution to journalJournal articleResearchpeer-review

Abstract

Real‐time simulations are used to a significant extent in many engineering fields. However, if nonlinearities are included, the real‐time requirement significantly limits the size and complexity of numerical models. The present work constitutes the second of two papers where a general basis method to simulate kinematic nonlinear structures more efficiently is introduced. The advantage of the basis formulation is that it enables the number of basis vectors to be increased without increasing the number of unknown basis co‐ordinates. This allows for larger numerical kinematically nonlinear models to run in real time. The basis is organized from a Taylor series that includes the system mode shapes and their complete first‐order modal derivatives derived in Part I. The Taylor series predicts fixed linear relations between the modal co‐ordinates of the system mode shapes and the modal derivatives, respectively. Thus, the full solution is known solely by determining the modal co‐ordinates of the mode shapes, which significantly minimizes the computational costs. Furthermore, it is illustrated that the stability of the Taylor basis formulation is dependent on the mode shape frequencies only, allowing the applied time steps to be significantly larger than in standard nonlinear basis analysis. An example illustrates a case where the computational time can be decreased by one order of magnitude using a Taylor basis formulation compared with a standard basis formulation including identical basis vectors.
Original languageEnglish
JournalEarthquake Engineering and Structural Dynamics
Volume48
Issue number8
Pages (from-to)929-948
ISSN0098-8847
DOIs
Publication statusPublished - 2019

Keywords

  • Basis projection
  • Finite element analysis
  • Kinematic nonlinearities
  • Modal derivatives
  • Real-time simulations
  • Taylor basis

Cite this

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title = "A Taylor basis for kinematic nonlinear real‐time simulations. Part II: The Taylor basis",
abstract = "Real‐time simulations are used to a significant extent in many engineering fields. However, if nonlinearities are included, the real‐time requirement significantly limits the size and complexity of numerical models. The present work constitutes the second of two papers where a general basis method to simulate kinematic nonlinear structures more efficiently is introduced. The advantage of the basis formulation is that it enables the number of basis vectors to be increased without increasing the number of unknown basis co‐ordinates. This allows for larger numerical kinematically nonlinear models to run in real time. The basis is organized from a Taylor series that includes the system mode shapes and their complete first‐order modal derivatives derived in Part I. The Taylor series predicts fixed linear relations between the modal co‐ordinates of the system mode shapes and the modal derivatives, respectively. Thus, the full solution is known solely by determining the modal co‐ordinates of the mode shapes, which significantly minimizes the computational costs. Furthermore, it is illustrated that the stability of the Taylor basis formulation is dependent on the mode shape frequencies only, allowing the applied time steps to be significantly larger than in standard nonlinear basis analysis. An example illustrates a case where the computational time can be decreased by one order of magnitude using a Taylor basis formulation compared with a standard basis formulation including identical basis vectors.",
keywords = "Basis projection, Finite element analysis, Kinematic nonlinearities, Modal derivatives, Real-time simulations, Taylor basis",
author = "Sebastian Andersen and Poulsen, {Peter Noe}",
year = "2019",
doi = "10.1002/eqe.3175",
language = "English",
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pages = "929--948",
journal = "Earthquake Engineering and Structural Dynamics",
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}

A Taylor basis for kinematic nonlinear real‐time simulations. Part II: The Taylor basis. / Andersen, Sebastian; Poulsen, Peter Noe.

In: Earthquake Engineering and Structural Dynamics, Vol. 48, No. 8, 2019, p. 929-948.

Research output: Contribution to journalJournal articleResearchpeer-review

TY - JOUR

T1 - A Taylor basis for kinematic nonlinear real‐time simulations. Part II: The Taylor basis

AU - Andersen, Sebastian

AU - Poulsen, Peter Noe

PY - 2019

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AB - Real‐time simulations are used to a significant extent in many engineering fields. However, if nonlinearities are included, the real‐time requirement significantly limits the size and complexity of numerical models. The present work constitutes the second of two papers where a general basis method to simulate kinematic nonlinear structures more efficiently is introduced. The advantage of the basis formulation is that it enables the number of basis vectors to be increased without increasing the number of unknown basis co‐ordinates. This allows for larger numerical kinematically nonlinear models to run in real time. The basis is organized from a Taylor series that includes the system mode shapes and their complete first‐order modal derivatives derived in Part I. The Taylor series predicts fixed linear relations between the modal co‐ordinates of the system mode shapes and the modal derivatives, respectively. Thus, the full solution is known solely by determining the modal co‐ordinates of the mode shapes, which significantly minimizes the computational costs. Furthermore, it is illustrated that the stability of the Taylor basis formulation is dependent on the mode shape frequencies only, allowing the applied time steps to be significantly larger than in standard nonlinear basis analysis. An example illustrates a case where the computational time can be decreased by one order of magnitude using a Taylor basis formulation compared with a standard basis formulation including identical basis vectors.

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KW - Finite element analysis

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